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MU-NLPC

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Calc-math_qa

like 4

math_qa__L8XqMEwIvE4ekW6c

a college has classes from 10 : 00 am until 1 : 40 pm . in this duration , there are 5 periods . if 5 minutes are provided between each period to leave one class and enter the next class , how many minutes long is each period ? Answers A) 38 min B) 41 min C) 40 min D) 42 min E) 52 min

<gadget id="calculator">3 * 60</gadget> <output>180</output> <gadget id="calculator">40 + 180</gadget> <output>220</output> <gadget id="calculator">5 * 4</gadget> <output>20</output> <gadget id="calculator">220 - 20</gadget> <output>200</output> <gadget id="calculator">200 / 5</gadget> <output>40</output> <result>C</result>

C

a college has classes from 10 : 00 am until 1 : 40 pm . in this duration , there are 5 periods . if 5 minutes are provided between each period to leave one class and enter the next class , how many minutes long is each period ?

divide(subtract(add(40, multiply(const_3, const_60)), multiply(5, const_4)), 5)

multiply(const_3,const_60)|multiply(n4,const_4)|add(n3,#0)|subtract(#2,#1)|divide(#3,n4)

the total time is 220 minutes . there are four breaks of five minutes between the classes for a total of 20 minutes . the total class time is 200 minutes . 200 / 5 classes = 40 minutes per class the answer is c .

other

math_qa__16cOM5kHNdmpdObk

A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 5 points if you must draw exactly 3 “low” cards? Answers. A) 1 B) 2 C) 3 D) 4 E) 5

<gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">12 * 2</gadget> <output>24</output> <gadget id="calculator">24 * 1</gadget> <output>24</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">6 * 1</gadget> <output>6</output> <gadget id="calculator">24 / 6</gadget> <output>4</output> <result>D</result>

D

A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 5 points if you must draw exactly 3 “low” cards?

divide(multiply(multiply(multiply(const_4, 3), 2), 1), multiply(multiply(3, 2), 1))

multiply(n5,const_4)|multiply(n1,n5)|multiply(n1,#0)|multiply(n3,#1)|multiply(n3,#2)|divide(#4,#3)

to get a 5 , you need one high and three lows ( you could have had 2 highs and one low , but the constraint is that you must have three low cards ) hlll = 4 ! 3 ! = 4 4 ! is the number of ways you can arrange these four spaces . divide by 3 ! because you you repeat three low cards ans : d

general

math_qa__bwfX6DUPBhK6DwmC

John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/3:1/5 . What is the minimum no. of pencils that the person should have? Choose the correct choice from the following choices: A) 41 B) 65 C) 70 D) 77 E) 98

<gadget id="calculator">lcm(2, 3)</gadget> <output>6</output> <gadget id="calculator">lcm(6, 3)</gadget> <output>6</output> <gadget id="calculator">lcm(6, 5)</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <gadget id="calculator">30 / 3</gadget> <output>10</output> <gadget id="calculator">15 + 10</gadget> <output>25</output> <gadget id="calculator">25 + 10</gadget> <output>35</output> <gadget id="calculator">30 / 5</gadget> <output>6</output> <gadget id="calculator">35 + 6</gadget> <output>41</output> <result>A</result>

A

John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/3:1/5 . What is the minimum no. of pencils that the person should have?

add(add(add(divide(lcm(lcm(lcm(2, 3), 3), 5), 2), divide(lcm(lcm(lcm(2, 3), 3), 5), 3)), divide(lcm(lcm(lcm(2, 3), 3), 5), 3)), divide(lcm(lcm(lcm(2, 3), 3), 5), 5))

lcm(n2,n3)|lcm(n3,#0)|lcm(n4,#1)|divide(#2,n2)|divide(#2,n3)|divide(#2,n4)|add(#3,#4)|add(#6,#4)|add(#7,#5)|

rakesh : rahul : ranjan : rohit = 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,3 and 5 is 30 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 2 x 30 ) = 15 . rahul = ( 1 / 3 x 30 ) = 10 . ranjan = ( 1 / 3 x 30 ) = 10 . rohit = ( 1 / 5 x 30 ) = 6 . step 3 : total number of pencils are ( 15 x + 10 x + 10 x + 6 x ) = 41 x . for minimum number of pencils x = 1 . the person should have at least 41 pencils . a )

other

math_qa__b9wb9gePmEjLsMyk

The marks obtained by Vijay and Amith are in the ratio 4:7 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of? Choose the correct answer: A) 6 : 8 B) 6 : 1 C) 6 : 5 D) 6 : 7 E) 6 : 3

<gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">7 * 2</gadget> <output>14</output> <gadget id="calculator">12 / 14</gadget> <output>6/7 = around 0.857143</output> <result>D</result>

D

The marks obtained by Vijay and Amith are in the ratio 4:7 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?

divide(multiply(4, 3), multiply(7, 2))

multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)|

"4 : 7 3 : 2 - - - - - - - 12 : 21 : 14 12 : 14 6 : 7 answer : d"

other

math_qa__o9wAefB5qeX1E6Y9

In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is Choose the correct choice from the following choices A) 35 B) 37 C) 38 D) 41 E) 42

<gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">8 + 10</gadget> <output>18</output> <gadget id="calculator">20 + 18</gadget> <output>38</output> <result>C</result>

C

In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is

add(multiply(const_2, 10), add(8, 10))

add(n0,n3)|multiply(n0,const_2)|add(#0,#1)|

"explanation : let b ' s age = x years . then , as age = ( x + 8 ) years . ( x + 8 + 10 ) = 2 ( x — 10 ) hence x = 38 . present age of b = 38 years answer : option c"

general

math_qa__wDUVsMldDrWH1Ks3

An assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time? Choose the most appropriate option: A) 38 B) 40 C) 42 D) 45 E) 50

<gadget id="calculator">60 * 2</gadget> <output>120</output> <gadget id="calculator">60 / 36</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">(5/3) + 1</gadget> <output>8/3 = around 2.666667</output> <gadget id="calculator">120 / (8/3)</gadget> <output>45</output> <result>D</result>

D

An assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?

divide(multiply(60, const_2), add(divide(60, 36), const_1))

divide(n1,n0)|multiply(n1,const_2)|add(#0,const_1)|divide(#1,#2)

the time to produce the first 60 cogs is 60 / 36 = 5 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 8 / 3 ) hours = 45 cogs per hour . the answer is d .

general

math_qa__p2x0I5datUrayADb

If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 2 is subtracted and divided by 13? Choose the correct choice from the following answers: A) 4 B) 7 C) 8 D) 5 E) 3

<gadget id="calculator">7 * 7</gadget> <output>49</output> <gadget id="calculator">49 + 5</gadget> <output>54</output> <gadget id="calculator">54 - 2</gadget> <output>52</output> <gadget id="calculator">52 / 13</gadget> <output>4</output> <result>A</result>

A

If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 2 is subtracted and divided by 13?

divide(subtract(add(multiply(7, 7), 5), 2), 13)

multiply(n1,n1)|add(n0,#0)|subtract(#1,n3)|divide(#2,n4)|

"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 2 ) / 13 = ( 54 - 2 ) / 13 = 4 answer : option a"

general

math_qa__1kpiBJcRgFCV0paY

A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 5 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip? Choose the correct choice from the following choices A) 4 B) 5 C) 8 D) 10.72 E) 15

<gadget id="calculator">14 ** 2</gadget> <output>196</output> <gadget id="calculator">5 ** 2</gadget> <output>25</output> <gadget id="calculator">196 - 25</gadget> <output>171</output> <gadget id="calculator">171 ** (1/2)</gadget> <output>3*sqrt(19) = around 13.076697</output> <gadget id="calculator">(3*sqrt(19)) - 4</gadget> <output>-4 + 3*sqrt(19) = around 9.076697</output> <gadget id="calculator">(-4 + 3*sqrt(19)) ** 2</gadget> <output>(-4 + 3*sqrt(19))**2 = around 82.386425</output> <gadget id="calculator">196 - ((-4 + 3*sqrt(19))**2)</gadget> <output>196 - (-4 + 3*sqrt(19))**2 = around 113.613575</output> <gadget id="calculator">(196 - (-4 + 3*sqrt(19))**2) ** (1/2)</gadget> <output>sqrt(196 - (-4 + 3*sqrt(19))**2) = around 10.658967</output> <result>D</result>

D

A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 5 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?

sqrt(subtract(power(14, const_2), power(subtract(sqrt(subtract(power(14, const_2), power(5, const_2))), 4), const_2)))

power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)|subtract(#3,n2)|power(#4,const_2)|subtract(#0,#5)|sqrt(#6)|

"14 ^ 2 - 5 ^ 2 = 171 it means that the height is equal to 13.07 ~ = 13 . since the top of the ladder slips down 4 feet , then the height of the wall = 13 - 4 = 9 the bottom = sqrt ( 14 ^ 2 - 9 ^ 2 ) = sqrt ( 196 - 81 ) = 10.72 ans is d"

gain

math_qa__UMn7eW296V1TCmfe

A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay? Select the correct option A) 360 B) 227 C) 268 D) 198 E) 176

<gadget id="calculator">12 * 8</gadget> <output>96</output> <gadget id="calculator">16 * 9</gadget> <output>144</output> <gadget id="calculator">96 + 144</gadget> <output>240</output> <gadget id="calculator">18 * 6</gadget> <output>108</output> <gadget id="calculator">240 + 108</gadget> <output>348</output> <gadget id="calculator">870 / 348</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/2) * 144</gadget> <output>360</output> <result>A</result>

A

A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?

multiply(divide(870, add(add(multiply(12, 8), multiply(16, 9)), multiply(18, 6))), multiply(16, 9))

multiply(n1,n2)|multiply(n3,n4)|multiply(n5,n6)|add(#0,#1)|add(#3,#2)|divide(n0,#4)|multiply(#5,#1)|

"12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 870 = 360 answer : a"

general

math_qa__EklPi4jwEHX0Wd2p

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each. The radius of the sphere is Choose the correct choice from the following answers: A) 3 cm B) 4 cm C) 6 cm D) 8 cm E) none

<gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">6 * 3</gadget> <output>18</output> <gadget id="calculator">pi * 18</gadget> <output>18*pi = around 56.548668</output> <gadget id="calculator">(18*pi) * 2</gadget> <output>36*pi = around 113.097336</output> <gadget id="calculator">pi * 4</gadget> <output>4*pi = around 12.566371</output> <gadget id="calculator">(36*pi) / (4*pi)</gadget> <output>9</output> <gadget id="calculator">9 ** (1/2)</gadget> <output>3</output> <result>A</result>

A

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each. The radius of the sphere is

sqrt(divide(multiply(multiply(const_pi, multiply(6, divide(6, const_2))), const_2), multiply(const_pi, const_4)))

divide(n0,const_2)|multiply(const_4,const_pi)|multiply(n0,#0)|multiply(#2,const_pi)|multiply(#3,const_2)|divide(#4,#1)|sqrt(#5)|

"solution 4 î r 2 = 2 î 3 x 6 â ‡ ’ r 2 = ( 3 x 6 / 2 ) â ‡ ’ 9 â ‡ ’ r = 3 cm . answer a"

geometry

math_qa__A0alX9LTIpqp6mNa

The speed of a railway engine is 96 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is: Select the correct option. A) 19 B) 18 C) 16 D) 17 E) 14

<gadget id="calculator">96 - 24</gadget> <output>72</output> <gadget id="calculator">9 ** (1/2)</gadget> <output>3</output> <gadget id="calculator">72 / 3</gadget> <output>24</output> <gadget id="calculator">96 / 24</gadget> <output>4</output> <gadget id="calculator">4 ** 2</gadget> <output>16</output> <result>C</result>

