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Calc-math_qa

like 4

math_qa__5RhmcMvMNkXXa1oX

Saleem bought 4 baskets with the average cost of $4. If Saleem also buys the fifth basket with the price of $ 8, what is the average (arithmetic mean) price of those 5 baskets? Choose the correct choice from the following choices A) $ 4.50 B) $ 6.00 C) $ 4.00 D) $ 5.50 E) $ 4.80

<gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">16 + 8</gadget> <output>24</output> <gadget id="calculator">24 / 5</gadget> <output>24/5 = around 4.8</output> <result>E</result>

E

Saleem bought 4 baskets with the average cost of $4. If Saleem also buys the fifth basket with the price of $ 8, what is the average (arithmetic mean) price of those 5 baskets?

divide(add(multiply(4, 4), 8), 5)

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

4 baskets - > total cost = 4 * avg cost = 4 * 4 = 16 fifth basket cost = 8 total cost for 5 baskets = 16 + 8 = 24 am = 24 / 5 = 4.80 answer : e

general

math_qa__huuw5KH81T9LfoDT

When n is divided by 5 the remainder is 3. What is the remainder when n^2 is divided by 5? Choices: A) 0 B) 1 C) 2 D) 3 E) 4

<gadget id="calculator">5 + 3</gadget> <output>8</output> <gadget id="calculator">8 ** 2</gadget> <output>64</output> <gadget id="calculator">64 % 5</gadget> <output>4</output> <result>E</result>

E

When n is divided by 5 the remainder is 3. What is the remainder when n^2 is divided by 5?

reminder(power(add(5, 3), 2), 5)

add(n0,n1)|power(#0,n2)|reminder(#1,n0)

n = 5 x + 3 , for some integer x n ^ 2 = ( 5 x + 3 ) ^ 2 = 5 y + 9 , for some integer y when we divide this by 5 , the remainder is 4 . the answer is e .

general

math_qa__t73YX3drWCOQOGAa

In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is? Choose the correct option: A) 5 km / hr B) 1 km / hr C) 6 km / hr D) 3 km / hr E) 7 km / hr

<gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">30 / 6</gadget> <output>5</output> <result>A</result>

A

In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?

divide(30, multiply(2, const_3))

multiply(n1,const_3)|divide(n0,#0)

a 5 km / hr let abhay ' s speed be x km / / hr . then , 30 / x - 30 / 2 x = 3 x = 5 km / hr .

physics

math_qa__FFPnaTzfIVWSFlEO

From a pack of 52 cards, 1 card is drawn at random. What is the probability that a jack, queen, or king is drawn? Choose the correct answer A) 1 / 4 B) 1 / 12 C) 2 / 13 D) 3 / 13 E) 3 / 26

<gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">12 / 52</gadget> <output>3/13 = around 0.230769</output> <result>D</result>

D

From a pack of 52 cards, 1 card is drawn at random. What is the probability that a jack, queen, or king is drawn?

divide(multiply(const_4, const_3), 52)

multiply(const_3,const_4)|divide(#0,n0)

the total number of cards is 52 . the number of jacks , queens , or kings is 12 . p ( jack , queen , king ) = 12 / 52 = 3 / 13 the answer is d .

probability

math_qa__PAI7dmoA2LvcW6Iv

A sum was put at simple interest at a certain rate for 9 years Had it been put at 5% higher rate, it would have fetched 1350 more. Find the sum. Answers: A) 3000 B) 3100 C) 3200 D) 3300 E) 3400

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/20) * 9</gadget> <output>9/20 = around 0.45</output> <gadget id="calculator">1_350 / (9/20)</gadget> <output>3_000</output> <result>A</result>

A

A sum was put at simple interest at a certain rate for 9 years Had it been put at 5% higher rate, it would have fetched 1350 more. Find the sum.

divide(1350, multiply(divide(5, const_100), 9))