C

The speed of a railway engine is 96 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:

power(divide(96, divide(subtract(96, 24), sqrt(9))), const_2)

sqrt(n2)|subtract(n0,n1)|divide(#1,#0)|divide(n0,#2)|power(#3,const_2)|

"the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 42 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 96 - k * sqrt ( 9 ) = 96 - 3 k k = 24 now , we need to know : what value of n makes s go to zero ? 0 = 96 - 24 * sqrt ( n ) 24 * sqrt ( n ) = 96 sqrt ( n ) = 4 n = 4 ^ 2 = 16 thus , 16 is the maximum number of cars the engine can pull and still move . c"

physics

math_qa__uh6ICJvm1zSWQ74T

Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $870.What was original rent of friend whose rent is increased? Choose the correct choice from the following options A) 800 B) 1400 C) 1000 D) 1100 E) 1200

<gadget id="calculator">870 - 800</gadget> <output>70</output> <gadget id="calculator">70 * 4</gadget> <output>280</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">280 / (1/5)</gadget> <output>1_400</output> <result>B</result>

B

Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $870.What was original rent of friend whose rent is increased?

divide(multiply(subtract(870, 800), 4), divide(20, const_100))

divide(n2,const_100)|subtract(n3,n1)|multiply(n0,#1)|divide(#2,#0)|

"0.2 x = 4 ( 870 - 800 ) 0.2 x = 280 x = 1400 answer b"

general

math_qa__Afb6LIYu1a70IWMI

If N = 2^0.3 and N^b = 16, b must equal Choose the most appropriate option: A) 3 / 80 B) 3 / 5 C) 4 D) 5 / 3 E) 40 / 3

<gadget id="calculator">log(16)</gadget> <output>log(16) = around 2.772589</output> <gadget id="calculator">2 ** 0.3</gadget> <output>1.231144</output> <gadget id="calculator">log(1.231144)</gadget> <output>0.207944</output> <gadget id="calculator">log(16) / 0.207944</gadget> <output>4.80898703497095*log(16) = around 13.333343</output> <result>E</result>

E

If N = 2^0.3 and N^b = 16, b must equal

divide(log(16), log(power(2, 0.3)))

log(n2)|power(n0,n1)|log(#1)|divide(#0,#2)|

"30 / 100 = 3 / 10 n = 2 ^ 3 / 10 n ^ b = 2 ^ 4 ( 2 ^ 3 / 10 ) ^ b = 2 ^ 4 b = 40 / 3 answer : e"

general

math_qa__3TyyDj5ofk3EvWfI

The average mark of the students of a class in a particular exam is 90. If 3 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam? Choose the correct choice from the following answers. A) 25 B) 35 C) 23 D) 22 E) 33

<gadget id="calculator">95 * 3</gadget> <output>285</output> <gadget id="calculator">3 * 40</gadget> <output>120</output> <gadget id="calculator">285 - 120</gadget> <output>165</output> <gadget id="calculator">95 - 90</gadget> <output>5</output> <gadget id="calculator">165 / 5</gadget> <output>33</output> <result>E</result>

E

The average mark of the students of a class in a particular exam is 90. If 3 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam?

divide(subtract(multiply(95, 3), multiply(3, 40)), subtract(95, 90))

multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)|

"let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 3 ) students = 80 ( x - 3 ) 90 x - ( 3 * 40 ) = 95 ( x - 3 ) 165 = 5 x = > x = 33 answer : e"

general

math_qa__m6mkoUjt32SYvDBR

A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 6.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ? Choices A) 16.5 % B) 14 % C) 35 % D) 55 % E) 65 %

<gadget id="calculator">3.5 - 3</gadget> <output>0.5</output> <gadget id="calculator">6.5 - 3</gadget> <output>3.5</output> <gadget id="calculator">0.5 / 3.5</gadget> <output>0.142857</output> <gadget id="calculator">0.142857 * 100</gadget> <output>14.2857</output> <result>B</result>

B

A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 6.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?

multiply(divide(subtract(3.5, 3), subtract(6.5, 3)), const_100)

subtract(n1,n2)|subtract(n3,n2)|divide(#0,#1)|multiply(#2,const_100)

the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.065 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 65 f - - > s = 6 f - - > f / s = 1 / 6 - - > f / ( s + f ) = 1 / ( 1 + 6 ) = 1 / 7 = 0.14 . answer : b .

gain

math_qa__SOdXoSOQ0e1OF0MG

machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 7 hours . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ? Choose one: A) 8 B) 21 C) 24 D) 27 E) 30

<gadget id="calculator">1 / 7</gadget> <output>1/7 = around 0.142857</output> <gadget id="calculator">3 * (1/7)</gadget> <output>3/7 = around 0.428571</output> <gadget id="calculator">(1/7) + (3/7)</gadget> <output>4/7 = around 0.571429</output> <gadget id="calculator">(4/7) + (4/7)</gadget> <output>8/7 = around 1.142857</output> <gadget id="calculator">3 * (4/7)</gadget> <output>12/7 = around 1.714286</output> <gadget id="calculator">(8/7) + (12/7)</gadget> <output>20/7 = around 2.857143</output> <gadget id="calculator">1 / (20/7)</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">(7/20) * 60</gadget> <output>21</output> <result>B</result>

B

machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 7 hours . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?

multiply(divide(const_1, add(add(add(divide(const_1, 7), multiply(3, divide(const_1, 7))), add(divide(const_1, 7), multiply(3, divide(const_1, 7)))), multiply(3, add(divide(const_1, 7), multiply(3, divide(const_1, 7)))))), const_60)

divide(const_1,n3)|multiply(n0,#0)|add(#0,#1)|add(#2,#2)|multiply(n0,#2)|add(#3,#4)|divide(const_1,#5)|multiply(#6,const_60)

c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 420 minutes , so its rate is 1 / 420 of the work per minute . the combined rate is 20 / 420 = 1 / 21 so the work will be completed in 21 minutes . the answer is b .

physics

math_qa__EOQWl8djl4VJPB8k

In a company the manager wants to give some gifts to all of the workers. In each block there are about 200 workers are there. The total amount for giving the gifts for all the workers is $6000. The worth of the gift is 2$. How many blocks are there in the company? Pick: A) 10 B) 12 C) 18 D) 20 E) 15

<gadget id="calculator">6_000 / 2</gadget> <output>3_000</output> <gadget id="calculator">3_000 / 200</gadget> <output>15</output> <result>E</result>

E

In a company the manager wants to give some gifts to all of the workers. In each block there are about 200 workers are there. The total amount for giving the gifts for all the workers is $6000. The worth of the gift is 2$. How many blocks are there in the company?

divide(divide(6000, 2), 200)

divide(n1,n2)|divide(#0,n0)|

"each employee will get a gift worth of = $ 2 total employees = 6000 / 2 = 3000 total blocks = 3000 / 200 = 15 correct option is e"

general

math_qa__XbTwrYslR5VrR7xq

A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? Pick. A) 500 B) 289 C) 350 D) 882 E) 281

<gadget id="calculator">300 / 18</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">(50/3) * 48</gadget> <output>800</output> <gadget id="calculator">800 - 300</gadget> <output>500</output> <result>A</result>

A

A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

subtract(multiply(divide(300, 18), 48), 300)

divide(n0,n2)|multiply(n1,#0)|subtract(#1,n0)|

"speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 48 = 50 / 3 3 ( x + 300 ) = 2400 è x = 500 m . answer : a"

physics

math_qa__Uq4KgOu4qQ46wXKi

From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 12 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? Answers A) 38 B) 39 C) 40 D) 41 E) 42

<gadget id="calculator">100 + 12</gadget> <output>112</output> <gadget id="calculator">100 / 112</gadget> <output>25/28 = around 0.892857</output> <gadget id="calculator">(25/28) * 45</gadget> <output>1_125/28 = around 40.178571</output> <result>C</result>

C

From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 12 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?

multiply(divide(const_100, add(const_100, 12)), 45)

add(n4,const_100)|divide(const_100,#0)|multiply(n7,#1)|

"soln : - 12 x = 45 - - > 28 / 25 * x = 45 - - > x = 45 * 25 / 28 = 1125 / 28 = ~ 40 answer : c ."

gain

math_qa__VJ0r0U1FyMFfmUkI

Andrew purchased 14kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg. How much amount did he pay to the shopkeeper? Choose the correct answer A) 1000 B) 1376 C) 1456 D) 1900 E) 1566

<gadget id="calculator">14 * 54</gadget> <output>756</output> <gadget id="calculator">10 * 62</gadget> <output>620</output> <gadget id="calculator">756 + 620</gadget> <output>1_376</output> <result>B</result>

B

Andrew purchased 14kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg. How much amount did he pay to the shopkeeper?

add(multiply(14, 54), multiply(10, 62))

multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|

"cost of 14 kg grapes = 54 × 14 = 756 . cost of 10 kg of mangoes = 62 x 10 = 620 . total cost he has to pay = 756 + 620 = 1376 b"

gain

math_qa__lW7bNLbeoKDwhXwA

Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train? Choose the correct choice: A) 100 m B) 75 m C) 120 m D) 50 m E) 70 m

<gadget id="calculator">50 - 32</gadget> <output>18</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">18 * (5/18)</gadget> <output>5</output> <gadget id="calculator">5 * 15</gadget> <output>75</output> <result>B</result>

B

Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?

multiply(multiply(subtract(50, 32), const_0_2778), 15)

subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1)

since both trains move in same direction so : average speed = 50 - 32 = 18 kmph = 5 mps speeed = length of train / time length of train = 5 * 15 = 75 m answer : b

physics

math_qa__2rFpmA8MsF1VpWoV

How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? Choose the correct choice from the following choices A) 21.4 sec B) 77 sec C) 25 sec D) 18 sec E) 17 sec

<gadget id="calculator">150 + 100</gadget> <output>250</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">42 * (5/18)</gadget> <output>35/3 = around 11.666667</output> <gadget id="calculator">250 / (35/3)</gadget> <output>150/7 = around 21.428571</output> <result>A</result>

A

How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph?

divide(add(150, 100), multiply(42, const_0_2778))

add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)|

"d = 100 + 150 = 250 s = 42 * 5 / 18 = 11.7 mps t = 250 / 11.7 = 21.4 sec answer : a"

physics

math_qa__1OKEDrguqCrEqKWB

Two cars of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? Choose the correct choice from the following answers: A) 10 sec B) 30 sec C) 40 sec D) 20 s E) 50 sec

<gadget id="calculator">280 + 120</gadget> <output>400</output> <gadget id="calculator">42 + 30</gadget> <output>72</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">72 * (5/18)</gadget> <output>20</output> <gadget id="calculator">400 / 20</gadget> <output>20</output> <result>D</result>

D

Two cars of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?

divide(add(280, 120), multiply(add(42, 30), const_0_2778))

add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)

d relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 s .

physics

math_qa__m7C5a0vi4PAlCAv8

A student is ranked 6th from right and 5th from left. How many students are there in totality ? Choose the correct answer. A) 10 B) 19 C) 20 D) 21 E) 22

<gadget id="calculator">6 + 5</gadget> <output>11</output> <gadget id="calculator">11 - 1</gadget> <output>10</output> <result>A</result>

A

A student is ranked 6th from right and 5th from left. How many students are there in totality ?

subtract(add(6, 5), const_1)

add(n0,n1)|subtract(#0,const_1)|

"from right 6 , from left 5 total = 6 + 5 - 1 = 10 answer : a"

general

math_qa__DRTYrIBB3Xjpj6y4

If 6 men can reap 60 acres of land in 10 days, how many acres of land can 12 men reap in 20 days? Select the correct option: A) 120 B) 360 C) 240 D) 182 E) 1000