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

"difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 1350 = p × 9 x 5 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 1350 × 100 / 9 x 5 = 3000 answer a"

gain

math_qa__1J2ecgJ00aI5v9tD

Three table runners have a combined area of 224 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner? Pick one. A) 18 square inches B) 20 square inches C) 24 square inches D) 28 square inches E) 30 square inches

<gadget id="calculator">224 - 24</gadget> <output>200</output> <gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">175 * (4/5)</gadget> <output>140</output> <gadget id="calculator">200 - 140</gadget> <output>60</output> <gadget id="calculator">60 / 2</gadget> <output>30</output> <result>E</result>

E

Three table runners have a combined area of 224 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?

divide(subtract(subtract(224, 24), multiply(175, divide(80, const_100))), const_2)

divide(n1,const_100)|subtract(n0,n3)|multiply(n2,#0)|subtract(#1,#2)|divide(#3,const_2)|

"total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 224 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 224 - 24 - 140 all three = 30 answer : e"

geometry

math_qa__XsLSr606uCkGg6XL

This year, MBB Consulting fired 9% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction? Choose the correct choice from the following answers: A) 98.5 % B) 100.1 % C) 102.8 % D) 104.5 % E) 105.0 %

<gadget id="calculator">100 * 10</gadget> <output>1_000</output> <gadget id="calculator">100 + 1_000</gadget> <output>1_100</output> <gadget id="calculator">100 - 9</gadget> <output>91</output> <gadget id="calculator">91 + 4</gadget> <output>95</output> <gadget id="calculator">1_100 * 95</gadget> <output>104_500</output> <gadget id="calculator">104_500 / 1_000</gadget> <output>209/2 = around 104.5</output> <result>B</result>

B

This year, MBB Consulting fired 9% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?

divide(multiply(add(const_100, multiply(const_100, const_10)), add(subtract(const_100, 9), const_4)), multiply(const_100, const_10))

multiply(const_10,const_100)|subtract(const_100,n0)|add(#0,const_100)|add(#1,const_4)|multiply(#2,#3)|divide(#4,#0)

100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 9 % reduction in employees lead to 91 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 91 employees is 91 * 1100 = 100100 now the new salary is more than previous salary by x % . x = ( 100100 / 100000 ) * 100 = 100.1 % so the answer is b

general

math_qa__ibM1FBhGJxzaHuv2

If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 = Pick one: A) 0 B) 1 C) 35 D) 120 E) 245

<gadget id="calculator">1 - 1</gadget> <output>0</output> <gadget id="calculator">5 ** 0</gadget> <output>1</output> <gadget id="calculator">0 ** 5</gadget> <output>0</output> <gadget id="calculator">1 - 0</gadget> <output>1</output> <result>B</result>

B

If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 =

subtract(power(5, subtract(const_1, const_1)), power(subtract(const_1, const_1), 5))

subtract(const_1,const_1)|power(n2,#0)|power(#0,n2)|subtract(#1,#2)|

"8 + 2 + 3 + 4 + 3 + 5 = 25 , so this number is not divisible by 3 and thus not divisible by 15 . therefore , k = 0 5 ^ k - k ^ 5 = 1 - 0 = 1 the answer is b ."

general

math_qa__lUPX4HIvIgPumLMg

The number of the members of a club is more than 10 and less than 40. When 3 people sit at a table, other people exactly divided to 6-people groups (6 people sit at a table) or 5-people groups (5 people sit at a table). If the members are divided to 7-people groups, how many people will be left? Choose the correct option: A) 0 . B) 1 . C) 2 . D) 4 . E) 5 .