<gadget id="calculator">12 / 6</gadget> <output>2</output> <gadget id="calculator">20 / 10</gadget> <output>2</output> <gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">60 * 4</gadget> <output>240</output> <result>C</result>

C

If 6 men can reap 60 acres of land in 10 days, how many acres of land can 12 men reap in 20 days?

multiply(60, multiply(divide(12, 6), divide(20, 10)))

divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)|

"6 men 60 acres 10 days 12 men ? 20 days 60 * 12 / 6 * 20 / 10 60 * 2 * 2 60 * 4 = 240 answer : c"

physics

math_qa__3fT5WxKaF5GAYblW

Solve for x and check: 15x = 165 Choose the correct option: A) 98 B) 165 C) 180 D) 253 E) none of these

<gadget id="calculator">165 / 15</gadget> <output>11</output> <gadget id="calculator">15 * 11</gadget> <output>165</output> <result>B</result>

B

Solve for x and check: 15x = 165

multiply(15, divide(165, 15))

divide(n1,n0)|multiply(n0,#0)

solution : dividing each side by 15 , we obtain ( 15 x / 15 ) = ( 165 / 15 ) therefore : x = 11 check : 15 x = 165 ( 15 * 11 ) = 165 165 = 165 answer : b

general

math_qa__fz3QoIaCrrQWmozE

If Ram and Gohul can do a job in 10 days and 15 days independently. How many days would they take to complete the same job working simultaneously? Answers: A) 5 B) 8 C) 4 D) 7 E) 6

<gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">(1/10) + (1/15)</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / (1/6)</gadget> <output>6</output> <result>E</result>

E

If Ram and Gohul can do a job in 10 days and 15 days independently. How many days would they take to complete the same job working simultaneously?

inverse(add(divide(const_1, 10), divide(const_1, 15)))

divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2)|

"if total work is x . ram rate of working = x / 10 per day . gohul rate of working = x / 15 per day . rate of work = ( x / 10 ) + ( x / 15 ) = 30 x / 5 x = 6 days answer is option e"

physics

math_qa__LGoJeTXmPeVvirtF

What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? Choose the correct answer A) 64.19 B) 64.12 C) 40.5 D) 64.1 E) 64.11

<gadget id="calculator">8 / 100</gadget> <output>2/25 = around 0.08</output> <gadget id="calculator">(2/25) + 1</gadget> <output>27/25 = around 1.08</output> <gadget id="calculator">(27/25) ** 4</gadget> <output>531_441/390_625 = around 1.360489</output> <gadget id="calculator">1_000 * (531_441/390_625)</gadget> <output>4_251_528/3_125 = around 1_360.48896</output> <gadget id="calculator">(4_251_528/3_125) - 1_000</gadget> <output>1_126_528/3_125 = around 360.48896</output> <gadget id="calculator">1_000 * (2/25)</gadget> <output>80</output> <gadget id="calculator">80 * 4</gadget> <output>320</output> <gadget id="calculator">(1_126_528/3_125) - 320</gadget> <output>126_528/3_125 = around 40.48896</output> <result>C</result>

C

What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?

subtract(subtract(multiply(1000, power(add(divide(8, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(8, const_100)), 4))

divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|multiply(n2,#2)|power(#1,n2)|multiply(n1,#4)|subtract(#5,n1)|subtract(#6,#3)|

"s . i . = ( 1000 * 8 * 4 ) / 100 = rs . 320 c . i . = [ 1000 * ( 1 + 8 / 100 ) 4 - 1000 ] = rs . 360.5 difference = ( 360.5 - 320 ) = rs . 40.5 answer : c"

gain

math_qa__PXJf7mVJb0xxaabW

A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 40 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? Choose the correct choice from the following answers: A) 40 B) 45 C) 50 D) 55 E) 67.5

<gadget id="calculator">120 / 2</gadget> <output>60</output> <gadget id="calculator">60 + 120</gadget> <output>180</output> <gadget id="calculator">180 / 40</gadget> <output>9/2 = around 4.5</output> <gadget id="calculator">(9/2) / 4</gadget> <output>9/8 = around 1.125</output> <gadget id="calculator">(9/8) * 60</gadget> <output>135/2 = around 67.5</output> <result>E</result>

E

A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 40 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?

multiply(divide(divide(add(divide(120, const_2), 120), 40), const_4), divide(120, const_2))

divide(n0,const_2)|add(n0,#0)|divide(#1,n1)|divide(#2,const_4)|multiply(#3,#0)|

"a - b = 120 miles b - c = 60 miles avg speed = 40 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 40 = 180 / 4 t t = 67.5 b - c = 67.5 mph answer e"

physics

math_qa__tLkU2ngfNT4Jswrc

Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 Select the correct option: A) 0 B) 1 C) 2 D) 3 E) 4

<gadget id="calculator">50 + 50</gadget> <output>100</output> <gadget id="calculator">100 + 97</gadget> <output>197</output> <gadget id="calculator">197 + 97</gadget> <output>294</output> <gadget id="calculator">294 + 97</gadget> <output>391</output> <gadget id="calculator">391 + 120</gadget> <output>511</output> <gadget id="calculator">511 + 125</gadget> <output>636</output> <gadget id="calculator">636 + 155</gadget> <output>791</output> <gadget id="calculator">791 + 199</gadget> <output>990</output> <gadget id="calculator">990 + 199</gadget> <output>1_189</output> <gadget id="calculator">1_189 + 239</gadget> <output>1_428</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">1_428 / 11</gadget> <output>1_428/11 = around 129.818182</output> <gadget id="calculator">(1_428/11) / (1_428/11)</gadget> <output>1</output> <result>B</result>

B

Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239

divide(divide(add(add(add(add(add(add(add(add(add(add(50, 50), 97), 97), 97), 120), 125), 155), 199), 199), 239), add(const_10, const_1)), divide(add(add(add(add(add(add(add(add(add(add(50, 50), 97), 97), 97), 120), 125), 155), 199), 199), 239), add(const_10, const_1)))

add(n0,n0)|add(const_1,const_10)|add(n2,#0)|add(n2,#2)|add(n2,#3)|add(n5,#4)|add(n6,#5)|add(n7,#6)|add(n8,#7)|add(n8,#8)|add(n10,#9)|divide(#10,#1)|divide(#11,#11)

taking the prices of products in ascending order ( already arranged ) $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239 we see that median value is the 6 th value as there in total 11 values given arithmetic mean = total / number of entries = 1428 / 11 = 129.8181 we are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $ 120 and $ 129.81 , answer is 1 unit correct answer - b

general

math_qa__i0tOrtBMmhvaTDrY

The average age of an adult class is 40years. 15new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class? Choose the correct choice from the following choices. A) 8 B) 12 C) 15 D) 17 E) 18

<gadget id="calculator">40 - 4</gadget> <output>36</output> <gadget id="calculator">15 * 36</gadget> <output>540</output> <gadget id="calculator">15 * 32</gadget> <output>480</output> <gadget id="calculator">540 - 480</gadget> <output>60</output> <gadget id="calculator">60 / 4</gadget> <output>15</output> <result>C</result>

C

The average age of an adult class is 40years. 15new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?

divide(subtract(multiply(15, subtract(40, 4)), multiply(15, 32)), 4)

multiply(n1,n2)|subtract(n0,n3)|multiply(n1,#1)|subtract(#2,#0)|divide(#3,n3)|

"let original strength = y then , 40 y + 15 x 32 = ( y + 15 ) x 36 â ‡ ’ 40 y + 480 = 36 y + 540 â ‡ ’ 4 y = 60 â ˆ ´ y = 15 c"

general

math_qa__BBI1P6bS4DHViVKK

If log10 2 = 0.3010, then log2 10 is equal to: Options: A) 100 / 6 B) 289 / 4 C) 128 / 7 D) 456 / 6 E) 1000 / 301

<gadget id="calculator">1 / 0.301</gadget> <output>3.322259</output> <result>E</result>

E

If log10 2 = 0.3010, then log2 10 is equal to:

divide(const_1, 0.301)

divide(const_1,n2)

explanation : log 2 10 = 1 / log 102 = 1 / 0.3010 = 10000 / 3010 = 1000 / 301 answer e

general

math_qa__eROxkM5miDp063Hz

The area of a triangle is with base 8m and height 4m? Choose one. A) 88 m 2 B) 10 m 2 C) 16 m 2 D) 77 m 2 E) 31 m 2

<gadget id="calculator">(8 * 4) / 2</gadget> <output>16</output> <result>C</result>

C

The area of a triangle is with base 8m and height 4m?

triangle_area(8, 4)

triangle_area(n0,n1)|

"1 / 2 * 8 * 4 = 16 m 2 answer : c"

geometry

math_qa__d8xuzsKUFCWk4cxB

Set A consists of the integers from 4 to 15, inclusive, while set B consists of the integers from 6 to 20, inclusive. How many distinct integers do belong to the both sets at the same time? Choose the correct choice from the following choices: A) 5 B) 7 C) 8 D) 9 E) 10

<gadget id="calculator">6 + 4</gadget> <output>10</output> <result>E</result>

E

Set A consists of the integers from 4 to 15, inclusive, while set B consists of the integers from 6 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?

add(6, 4)

add(n0,n2)

a = { 4,5 , 6,7 , 8,9 , 10,11 , 12,13 , 14,15 } b = { 6 , 7,8 , 9,10 , 11,12 . . . 20 } thus we see that there are 10 distinct integers that are common to both . e is the correct answer .

other

math_qa__m2wFpWKxUS4uarRQ

What is the probability that the sum of two dice will yield a 9, and then when both are thrown again, their sum will again yield a 9? assume that each die has 8 sides with faces numbered 1 to 8. Choose the correct choice from the following answers. A) 1 / 64 B) 1 / 36 C) 1 / 12 D) 1 / 6 E) 1 / 3

<gadget id="calculator">8 ** 2</gadget> <output>64</output> <gadget id="calculator">8 / 64</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/8) * (1/8)</gadget> <output>1/64 = around 0.015625</output> <result>A</result>

A

What is the probability that the sum of two dice will yield a 9, and then when both are thrown again, their sum will again yield a 9? assume that each die has 8 sides with faces numbered 1 to 8.

multiply(divide(8, power(8, const_2)), divide(8, power(8, const_2)))

power(n2,const_2)|divide(n2,#0)|multiply(#1,#1)|

"solution - rolling dices is an independent event . the combinations to get 9 are ( 1,8 ) , ( 8,1 ) , ( 2,7 ) , ( 7,2 ) , ( 3,6 ) , ( 6,3 ) , ( 4,5 ) , ( 5,4 ) , and total combinations of both dices is 64 . the probability of getting 9 in first attempt is 8 / 64 = 1 / 8 . probability of getting 9 again in second attempt = ( 1 / 8 ) * ( 1 / 8 ) = 1 / 64 . ans a"

probability

math_qa__fTcvdH4xngWxUJQx

John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $20. What is the percent decrease? Choose the correct choice from the following options. A) 20 % B) 30 % C) 40 % D) 70 % E) 80 %

<gadget id="calculator">100 - 20</gadget> <output>80</output> <result>E</result>

E

John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $20. What is the percent decrease?

subtract(100, 20)

subtract(n0,n1)|

"the is always the difference between our starting and ending points . in this case , it ’ s 100 – 20 = 80 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 80 / 100 ) * 100 = ( 0.8 ) * 100 = 80 % . e"

general

math_qa__WyZU6jyGMf0aLVAe

A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent Q of the list price is the lowest possible sale price? Choose the correct option A) 20 B) 25 C) 30 D) 40 E) 50

<gadget id="calculator">80 / 2</gadget> <output>40</output> <result>D</result>

D

A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent Q of the list price is the lowest possible sale price?

divide(80, const_2)

divide(n3,const_2)|

"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is q = 40 % of 80 hence , d is the answer"

general

math_qa__h3Kas4DzYl3q3yJm

How many two-digit numbers yield a remainder of 1 when divided by both 4 and 17? Pick one: A) 0 B) 1 C) 2 D) 3 E) 4

<gadget id="calculator">17 * 4</gadget> <output>68</output> <gadget id="calculator">1 + 68</gadget> <output>69</output> <gadget id="calculator">69 - 68</gadget> <output>1</output> <result>B</result>

B

How many two-digit numbers yield a remainder of 1 when divided by both 4 and 17?

subtract(add(1, multiply(17, 4)), multiply(17, 4))

multiply(n1,n2)|add(n0,#0)|subtract(#1,#0)

easier to start with numbers that are of the form 17 p + 1 - - - > 18 , 35,52 , 69,86 . out of these , there is only one ( 69 ) is also of the form 4 q + 1 . thus 1 is the answer . b is the correct answer .

general

math_qa__Iu7SJHWVrTBjBTeW

A cylinder with 6 meter radius and 12 meter height is filled to capacity with water. If the content of the cylinder is used to fill several smaller cylinders of 4 meter diameter and 8 meter height, how many smaller cylinders will be filled to capacity? Pick: A) 13 B) 12 C) 4 D) 16 E) 18

<gadget id="calculator">pi * (6 ** 2) * 12</gadget> <output>432*pi = around 1_357.168026</output> <gadget id="calculator">pi * (2 ** 2) * 8</gadget> <output>32*pi = around 100.530965</output> <gadget id="calculator">(432*pi) / (32*pi)</gadget> <output>27/2 = around 13.5</output> <result>A</result>

A

A cylinder with 6 meter radius and 12 meter height is filled to capacity with water. If the content of the cylinder is used to fill several smaller cylinders of 4 meter diameter and 8 meter height, how many smaller cylinders will be filled to capacity?

divide(volume_cylinder(6, 12), volume_cylinder(const_2, 8))

volume_cylinder(n0,n1)|volume_cylinder(const_2,n3)|divide(#0,#1)

calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 1357.17 smaller cylinder volume = 100.53 therefore the number of cylinders b that can be filled to capacity = 1357.17 / 100.53 = 13.5 answer is a only 13 smaller cylinders can be filled to capacity .

geometry

math_qa__J0vCQ7YdX4DTgbGY

Sonika deposited Rs.12000 which amounted to Rs.19500 after 4 years at simple interest. Had the interest been 3% more. She would get how much? Choose the correct choice from the following: A) 20940 B) 21009 C) 23000 D) 23450 E) 30000

<gadget id="calculator">3 / 100</gadget> <output>3/100 = around 0.03</output> <gadget id="calculator">19_500 - 12_000</gadget> <output>7_500</output> <gadget id="calculator">7_500 / 4</gadget> <output>1_875</output> <gadget id="calculator">1_875 / 12_000</gadget> <output>5/32 = around 0.15625</output> <gadget id="calculator">(3/100) + (5/32)</gadget> <output>149/800 = around 0.18625</output> <gadget id="calculator">(149/800) * 12_000</gadget> <output>2_235</output> <gadget id="calculator">2_235 * 4</gadget> <output>8_940</output> <gadget id="calculator">8_940 + 12_000</gadget> <output>20_940</output> <result>A</result>

A

Sonika deposited Rs.12000 which amounted to Rs.19500 after 4 years at simple interest. Had the interest been 3% more. She would get how much?

add(multiply(multiply(add(divide(3, const_100), divide(divide(subtract(19500, 12000), 4), 12000)), 12000), 4), 12000)

divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)|

"( 12000 * 4 * 3 ) / 100 = 1440 19500 - - - - - - - - 20940 answer : a"

gain

math_qa__6PnQj3X9xNouR4Br

8 k 8 + k 88 - - - - - - - - 16 y 6 if k and y represent non - zero digits within the integers above , what is y ? Choose the correct choice from the following answers: A) 6 B) 7 C) 8 D) 9 E) 17

<gadget id="calculator">16 * 100</gadget> <output>1_600</output> <gadget id="calculator">1_600 + 6</gadget> <output>1_606</output> <gadget id="calculator">8 * 100</gadget> <output>800</output> <gadget id="calculator">800 + 8</gadget> <output>808</output> <gadget id="calculator">808 + 88</gadget> <output>896</output> <gadget id="calculator">1_606 - 896</gadget> <output>710</output> <gadget id="calculator">710 / 10</gadget> <output>71</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">71 / 11</gadget> <output>71/11 = around 6.454545</output> <gadget id="calculator">floor(71/11)</gadget> <output>6</output> <result>A</result>

A

8 k 8 + k 88 - - - - - - - - 16 y 6 if k and y represent non - zero digits within the integers above , what is y ?

floor(divide(divide(subtract(add(multiply(16, const_100), 6), add(add(multiply(8, const_100), 8), 88)), const_10), add(const_10, const_1)))

add(const_1,const_10)|multiply(n3,const_100)|multiply(n0,const_100)|add(n4,#1)|add(n0,#2)|add(n2,#4)|subtract(#3,#5)|divide(#6,const_10)|divide(#7,#0)|floor(#8)

8 k 8 k 88 - - - - - - - - 16 y 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * * ) . after that it ' s easy to get that k = 7 and y = 6 . answer : a .

general

math_qa__o0rybMTL1t3yj0Bb

A rectangular garden is to be twice as long as it is wide. If 900 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards? Choose one. A) 40 B) 50 C) 60 D) 200 E) 300

<gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">900 / 6</gadget> <output>150</output> <gadget id="calculator">150 * 2</gadget> <output>300</output> <result>E</result>

E

A rectangular garden is to be twice as long as it is wide. If 900 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?

multiply(divide(900, multiply(add(const_2, const_1), const_2)), const_2)

add(const_1,const_2)|multiply(#0,const_2)|divide(n0,#1)|multiply(#2,const_2)|

"alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 900 so , 2 ( l + b ) = 900 or , l + b = 450 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 200 l = 200 ; b = 100 l + b = 300 ( e ) 300 l = 300 ; b = 150 l + b = 450 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( e )"

geometry

math_qa__KpP8g5SsuyEoHt1w

In a manufacturing plant, it takes 36 machines 8 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? Choose the correct choice from the following A) 3 B) 6 C) 8 D) 9 E) 12

<gadget id="calculator">36 * 12</gadget> <output>432</output> <gadget id="calculator">432 * 8</gadget> <output>3_456</output> <gadget id="calculator">3_456 / 72</gadget> <output>48</output> <gadget id="calculator">48 / 8</gadget> <output>6</output> <result>B</result>

B

In a manufacturing plant, it takes 36 machines 8 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?

divide(divide(multiply(multiply(36, 12), 8), 72), 8)

multiply(n0,n4)|multiply(#0,n1)|divide(#1,n3)|divide(#2,n2)|

"the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 8 * 36 / 72 * 12 / 8 = 6 ans b"

physics

math_qa__As7j8vtrDNOKKlZU

At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year? Options. A) 70 B) 120 C) 100 D) 90 E) 110

<gadget id="calculator">10 * 4</gadget> <output>40</output> <gadget id="calculator">40 * 3</gadget> <output>120</output> <result>B</result>

B

At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year?

multiply(multiply(10, 4), 3)

multiply(n1,n2)|multiply(n0,#0)

let the total number of boys and girls at the beginning of the year be 3 x and 4 x respectively . now 10 boys and 20 girls are transferred to another school . thus no . of boys and girls students left in the school x are 3 x - 10 and 4 x - 20 respectively . the ratio of these boys and girls students = 4 / 5 thus we have ( 3 x - 10 ) / ( 4 x - 20 ) = 4 / 5 15 x - 50 = 16 x - 80 x = 30 thus total no . of boys at the beginning of the year = 4 ( 30 ) = 120 answer is option b

general

math_qa__p5DbhXAzxh8zkTPn

The total number of digits used in numbering the pages of a book having 360 pages is Choose the correct choice from the following options. A) 972 B) 990 C) 1098 D) 1305 E) 1405

<gadget id="calculator">360 * 3</gadget> <output>1_080</output> <gadget id="calculator">100 - 1</gadget> <output>99</output> <gadget id="calculator">1_080 - 99</gadget> <output>981</output> <gadget id="calculator">10 - 1</gadget> <output>9</output> <gadget id="calculator">981 - 9</gadget> <output>972</output> <result>A</result>

A

The total number of digits used in numbering the pages of a book having 360 pages is

subtract(subtract(multiply(360, const_3), subtract(const_100, const_1)), subtract(const_10, const_1))

multiply(n0,const_3)|subtract(const_100,const_1)|subtract(const_10,const_1)|subtract(#0,#1)|subtract(#3,#2)|

"total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 261 ) = ( 9 + 180 + 783 ) = 972 . answer : a"

general

math_qa__d7hadGQL83XFqzEK

A 2000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? Answers A) 8 B) 12 C) 18 D) 24 E) 48

<gadget id="calculator">6 + 4</gadget> <output>10</output> <gadget id="calculator">10 + 2</gadget> <output>12</output> <gadget id="calculator">2_000 / 2</gadget> <output>1_000</output> <gadget id="calculator">12 * 1_000</gadget> <output>12_000</output> <gadget id="calculator">12_000 / 1_000</gadget> <output>12</output> <result>B</result>

B

A 2000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

divide(multiply(add(add(6, 4), 2), divide(2000, 2)), const_1000)

add(n4,n5)|divide(n0,n2)|add(n2,#0)|multiply(#2,#1)|divide(#3,const_1000)|

"in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 1,000 by that net inflow to get the minutes ) - 12 min . answer b ."

physics

math_qa__fq7Fsip4OViYhqDO

Share Rs.4800 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? Choices: A) 900 B) 980 C) 1600 D) 1240 E) 1400

<gadget id="calculator">4_800 / 2</gadget> <output>2_400</output> <gadget id="calculator">4_800 / 6</gadget> <output>800</output> <gadget id="calculator">2_400 - 800</gadget> <output>1_600</output> <result>C</result>

C

Share Rs.4800 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?

subtract(divide(4800, 2), divide(4800, 6))

divide(n0,n1)|divide(n0,n3)|subtract(#0,#1)

amount received by sanjay . 4 / 12 x 4800 = 1600 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1600 . c

other

math_qa__lunoaA6g3qKEcDKB

The total circumference of two circles is 25. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii? Select. A) 5.7 B) 6.0 C) 4.0 D) 9.7 E) 18.0

<gadget id="calculator">25 / 3</gadget> <output>25/3 = around 8.333333</output> <gadget id="calculator">(25/3) / 3</gadget> <output>25/9 = around 2.777778</output> <gadget id="calculator">(25/3) * 2</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">(50/3) / 3</gadget> <output>50/9 = around 5.555556</output> <gadget id="calculator">(25/9) + (50/9)</gadget> <output>25/3 = around 8.333333</output> <gadget id="calculator">(25/3) / 2</gadget> <output>25/6 = around 4.166667</output> <result>C</result>

C

The total circumference of two circles is 25. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?

divide(add(divide(divide(25, const_3), const_3), divide(multiply(divide(25, const_3), const_2), const_3)), const_2)

divide(n0,const_3)|divide(#0,const_3)|multiply(#0,const_2)|divide(#2,const_3)|add(#1,#3)|divide(#4,const_2)|

"let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 25 where 2 r = r thus : 2 π r + 4 π r = 25 6 π r = 25 r = approx 1.33 π r + 2 r π = 25 3 π r = 25 r = approx 2.65 r + r = approx 3.98 = 4.0 answer : c"

general

math_qa__B3QSjsD4cywwRzgT

The length of a train and that of a platform are equal. If with a speed of 144 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Select the correct option. A) 757 B) 758 C) 718 D) 1200 E) 738