<gadget id="calculator">lcm(6, 5)</gadget> <output>30</output> <gadget id="calculator">30 + 3</gadget> <output>33</output> <gadget id="calculator">33 % 7</gadget> <output>5</output> <result>E</result>

E

The number of the members of a club is more than 10 and less than 40. When 3 people sit at a table, other people exactly divided to 6-people groups (6 people sit at a table) or 5-people groups (5 people sit at a table). If the members are divided to 7-people groups, how many people will be left?

reminder(add(lcm(6, 5), 3), 7)

lcm(n3,n5)|add(n2,#0)|reminder(#1,n7)|

"the number of members is 5 k + 3 = 6 j + 3 the only number in this range which satisfies this is 33 . 33 / 7 = 4 ( 7 ) + 5 the answer is e ."

general

math_qa__zJrBDqsZ6hQtv38h

find the number, difference between number and its 3/5 is 64. Choose one: A) 160 B) 163 C) 164 D) 165 E) 166

<gadget id="calculator">64 / 2</gadget> <output>32</output> <gadget id="calculator">32 * 5</gadget> <output>160</output> <result>A</result>

A

find the number, difference between number and its 3/5 is 64.

multiply(divide(64, const_2), 5)

divide(n2,const_2)|multiply(n1,#0)

explanation : let the number = x , then , x - ( 3 / 5 ) x = 64 , = > ( 2 / 5 ) x = 64 = > 2 x = 64 * 5 , = > x = 160 answer : option a

general

math_qa__siXj1A4gVL6IKLLl

The mean proportional between 234 and 104 is : Pick: A) 12 B) 39 C) 54 D) 64 E) 156

<gadget id="calculator">234 * 104</gadget> <output>24_336</output> <gadget id="calculator">24_336 ** (1/2)</gadget> <output>156</output> <result>E</result>

E

The mean proportional between 234 and 104 is :

sqrt(multiply(234, 104))

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

required mean proportion is = ( root of 234 ) ( root of 104 ) = root of ( 13 * 9 * 2 * 13 * 18 ) = ( 13 * 3 * 4 ) = 156 answer : e

general

math_qa__NAOgMRypfOYEq0CK

X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 43 Km/hr. However, he covers the distance from Y to X at an average speed of 35 Km/hr. His average speed during the whole journey in km/hr. is : Answers A) 34 B) 43 C) 40 D) 38.6 E) 29

<gadget id="calculator">43 - 10</gadget> <output>33</output> <gadget id="calculator">33 + 100</gadget> <output>133</output> <gadget id="calculator">133 + 133</gadget> <output>266</output> <gadget id="calculator">133 / 43</gadget> <output>133/43 = around 3.093023</output> <gadget id="calculator">133 / 35</gadget> <output>19/5 = around 3.8</output> <gadget id="calculator">(133/43) + (19/5)</gadget> <output>1_482/215 = around 6.893023</output> <gadget id="calculator">266 / (1_482/215)</gadget> <output>1_505/39 = around 38.589744</output> <result>D</result>

D

X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 43 Km/hr. However, he covers the distance from Y to X at an average speed of 35 Km/hr. His average speed during the whole journey in km/hr. is :

divide(add(add(subtract(43, const_10), const_100), add(subtract(43, const_10), const_100)), add(divide(add(subtract(43, const_10), const_100), 43), divide(add(subtract(43, const_10), const_100), 35)))

subtract(n0,const_10)|add(#0,const_100)|add(#1,#1)|divide(#1,n0)|divide(#1,n1)|add(#3,#4)|divide(#2,#5)|

"solution : average speed = 2 xy / x + y = 2 * 43 * 35 / 43 + 35 = 38.6 answer : d"

general

math_qa__kgpq9kKS47uM7EUT

A man walks West 10 miles, then turns right towards North and walks another 10 miles. How far is he from the place he started walking. Choose the correct option: A) 11.11 B) 10 C) 14.14 D) 16.15 E) 1

<gadget id="calculator">10 ** 2</gadget> <output>100</output> <gadget id="calculator">100 + 100</gadget> <output>200</output> <gadget id="calculator">200 ** (1/2)</gadget> <output>10*sqrt(2) = around 14.142136</output> <result>C</result>

C

A man walks West 10 miles, then turns right towards North and walks another 10 miles. How far is he from the place he started walking.