<gadget id="calculator">144 * 1_000</gadget> <output>144_000</output> <gadget id="calculator">60 / 1</gadget> <output>60</output> <gadget id="calculator">144_000 / 60</gadget> <output>2_400</output> <gadget id="calculator">2_400 / 2</gadget> <output>1_200</output> <result>D</result>

D

The length of a train and that of a platform are equal. If with a speed of 144 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?

divide(divide(multiply(144, const_1000), divide(const_60, const_1)), const_2)

divide(const_60,const_1)|multiply(n0,const_1000)|divide(#1,#0)|divide(#2,const_2)|

"speed = [ 144 * 5 / 18 ] m / sec = 40 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 40 è x = 40 * 60 / 2 = 1200 answer : d"

physics

math_qa__bQVQkjCjxbvVwEMq

The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $20.50. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour? Select A) 347.4 B) 987.4 C) 877.4 D) 637.4 E) 667.4

<gadget id="calculator">24 / 10</gadget> <output>12/5 = around 2.4</output> <gadget id="calculator">20.5 * 6</gadget> <output>123</output> <gadget id="calculator">123 / 2</gadget> <output>123/2 = around 61.5</output> <gadget id="calculator">(12/5) * (123/2)</gadget> <output>738/5 = around 147.6</output> <gadget id="calculator">4 * (738/5)</gadget> <output>2_952/5 = around 590.4</output> <gadget id="calculator">3 * (123/2)</gadget> <output>369/2 = around 184.5</output> <gadget id="calculator">(2_952/5) + (369/2)</gadget> <output>7_749/10 = around 774.9</output> <gadget id="calculator">5 * 20.5</gadget> <output>102.5</output> <gadget id="calculator">(7_749/10) + 102.5</gadget> <output>877.4</output> <result>C</result>

C

The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $20.50. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?

add(add(multiply(4, multiply(divide(24, 10), divide(multiply(20.50, 6), 2))), multiply(3, divide(multiply(20.50, 6), 2))), multiply(5, 20.50))

divide(n1,n0)|multiply(n2,n4)|multiply(n4,n7)|divide(#1,n3)|multiply(#0,#3)|multiply(n6,#3)|multiply(n5,#4)|add(#6,#5)|add(#7,#2)|

"c $ 877.40 let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = $ 877.40"

general

math_qa__CBlMd0jb35Yr3AuL

A is 1.5 times as fast as B. A alone can do the work in 30 days. If A and B working together in how many days will the work be completed? Choose the correct choice from the following. A) 23 B) 18 C) 21 D) 24 E) 25

<gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">(1/30) / 1.5</gadget> <output>0.022222</output> <gadget id="calculator">(1/30) + 0.022222</gadget> <output>0.055555</output> <gadget id="calculator">1 / 0.055555</gadget> <output>18.00018</output> <result>B</result>

B

A is 1.5 times as fast as B. A alone can do the work in 30 days. If A and B working together in how many days will the work be completed?

divide(const_1, add(divide(const_1, 30), divide(divide(const_1, 30), 1.5)))

divide(const_1,n1)|divide(#0,n0)|add(#0,#1)|divide(const_1,#2)|

"a can finish 1 work in 30 days b can finish 1 / 1.5 work in 30 days - since a is 1.5 faster than b this means b can finish 1 work in 30 * 1.5 days = 45 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 45 * 30 / ( 45 + 30 ) = 20 * 30 / 50 = 18 days so answer is b"

physics

math_qa__ZLWNgQBhX7NPIF9f

If the numbers 1 to 95 are written on 95 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite? Choices A) 1 / 50 B) 1 / 25 C) 1 / 95 D) 1 E) 2

<gadget id="calculator">1 / 95</gadget> <output>1/95 = around 0.010526</output> <result>C</result>

C

If the numbers 1 to 95 are written on 95 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?

divide(1, 95)

divide(n0,n1)|

"there are 25 primes , 69 composite numbers from 1 to 95 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 95 . answer : c"

other

math_qa__n7qHhFbkY4GDl6wB

A watch was sold at a loss of 10%. If it was sold for Rs.168 more, there would have been a gain of 4%. What is the cost price? Choose one A) s : 1000 B) s : 1067 C) s : 1200 D) s : 1028 E) s : 1027

<gadget id="calculator">168 * 100</gadget> <output>16_800</output> <gadget id="calculator">100 + 4</gadget> <output>104</output> <gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">104 - 90</gadget> <output>14</output> <gadget id="calculator">16_800 / 14</gadget> <output>1_200</output> <result>C</result>

C

A watch was sold at a loss of 10%. If it was sold for Rs.168 more, there would have been a gain of 4%. What is the cost price?

divide(multiply(168, const_100), subtract(add(const_100, 4), subtract(const_100, 10)))

add(const_100,n2)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#2)|divide(#1,#3)|

"90 % 104 % - - - - - - - - 14 % - - - - 168 100 % - - - - ? = > rs : 1200 answer : c"

gain

math_qa__yFO7YADYIhdGaoKK

A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? Options A) 2 B) 3 C) 4 D) 5 E) 6

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/2) - (1/3)</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / (1/6)</gadget> <output>6</output> <result>E</result>

E

A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?

divide(const_1, subtract(divide(const_1, 2), divide(const_1, 3)))

divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)

the rate of the pump + leak = 1 / 3 1 / 2 - leak ' s rate = 1 / 3 leak ' s rate = 1 / 2 - 1 / 3 = 1 / 6 the leak will empty the tank in 6 hours . the answer is e .

physics

math_qa__MbvFXhAxxPFg3pJJ

If each edge of a cube is doubled, then its volume : Answers A) becomes 8 times B) becomes 9 times C) is double D) becomes 6 times E) none

<gadget id="calculator">2 ** 3</gadget> <output>8</output> <result>A</result>

A

If each edge of a cube is doubled, then its volume :

power(const_2, const_3)

power(const_2,const_3)

sol . let original edge = a . then , volume = a ³ new edge = 2 a . so , new volume = ( 2 a ) ³ = 8 a ³ ∴ volume becomes 8 times answer a

geometry

math_qa__uaNUSIeMNoT2jlNi

On a trip, a cyclist averaged 9 miles per hour for the first 18 miles and 10 miles per hour for the remaining 12 miles. If the cyclist returned immediately via the same route and took a total of 7.2 hours for the round trip, what was the average speed (in miles per hour) for the return trip? Select. A) 6.9 B) 7.2 C) 7.5 D) 7.8 E) 8.1

<gadget id="calculator">18 + 12</gadget> <output>30</output> <gadget id="calculator">18 / 9</gadget> <output>2</output> <gadget id="calculator">12 / 10</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">2 + (6/5)</gadget> <output>16/5 = around 3.2</output> <gadget id="calculator">7.2 - (16/5)</gadget> <output>4</output> <gadget id="calculator">30 / 4</gadget> <output>15/2 = around 7.5</output> <result>C</result>

C

On a trip, a cyclist averaged 9 miles per hour for the first 18 miles and 10 miles per hour for the remaining 12 miles. If the cyclist returned immediately via the same route and took a total of 7.2 hours for the round trip, what was the average speed (in miles per hour) for the return trip?

divide(add(18, 12), subtract(7.2, add(divide(18, 9), divide(12, 10))))

add(n1,n3)|divide(n1,n0)|divide(n3,n2)|add(#1,#2)|subtract(n4,#3)|divide(#0,#4)|

"the time to go 30 miles was 18 / 9 + 12 / 10 = 2 + 1.2 = 3.2 hours . the average speed for the return trip was 30 miles / 4 hours = 7.5 mph . the answer is c ."

physics

math_qa__DZYseXwbOCjqZf1P

In Town P, 60 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town P are females? Answers. A) 20 % B) 25 % C) 30 % D) 35 % E) 40 %

<gadget id="calculator">60 - 42</gadget> <output>18</output> <gadget id="calculator">18 / 60</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 100</gadget> <output>30</output> <result>C</result>

C

In Town P, 60 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town P are females?

multiply(divide(subtract(60, 42), 60), const_100)

subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|

"the percent of the population who are employed females is 60 - 42 = 18 % the percent of employed people who are female is 18 % / 60 % = 30 % . the answer is c ."

gain

math_qa__GoCMQPXkn2TgUOOT

An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 5 ? Select the correct option: A) 1 / 9 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 2 / 5

<gadget id="calculator">100 / 5</gadget> <output>20</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 2</gadget> <output>2/5 = around 0.4</output> <result>E</result>

E

An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 5 ?

multiply(divide(divide(100, 5), 100), const_2.0)

divide(n1,n3)|divide(#0,n1)|multiply(const_2.0,#1)|

"n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 , 4 , 5 } , { 6 , 7 , 8 , 9 , 10 } , . . . , { 96 , 97 , 98 , 99,100 } there is exactly 1 numbers out of 5 satisfying the above condition . for example in { 1 , 2 , 3 , 4 , 5 } n can be : 4 or 5 . thus , the overall probability is 2 / 5 . answer : d ."

general

math_qa__HwGGIuA8g7K7b2VS

Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? Choose the correct answer. A) 20 B) 21 C) 22 D) 23 E) 25

<gadget id="calculator">18 / 2</gadget> <output>9</output> <gadget id="calculator">34 - 18</gadget> <output>16</output> <gadget id="calculator">9 + 16</gadget> <output>25</output> <result>E</result>

E

Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?

add(divide(18, const_2), subtract(34, 18))

divide(n0,const_2)|subtract(n1,n0)|add(#0,#1)|

"check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 22 , child = 11 , years ago = 34 - 22 = 12 - - > child ' s age now = 11 + 12 = 23 . answer : e ."

general

math_qa__7F8vUjHBO6EPyiBg

Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? Options A) 2.8 % B) 3.6 % C) 4.4 % D) 5 % E) 6.0 %

<gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">50 * (1/25)</gadget> <output>2</output> <gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">30 * (1/10)</gadget> <output>3</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/20) * 100</gadget> <output>5</output> <result>D</result>

D

Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?

multiply(divide(add(multiply(50, divide(4, const_100)), multiply(30, divide(10, const_100))), const_100), const_100)

divide(n3,const_100)|divide(n4,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(#2,#3)|divide(#4,const_100)|multiply(#5,const_100)

let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2 tax on others = 3 percentage = 5 / 100 = 5 % answer : d

general

math_qa__Q01MfRC7WlZwDXIi

Jeff has 252 ounces of peanut butter in 16, 28. and 40 ounce jars. He has an equal number of each sized jar. How many jars of peanut butter does Jeff have? Choose the most appropriate option: A) 9 B) 8 C) 7 D) 10 E) 11

<gadget id="calculator">16 + 28</gadget> <output>44</output> <gadget id="calculator">44 + 40</gadget> <output>84</output> <gadget id="calculator">252 / 84</gadget> <output>3</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <result>A</result>

A

Jeff has 252 ounces of peanut butter in 16, 28. and 40 ounce jars. He has an equal number of each sized jar. How many jars of peanut butter does Jeff have?

multiply(divide(252, add(add(16, 28), 40)), const_3)

add(n1,n2)|add(n3,#0)|divide(n0,#1)|multiply(#2,const_3)

let p equal the number of each sized jar then 16 p + 28 p + 40 p = 252 84 p = 252 p = 3 therefore , the total number of jars of peanut butter jeff has = 3 p = 9 answer : a

general

math_qa__RP2g7rQpPpmQCzNW

If 20 men can build a wall 66 metres long in 12 days, what length of a similar can be built by 86 men in 8 days? Select A) 189.2 mtrs B) 378.4 mtrs C) 478.4 mtrs D) 488.4 mtrs E) 578.4 mtrs

<gadget id="calculator">86 * 8</gadget> <output>688</output> <gadget id="calculator">20 * 12</gadget> <output>240</output> <gadget id="calculator">688 / 240</gadget> <output>43/15 = around 2.866667</output> <gadget id="calculator">66 * (43/15)</gadget> <output>946/5 = around 189.2</output> <result>A</result>

A

If 20 men can build a wall 66 metres long in 12 days, what length of a similar can be built by 86 men in 8 days?

multiply(66, divide(multiply(86, 8), multiply(20, 12)))

multiply(n3,n4)|multiply(n0,n2)|divide(#0,#1)|multiply(n1,#2)|

"if 20 men can build a wall 66 metres long in 12 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 12 * 20 ) = 189.2 mtrs answer : a"

physics

math_qa__Vaw38jveQbe7xuyS

Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 4 inches tall. How tall are the sculpture andbase together? Pick one. A) 3.17 feet B) 3.2 feet C) 3.3 feet D) 3.4 feet E) 3.5 feet

<gadget id="calculator">2 + 10</gadget> <output>12</output> <gadget id="calculator">12 * 2</gadget> <output>24</output> <gadget id="calculator">24 + 10</gadget> <output>34</output> <gadget id="calculator">34 + 4</gadget> <output>38</output> <gadget id="calculator">38 / 12</gadget> <output>19/6 = around 3.166667</output> <result>A</result>

A

Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 4 inches tall. How tall are the sculpture andbase together?

divide(add(add(multiply(add(2, 10), 2), const_10), 4), add(2, 10))

add(n0,n1)|multiply(n0,#0)|add(#1,const_10)|add(n2,#2)|divide(#3,#0)

we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 4 = 38 38 / 12 = 3.17 feet answer : a

geometry

math_qa__7iJ7WvEOcatrFZb2

The average of 6 no.'s is 2.5. The average of 2 of them is 1.1, while the average of the other 2 is 1.4. What is the average of the remaining 2 no's? Choose one A) 2.3 B) 2.6 C) 3.6 D) 4.5 E) 5

<gadget id="calculator">6 * 2.5</gadget> <output>15</output> <gadget id="calculator">2 * 1.1</gadget> <output>2.2</output> <gadget id="calculator">2 * 1.4</gadget> <output>2.8</output> <gadget id="calculator">2.2 + 2.8</gadget> <output>5</output> <gadget id="calculator">15 - 5</gadget> <output>10</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <result>E</result>

E

The average of 6 no.'s is 2.5. The average of 2 of them is 1.1, while the average of the other 2 is 1.4. What is the average of the remaining 2 no's?

divide(subtract(multiply(6, 2.5), add(multiply(2, 1.1), multiply(2, 1.4))), 2)

multiply(n0,n1)|multiply(n2,n3)|multiply(n2,n5)|add(#1,#2)|subtract(#0,#3)|divide(#4,n2)|

"sum of the remaining two numbers = ( 2.5 * 6 ) - [ ( 1.1 * 2 ) + ( 1.4 * 2 ) ] = 15 - ( 2.2 + 2.8 ) = 15 - 5 = 10 required average = ( 10 / 2 ) = 5 answer : e"

general

math_qa__6c8EOY7GXefZ3ZBe

a is an integer greater than 9 but less than 21, b is an integer greater than 19 but less than 31, what is the range of a/b? Choose the correct option A) 1 / 4 B) 1 / 2 C) 2 / 3 D) 1 E) 5 / 4

<gadget id="calculator">21 - 1</gadget> <output>20</output> <gadget id="calculator">19 + 1</gadget> <output>20</output> <gadget id="calculator">20 / 20</gadget> <output>1</output> <gadget id="calculator">9 + 1</gadget> <output>10</output> <gadget id="calculator">31 - 1</gadget> <output>30</output> <gadget id="calculator">10 / 30</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (1/3)</gadget> <output>2/3 = around 0.666667</output> <result>C</result>

C

a is an integer greater than 9 but less than 21, b is an integer greater than 19 but less than 31, what is the range of a/b?

subtract(divide(subtract(21, const_1), add(19, const_1)), divide(add(9, const_1), subtract(31, const_1)))

add(n2,const_1)|add(n0,const_1)|subtract(n1,const_1)|subtract(n3,const_1)|divide(#2,#0)|divide(#1,#3)|subtract(#4,#5)

min value of a / b will be when b is highest and a is lowest - - - > a = 10 and b = 30 so , a / b = 1 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 20 and b = 20 so , a / b = 1 range is 1 - ( 1 / 3 ) = 2 / 3 . answer should be c

general

math_qa__5V5tPVTBwuCIuryS

If 18 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip? Answers A) 95 B) 90 C) 85 D) 78 E) 72

<gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">18 / (1/4)</gadget> <output>72</output> <result>E</result>

E

If 18 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?

divide(18, divide(subtract(100, 75), 100))

subtract(n1,n2)|divide(#0,n1)|divide(n0,#1)|

"let x be the number of students in the school . 0.18 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.18 x / 0.25 = 0.72 x students went to the camping which is 72 % . the answer is e"

general

math_qa__oQBZOyKCcwJrdAT3

A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $5 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues? Select the correct option: A) $ 28 B) $ 82 C) $ 110 D) $ 138 E) $ 195

<gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">16 * 1_000</gadget> <output>16_000</output> <gadget id="calculator">5 * 100</gadget> <output>500</output> <gadget id="calculator">16_000 + 500</gadget> <output>16_500</output> <gadget id="calculator">80 + 5</gadget> <output>85</output> <gadget id="calculator">85 * 150</gadget> <output>12_750</output> <gadget id="calculator">16_500 + 12_750</gadget> <output>29_250</output> <gadget id="calculator">29_250 / 150</gadget> <output>195</output> <result>E</result>

E

A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $5 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?

divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(5, const_100)), multiply(add(80, 5), 150)), 150)

add(n0,n1)|multiply(const_4,const_4)|multiply(n1,const_100)|multiply(#1,const_1000)|multiply(n3,#0)|add(#3,#2)|add(#5,#4)|divide(#6,n3)

by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me .

general

math_qa__X8g5vpif4NSDHmj5

A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month,70 percent of books that were loaned out are returned and there are 60 books in the special collection at that time, how many books of the special collection were loaned out during that month? Choose the correct choice from the following answers. A) 20 B) 30 C) 35 D) 40 E) 50

<gadget id="calculator">75 - 60</gadget> <output>15</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">1 - (7/10)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">15 / (3/10)</gadget> <output>50</output> <result>E</result>

E

A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month,70 percent of books that were loaned out are returned and there are 60 books in the special collection at that time, how many books of the special collection were loaned out during that month?

divide(subtract(75, 60), subtract(const_1, divide(70, const_100)))

divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2)|

"i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 60 books , thus 76 - 60 = 16 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 50 . answer : e ."

gain

math_qa__9TGnHH1qObbhHVFg

The average age of an adult class is 50 years. 12 new students with an avg age of 32 years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class? Choose the correct choice from the following options A) 10 B) 12 C) 42 D) 20 E) 22

<gadget id="calculator">50 - 4</gadget> <output>46</output> <gadget id="calculator">12 * 46</gadget> <output>552</output> <gadget id="calculator">12 * 32</gadget> <output>384</output> <gadget id="calculator">552 - 384</gadget> <output>168</output> <gadget id="calculator">168 / 4</gadget> <output>42</output> <result>C</result>

C

The average age of an adult class is 50 years. 12 new students with an avg age of 32 years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class?

divide(subtract(multiply(12, subtract(50, 4)), multiply(12, 32)), 4)

multiply(n1,n2)|subtract(n0,n3)|multiply(n1,#1)|subtract(#2,#0)|divide(#3,n3)|

"let original strength = y then , 50 y + 12 x 32 = ( y + 12 ) x 46 â ‡ ’ 50 y + 384 = 46 y + 552 â ‡ ’ 4 y = 168 â ˆ ´ y = 42 c"

general

math_qa__PNoCuqYKMEvH2A8T

Anne and Katherine are both saving money from their summer jobs to buy bicycles. If Anne had $150 less, she would have exactly 1/3 as much as Katherine. And if Katherine had twice as much, she would have exactly 3 times as much as Anne. How much money have they saved together? ( Choose the correct choice from the following answers: A) $ 300 B) $ 400 C) $ 450 D) $ 625 E) $ 750

<gadget id="calculator">3 * 150</gadget> <output>450</output> <gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(2/3) * 450</gadget> <output>300</output> <gadget id="calculator">450 + 300</gadget> <output>750</output> <result>E</result>

E

Anne and Katherine are both saving money from their summer jobs to buy bicycles. If Anne had $150 less, she would have exactly 1/3 as much as Katherine. And if Katherine had twice as much, she would have exactly 3 times as much as Anne. How much money have they saved together? (

add(multiply(3, 150), multiply(divide(const_2, 3), multiply(3, 150)))

divide(const_2,n2)|multiply(n0,n2)|multiply(#0,#1)|add(#1,#2)

if anne had $ 150 less , katherine would have three times more than anne . make this statement into an equation and simplify : 3 ( a – 150 ) = k 3 a – 450 = k and if katherine had twice as much , she would have three times more than anne : 2 k = 3 a substitute 3 a – 450 for k into the last equation and solve for a 2 ( 3 a – 450 ) = 3 a 6 a – 900 = 3 a – 900 = – 3 a 300 = a now substitute 300 for a into the same equation and solve for k : 2 k = 3 ( 300 ) 2 k = 900 k = 450 thus , together anne and katherine have 300 + 450 = 750 correct answer e ) $ 750

general

math_qa__4oqRpkxvUb3m32U3

A’s speed is 32/27 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat? Answers: A) 5 / 32 B) 5 / 27 C) 1 / 27 D) 1 / 32 E) 27 / 32

<gadget id="calculator">32 - 27</gadget> <output>5</output> <gadget id="calculator">5 / 32</gadget> <output>5/32 = around 0.15625</output> <result>A</result>

A

A’s speed is 32/27 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?

divide(subtract(32, 27), 32)

subtract(n0,n1)|divide(#0,n0)|

"we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 32 meters , b covers 27 meters in that time . so if the race is 32 meters long , when a reaches the finish line , b would be 5 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 5 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 32 meters ) would be the same as the time required by b ( to cover 27 meters ) to reach the finish line . so b should get a head start of 5 / 32 th of the race . answer ( a )"

general

math_qa__zV2X0ABnaMzmyDR9

How many cubes of 4 cm edge can be put in a cubical box of 1 m edge. Pick one: A) 17725 cm B) 15625 cm C) 12786 cm D) 12617 cm E) 12187 cm

<gadget id="calculator">1 ** 3</gadget> <output>1</output> <gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">(1/25) ** 3</gadget> <output>1/15_625 = around 0.000064</output> <gadget id="calculator">1 / (1/15_625)</gadget> <output>15_625</output> <result>B</result>

B

How many cubes of 4 cm edge can be put in a cubical box of 1 m edge.

divide(volume_cube(1), volume_cube(divide(4, const_100)))

divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)|

"number of cubes = 100 â ˆ — 100 â ˆ — 100 / 4 * 4 * 4 = 15625 note : 1 m = 100 cm answer : b"

physics

math_qa__28T6Cjdqcw9a94Pn

If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C? Choose the correct choice from the following A) 5 / ( √ 6 ) B) 5 · √ ( 2 / 3 ) C) 5 · √ ( 3 / 2 ) D) 5 · √ 3 E) 5 · √ 6

<gadget id="calculator">5 * 1</gadget> <output>5</output> <result>B</result>

B

If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?

multiply(5, const_1)

multiply(n0,const_1)

n cube c , let ' s say that each side has side length x so , the diagonal = √ ( x ² + x ² + x ² ) = √ ( 3 x ² ) here , we ' re told that the diagonal has length 5 , so we can write : 5 = √ ( 3 x ² ) square both sides to get : 25 = 3 x ² divide both sides by 3 to get : 25 / 3 = x ² square root both sides : √ ( 25 / 3 ) = x or . . . . ( √ 25 ) / ( √ 3 ) = x simplify : 5 / ( √ 3 ) = x answer : b

geometry

math_qa__Ze2z9TTjaWUDe9cK

A train running at the speed of 58 km/hr crosses a pole in 9 sec. What is the length of the train? Choose the correct choice from the following answers A) 145 m B) 786 m C) 566 m D) 546 m E) 445 m

<gadget id="calculator">58 * 1_000</gadget> <output>58_000</output> <gadget id="calculator">58_000 / 3_600</gadget> <output>145/9 = around 16.111111</output> <gadget id="calculator">(145/9) * 9</gadget> <output>145</output> <result>A</result>

A

A train running at the speed of 58 km/hr crosses a pole in 9 sec. What is the length of the train?

multiply(divide(multiply(58, const_1000), const_3600), 9)

multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|

"speed = 58 * 5 / 18 = 145 / 9 m / sec length of the train = speed * time = 145 / 9 * 9 = 145 m answer : a"

physics

math_qa__kGU2smXkGIiLD9Sm

If x and y are both odd prime numbers and x < y, how many distinct positive integer W factors does 2xy have? Choose the correct option: A) 3 B) 4 C) 6 D) 8 E) 12

<gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <result>D</result>

D

If x and y are both odd prime numbers and x < y, how many distinct positive integer W factors does 2xy have?

multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1))

add(const_1,const_1)|multiply(n0,#0)|multiply(#0,#1)|

since 2 xy prime w factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .

other

math_qa__2i8J7RC6re8JZrzX

if it takes 4 identical printing presses exactly 6 hours to print 8000 newspapers , how long would it take 2 of these presses to print 6000 newspapers ? Choose the correct answer A) 5 hrs B) 7 hrs C) 8 hrs D) 9 hrs 50 mins E) 9 hrs

<gadget id="calculator">4 / 2</gadget> <output>2</output> <gadget id="calculator">6_000 / 8_000</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">2 * (3/4)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">6 * (3/2)</gadget> <output>9</output> <result>E</result>

E

if it takes 4 identical printing presses exactly 6 hours to print 8000 newspapers , how long would it take 2 of these presses to print 6000 newspapers ?

multiply(6, multiply(divide(4, 2), divide(6000, 8000)))

divide(n0,n3)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)

4 presses - 8,000 newspapers - 6 hours ; 2 presses - 4,000 newspapers - 6 hours ; ( 360 mins ) 2 presses - 6,000 newspapers - 360 / 4000 * 6000 = 540 mins = 9 hrs answer : e

physics

math_qa__G0r5iS35DYPHVOsj

A batsman in his 12th innings makes a score of 55 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’? Choose the correct option: A) 42 B) 43 C) 44 D) 45 E) 46

<gadget id="calculator">12 * 1</gadget> <output>12</output> <gadget id="calculator">55 - 12</gadget> <output>43</output> <gadget id="calculator">43 + 1</gadget> <output>44</output> <result>C</result>

C

A batsman in his 12th innings makes a score of 55 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’?

add(subtract(55, multiply(12, 1)), 1)

multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)|

"let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 1 ) + 55 ∴ x = 44 answer c"

general

math_qa__EDWMyHzLWg6tyrVl

Find large number from below question The difference of two numbers is 2415. On dividing the larger number by the smaller, we get 21 as quotient and the 15 as remainder Choose the correct choice from the following A) 1209 B) 1324 C) 1245 D) 1300 E) 2535

<gadget id="calculator">2_415 - 15</gadget> <output>2_400</output> <gadget id="calculator">21 - 1</gadget> <output>20</output> <gadget id="calculator">2_400 / 20</gadget> <output>120</output> <gadget id="calculator">120 * 21</gadget> <output>2_520</output> <result>E</result>

E

Find large number from below question The difference of two numbers is 2415. On dividing the larger number by the smaller, we get 21 as quotient and the 15 as remainder

multiply(divide(subtract(2415, 15), subtract(21, const_1)), 21)

subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)|

"let the smaller number be x . then larger number = ( x + 2415 ) . x + 2415 = 21 x + 15 20 x = 2400 x = 120 large number = 120 + 2415 = 2535 answer : e"

general

math_qa__twAxf32hzuNWHDuN

In an examination, a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 30 questions and secures 130 marks, the no of questions he attempts correctly is : Pick one: A) 35 B) 40 C) 90 D) 88 E) 37

<gadget id="calculator">130 + 30</gadget> <output>160</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">160 / 4</gadget> <output>40</output> <result>B</result>

B

In an examination, a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 30 questions and secures 130 marks, the no of questions he attempts correctly is :

divide(add(130, 30), add(3, 1))

add(n2,n3)|add(n0,n1)|divide(#0,#1)

let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 3 x – ( 30 – x ) = 130 = > 4 x = 160 = > x = 40 answer : b

physics

math_qa__iNV2cxNZE53cCbbB

A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.3 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? Choose the correct choice from the following answers A) 2.0 B) 2.5 C) 3.0 D) 3.5 E) 4.0

<gadget id="calculator">100 / 1_000</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">2.3 + (1/10)</gadget> <output>2.4</output> <gadget id="calculator">2.4 / 72</gadget> <output>0.033333</output> <gadget id="calculator">0.033333 * 60</gadget> <output>1.99998</output> <result>A</result>

A

A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.3 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

multiply(divide(add(2.3, divide(100, const_1000)), 72), const_60)

divide(n0,const_1000)|add(n2,#0)|divide(#1,n1)|multiply(#2,const_60)

72 km / hr = 1.2 km / min the total distance is 2.4 km . 2.4 / 1.2 = 2 minutes the answer is a .

physics

math_qa__441CSIAD7yUjcHUM

A garrison of 2000 men has provisions for 40 days. At the end of 20 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? Choose one A) 1888 B) 2766 C) 2999 D) 2000 E) 1712

<gadget id="calculator">2_000 * 40</gadget> <output>80_000</output> <gadget id="calculator">2_000 * 20</gadget> <output>40_000</output> <gadget id="calculator">80_000 - 40_000</gadget> <output>40_000</output> <gadget id="calculator">40_000 / 10</gadget> <output>4_000</output> <gadget id="calculator">4_000 - 2_000</gadget> <output>2_000</output> <result>D</result>

D

A garrison of 2000 men has provisions for 40 days. At the end of 20 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement?

subtract(divide(subtract(multiply(2000, 40), multiply(2000, 20)), 10), 2000)

multiply(n0,n1)|multiply(n0,n2)|subtract(#0,#1)|divide(#2,n3)|subtract(#3,n0)

2000 - - - - 40 2000 - - - - 20 x - - - - - 10 x * 10 = 2000 * 20 x = 4000 2000 - - - - - - - 2000 answer : d

physics

math_qa__I2fPy6FntPBFWIJv

We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? Choose the correct option: A) 36 B) 90 C) 40 D) 42 E) 44

<gadget id="calculator">85 * 6</gadget> <output>510</output> <gadget id="calculator">600 - 510</gadget> <output>90</output> <result>B</result>

B

We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy?

subtract(600, multiply(85, 6))

multiply(n0,n1)|subtract(n3,#0)|

"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 600 . 6 ( 85 - g ) + 7 g = 600 . 510 - 6 g + 7 g = 600 . g = 600 - 510 = 90 . the answer is b ."

general

math_qa__TwRfdzNw9D9rQRwT

If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed, what is the minimum number of questionnaires that should be mailed? Choose the correct choice from the following options. A) 1160 B) 1190 C) 1220 D) 1250 E) 1280

<gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">750 / (3/5)</gadget> <output>1_250</output> <result>D</result>

D

If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed, what is the minimum number of questionnaires that should be mailed?

divide(750, divide(60, const_100))

divide(n0,const_100)|divide(n1,#0)|

"let x be the minimum number of questionnaires to be mailed . 0.6 x = 750 x = 1250 the answer is d ."

gain

math_qa__ulMfyDghLJniGSRA

If the price of 357 apples is Rs.1517.25, what will be the approximate price of 49 dozens of such apples Choose the correct choice from the following answers A) rs . 2500 B) rs . 2300 C) rs . 2200 D) rs . 1400 E) none of these

<gadget id="calculator">49 * 12</gadget> <output>588</output> <gadget id="calculator">1_517.25 / 357</gadget> <output>4.25</output> <gadget id="calculator">588 * 4.25</gadget> <output>2_499</output> <result>A</result>

A

If the price of 357 apples is Rs.1517.25, what will be the approximate price of 49 dozens of such apples

multiply(multiply(49, const_12), divide(1517.25, 357))

divide(n1,n0)|multiply(n2,const_12)|multiply(#0,#1)|

"let the required price be x more apples , more price ( direct proportion ) hence we can write as apples 357 : ( 49 × 12 ) } : : 1517.25 : x ⇒ 357 x = ( 49 × 12 ) × 1517.25 ⇒ x = ( 49 × 12 × 1517.25 ) / 357 = ( 7 × 12 × 1517.25 ) / 51 = ( 7 × 4 × 1517.25 ) / 17 = 7 × 4 × 89.25 ≈ 2500 . answer a"

general

math_qa__uKHvE6IYBU0impXs

If 9 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days? Choose the correct choice. A) 127 B) 237 C) 387 D) 400 E) 481

<gadget id="calculator">36 * 30</gadget> <output>1_080</output> <gadget id="calculator">9 * 24</gadget> <output>216</output> <gadget id="calculator">216 / 80</gadget> <output>27/10 = around 2.7</output> <gadget id="calculator">1_080 / (27/10)</gadget> <output>400</output> <result>D</result>

D

If 9 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?

divide(multiply(36, 30), divide(multiply(9, 24), 80))

multiply(n3,n4)|multiply(n0,n2)|divide(#1,n1)|divide(#0,#2)|

"explanation : let the required no of hectares be x . then men - - - hectares - - - days 9 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 9 * 30 / 24 * 80 x = 400 answer : d"

physics

math_qa__jqR7DJ0BQ9yMir9Y

Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 144 seconds. The length of each train is: Choose the correct choice. A) 82 m B) 150 m C) 172 m D) 200 m E) none of these

<gadget id="calculator">46 - 36</gadget> <output>10</output> <gadget id="calculator">10 * 1_000</gadget> <output>10_000</output> <gadget id="calculator">10_000 / 3_600</gadget> <output>25/9 = around 2.777778</output> <gadget id="calculator">(25/9) * 144</gadget> <output>400</output> <gadget id="calculator">400 / 2</gadget> <output>200</output> <result>D</result>

D

Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 144 seconds. The length of each train is:

divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 144), const_2)

subtract(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n2,#2)|divide(#3,const_2)|

"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 144 secs the total distance traveled is 144 x 25 / 9 = 400 m . therefore the length of each train is = 400 / 2 = 200 m . answer d"

general

math_qa__fMpL2NNyEzDDnHOw

If an investor puts $900 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year? Choose the correct answer. A) $ 986.25 B) $ 988.25 C) $ 990.25 D) $ 992.25 E) $ 994.25

<gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">1 + (1/20)</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">(21/20) ** 2</gadget> <output>441/400 = around 1.1025</output> <gadget id="calculator">900 * (441/400)</gadget> <output>3_969/4 = around 992.25</output> <result>D</result>

D

If an investor puts $900 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?

multiply(900, power(add(const_1, divide(divide(10, const_2), const_100)), const_2))

divide(n1,const_2)|divide(#0,const_100)|add(#1,const_1)|power(#2,const_2)|multiply(n0,#3)

1.05 * 1.05 * 900 = $ 992.25 the answer is d .

gain

math_qa__NbJGujIveGqTIeKC

If the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is? Pick one: A) 8 B) 27 C) 10 D) 7 E) 19

<gadget id="calculator">3 * 100</gadget> <output>300</output> <gadget id="calculator">1 * 10</gadget> <output>10</output> <gadget id="calculator">300 + 10</gadget> <output>310</output> <gadget id="calculator">310 + 4</gadget> <output>314</output> <gadget id="calculator">314 / 100</gadget> <output>157/50 = around 3.14</output> <gadget id="calculator">2 * (157/50)</gadget> <output>157/25 = around 6.28</output> <gadget id="calculator">(157/25) * 21</gadget> <output>3_297/25 = around 131.88</output> <gadget id="calculator">1_056 / (3_297/25)</gadget> <output>8_800/1_099 = around 8.007279</output> <result>A</result>

A

If the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is?

divide(1056, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 21))

multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)|

"2 * 22 / 7 * 21 * x = 1056 = > x = 8 answer : a"

physics

math_qa__vgfc4fngph0IIBpW

For each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 60 color copies at Print Shop Y than at Print Shop X? Choose the correct choice from the following answers A) $ 80 B) $ 90 C) $ 100 D) $ 110 E) $ 120

<gadget id="calculator">2.75 * 60</gadget> <output>165</output> <gadget id="calculator">1.25 * 60</gadget> <output>75</output> <gadget id="calculator">165 - 75</gadget> <output>90</output> <result>B</result>

B

For each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 60 color copies at Print Shop Y than at Print Shop X?

subtract(multiply(2.75, 60), multiply(1.25, 60))

multiply(n1,n2)|multiply(n0,n2)|subtract(#0,#1)|

"the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 60 * $ 1.50 = $ 90 the answer is b ."

general

math_qa__iNU3GYbKBqkxaz5O

A train 180 m long running at 75 kmph crosses a platform in 40 sec. What is the length of the platform? Choose the correct choice from the following choices: A) 687 B) 638 C) 683 D) 726 E) 267

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">75 * (5/18)</gadget> <output>125/6 = around 20.833333</output> <gadget id="calculator">40 * (125/6)</gadget> <output>2_500/3 = around 833.333333</output> <gadget id="calculator">(2_500/3) - 180</gadget> <output>1_960/3 = around 653.333333</output> <result>C</result>

C

A train 180 m long running at 75 kmph crosses a platform in 40 sec. What is the length of the platform?

subtract(multiply(40, multiply(75, const_0_2778)), 180)

multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|

"d = 75 * 5 / 18 = 40 = 833 â € “ 150 = 683 answer : c"

physics

math_qa__ElNC6MskMeakTTXH

A train is 327 meter long is running at a speed of 40 km/hour. In what time will it pass a bridge of 122 meter length? Choose the correct choice from the following answers: A) 32.7 B) 41 C) 50.29 D) 40.41 E) 20.28

<gadget id="calculator">327 + 122</gadget> <output>449</output> <gadget id="calculator">40 * 1_000</gadget> <output>40_000</output> <gadget id="calculator">40_000 / 3_600</gadget> <output>100/9 = around 11.111111</output> <gadget id="calculator">449 / (100/9)</gadget> <output>4_041/100 = around 40.41</output> <result>D</result>

D

A train is 327 meter long is running at a speed of 40 km/hour. In what time will it pass a bridge of 122 meter length?

divide(add(327, 122), divide(multiply(40, const_1000), const_3600))

add(n0,n2)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#0,#2)|

"speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 100 / 9 m / sec total distance = 327 + 122 = 449 meter time = distance / speed = 449 * ( 9 / 100 ) = 40.41 seconds . answer : d"

physics

math_qa__KSu6OEHOHgzAWaoj

If a person walks at 16 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is: Choose one: A) 50 km B) 56 km C) 60 km D) 70 km E) 33.3 km

<gadget id="calculator">16 - 10</gadget> <output>6</output> <gadget id="calculator">20 / 6</gadget> <output>10/3 = around 3.333333</output> <gadget id="calculator">10 * (10/3)</gadget> <output>100/3 = around 33.333333</output> <result>E</result>

E

If a person walks at 16 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:

multiply(10, divide(20, subtract(16, 10)))

subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)|

"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 16 16 x = 10 x + 200 6 x = 200 x = 33.3 km . answer : e"

general

math_qa__pswzUlS7n7uf3fKz

If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Coe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Coe? Choose the correct option A) 15 B) 60 C) 75 D) 90 E) 105

<gadget id="calculator">55 - 40</gadget> <output>15</output> <gadget id="calculator">15 + 7.5</gadget> <output>22.5</output> <gadget id="calculator">22.5 / 15</gadget> <output>1.5</output> <gadget id="calculator">1.5 * 60</gadget> <output>90</output> <result>D</result>

D

If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Coe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Coe?

multiply(divide(add(subtract(55, 40), 7.5), subtract(55, 40)), const_60)

subtract(n0,n2)|add(n1,#0)|divide(#1,#0)|multiply(#2,const_60)

this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . coe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d

physics

math_qa__ojqgnbu0ApI4okny

In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 4. A has a start of 300 m. Then, A wins by: Choose the correct choice from the following choices: A) 60 m B) 20 m C) 43 m D) 20 m E) 100 m

<gadget id="calculator">500 - 300</gadget> <output>200</output> <gadget id="calculator">200 * 4</gadget> <output>800</output> <gadget id="calculator">800 / 2</gadget> <output>400</output> <gadget id="calculator">500 - 400</gadget> <output>100</output> <result>E</result>

E

In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 4. A has a start of 300 m. Then, A wins by:

subtract(500, divide(multiply(subtract(500, 300), 4), 2))

subtract(n0,n3)|multiply(n2,#0)|divide(#1,n1)|subtract(n0,#2)|

"to reach the winning post a will have to cover a distance of ( 500 - 300 ) m , i . e . , 200 m . while a covers 2 m , b covers 4 m . while a covers 200 m , b covers 4 x 200 / 2 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 100 m behind . a wins by 100 m . answer : e"

physics

math_qa__VsVVEOqyYVf1Xl7g

The two lines y=x and x=-8 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis? Pick one A) 28 B) 32 C) 36 D) 40 E) 44

<gadget id="calculator">8 * 8</gadget> <output>64</output> <gadget id="calculator">64 / 2</gadget> <output>32</output> <result>B</result>

B

The two lines y=x and x=-8 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?

divide(multiply(8, 8), const_2)

multiply(n0,n0)|divide(#0,const_2)|

"the point of intersection is ( - 8 , - 8 ) . the triangle has a base of length 8 and a height of 8 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 8 * 8 = 32 the answer is b ."

general

math_qa__cDbXmmohESXFw2Ro

A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? Choose one. A) $ 200 B) $ 177.78 C) $ 100 D) $ 277.78 E) $ 377.78

<gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 400</gadget> <output>160</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">160 / (3/5)</gadget> <output>800/3 = around 266.666667</output> <gadget id="calculator">(800/3) * (2/5)</gadget> <output>320/3 = around 106.666667</output> <gadget id="calculator">(320/3) / (3/5)</gadget> <output>1_600/9 = around 177.777778</output> <result>B</result>

B

A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?

divide(multiply(divide(multiply(divide(40, const_100), 400), divide(60, const_100)), divide(40, const_100)), divide(60, const_100))

divide(n2,const_100)|divide(n0,const_100)|multiply(n1,#0)|divide(#2,#1)|multiply(#3,#0)|divide(#4,#1)|

"let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 60 % of total amount . so total amount = 16000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 16000 * ( 100 / 60 ) * ( 40 / 100 ) = 32000 / 3 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 32000 / 3 / 60 = 32000 / 180 = 1600 / 9 = $ 177.78 ; answer : b"

general

math_qa__Egzze09fkKbi3mn5

The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number? Options. A) 78 B) 65 C) 58 D) 62 E) 48

<gadget id="calculator">6 * 58</gadget> <output>348</output> <gadget id="calculator">6 * 65</gadget> <output>390</output> <gadget id="calculator">348 + 390</gadget> <output>738</output> <gadget id="calculator">11 * 60</gadget> <output>660</output> <gadget id="calculator">738 - 660</gadget> <output>78</output> <result>A</result>

A

The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?

subtract(add(multiply(6, 58), multiply(6, 65)), multiply(11, 60))

multiply(n3,n4)|multiply(n3,n6)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2)|

"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 60 = 78 answer is a"

general

math_qa__at8YCotA8c4czZT0

Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount? Answers: A) 157 B) 213 C) 221 D) 223 E) 226

<gadget id="calculator">100 * 30</gadget> <output>3_000</output> <gadget id="calculator">3_000 / 16</gadget> <output>375/2 = around 187.5</output> <gadget id="calculator">(375/2) + 30</gadget> <output>435/2 = around 217.5</output> <gadget id="calculator">(435/2) * 5</gadget> <output>2_175/2 = around 1_087.5</output> <gadget id="calculator">(2_175/2) / 100</gadget> <output>87/8 = around 10.875</output> <gadget id="calculator">30 - (87/8)</gadget> <output>153/8 = around 19.125</output> <gadget id="calculator">3_000 / (153/8)</gadget> <output>8_000/51 = around 156.862745</output> <result>A</result>

A

Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

divide(multiply(100, 30), subtract(30, divide(multiply(add(divide(multiply(100, 30), 16), 30), 5), 100)))

multiply(n0,n1)|divide(#0,n2)|add(n1,#1)|multiply(n3,#2)|divide(#3,n0)|subtract(n1,#4)|divide(#0,#5)

for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 16 % of the cost : sell price = cost + $ 20 sell price = $ 125 + $ 20 thus , the sell price is $ 145 for each item . selling all 100 items gives the retailer . . . 100 ( $ 20 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 145 ) = $ 7.25 discount $ 137.75 = $ 125 + $ 12.75 now , the retailer makes a profit of just $ 12.75 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 12.75 ( x ) = $ 2,000 x = 2,000 / 12.75 x = 156.8627 = 157 items a

gain

math_qa__bIdE9uvcynwoXsHX

The population of a town is 8000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years? Choose the correct choice from the following options: A) 5100 B) 5120 C) 5200 D) 5400 E) 6480

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">8_000 * (1/10)</gadget> <output>800</output> <gadget id="calculator">8_000 - 800</gadget> <output>7_200</output> <gadget id="calculator">7_200 * (1/10)</gadget> <output>720</output> <gadget id="calculator">7_200 - 720</gadget> <output>6_480</output> <result>E</result>

E

The population of a town is 8000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?

subtract(subtract(8000, multiply(8000, divide(10, const_100))), multiply(subtract(8000, multiply(8000, divide(10, const_100))), divide(10, const_100)))

divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)|

"formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 ã — 90 / 100 = 6480 answer : e"

gain

math_qa__Lgr87w43FZZDNbfP

Jim’s Taxi Service charges an initial fee of $2.25 at the beginning of a trip and an additional charge of $0.15 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles? Select A) $ 3.15 B) $ 4.45 C) $ 3.60 D) $ 5.05 E) $ 5.40

<gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">3.6 / (2/5)</gadget> <output>9</output> <gadget id="calculator">0.15 * 9</gadget> <output>1.35</output> <gadget id="calculator">2.25 + 1.35</gadget> <output>3.6</output> <result>C</result>

C

Jim’s Taxi Service charges an initial fee of $2.25 at the beginning of a trip and an additional charge of $0.15 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?

add(2.25, multiply(0.15, divide(3.6, divide(2, 5))))

divide(n2,n3)|divide(n4,#0)|multiply(n1,#1)|add(n0,#2)|

"let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 15 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 15 = 2.25 + 9 * . 15 = 3.6 $ answer c"

general