sqrt(add(power(10, const_2), power(10, const_2)))

power(n0,const_2)|add(#0,#0)|sqrt(#1)

as we can see the man moves in configuration of a right angle triangle . the man has walked on the sides and now we need to calculate the length of the hypotenuse which is the distance of the man from the starting point to his current location . since we know the length of two sides , we can find the length of hypotenuse . as per pythagoras : a ^ 2 + b ^ 2 = c ^ 2 a = 10 b = 10 10 ^ 2 + 10 ^ 2 = c ^ 2 100 + 100 = c ^ 2 200 = c ^ 2 c = squareroot 200 c = 14.14 miles ans : c

physics

math_qa__84gywhK4HcCp33Rs

The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 60, then 1/m + 1/n is equal to Choose the correct choice from the following: A) 1 / 35 B) 3 / 35 C) 1 / 21 D) 2 / 35 E) none

<gadget id="calculator">6 * 210</gadget> <output>1_260</output> <gadget id="calculator">60 / 1_260</gadget> <output>1/21 = around 0.047619</output> <result>C</result>

C

The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 60, then 1/m + 1/n is equal to

divide(60, multiply(6, 210))

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

"answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 60 / 1260 = 1 / 21 correct option : c"

general

math_qa__rH62i1safI4NHLqH

A certain car uses 12 gallons of gasoline in traveling 300 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased? Choose the correct choice from the following answers: A) 2 B) 4 C) 5 D) 8 E) 10

<gadget id="calculator">300 / 10</gadget> <output>30</output> <gadget id="calculator">300 / 12</gadget> <output>25</output> <gadget id="calculator">30 - 25</gadget> <output>5</output> <result>C</result>

C

A certain car uses 12 gallons of gasoline in traveling 300 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?

subtract(divide(300, 10), divide(300, 12))

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

"300 / 10 = 30 . the difference is 30 - 25 = 5 . answer c"

physics

math_qa__1bukAc9zYgFgYHz4

A 300 m long train crosses a platform in 30 sec while it crosses a signal pole in 18 sec. What is the length of the platform? Options: A) 286 m B) 350 m C) 200 m D) 278 m E) 267 m

<gadget id="calculator">300 / 18</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">(50/3) * 30</gadget> <output>500</output> <gadget id="calculator">500 - 300</gadget> <output>200</output> <result>C</result>

C

A 300 m long train crosses a platform in 30 sec while it crosses a signal pole in 18 sec. What is the length of the platform?

subtract(multiply(speed(300, 18), 30), 300)

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

"speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 30 = 50 / 3 x = 200 m . answer : c"

physics

math_qa__0aFk3yIKOT9S3Yim

A train 110 m long is running with a speed of 65 km/hr. In what time will it pass a man who is running at 7 km/hr in the direction opposite to that in which the train is going? Pick: A) 5 B) 6 C) 4 D) 8.2 E) 5.5

<gadget id="calculator">65 + 7</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">110 / 20</gadget> <output>11/2 = around 5.5</output> <result>E</result>

E

A train 110 m long is running with a speed of 65 km/hr. In what time will it pass a man who is running at 7 km/hr in the direction opposite to that in which the train is going?

divide(110, multiply(add(65, 7), const_0_2778))

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

"speed of train relative to man = 65 + 7 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the men = 110 * 1 / 20 = 5.5 sec . answer : option e"

physics

math_qa__ahezDOEO9QfV1qLP

Marketing executives for a certain chewing gum company projected a 25 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ? Choose the most appropriate option. A) 53 % B) 58 % C) 60 % D) 64 % E) 75 %

<gadget id="calculator">100 - 25</gadget> <output>75</output> <gadget id="calculator">25 + 100</gadget> <output>125</output> <gadget id="calculator">75 / 125</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 100</gadget> <output>60</output> <result>C</result>

C

Marketing executives for a certain chewing gum company projected a 25 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?

multiply(divide(subtract(const_100, 25), add(25, const_100)), const_100)

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

"last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 125 . actual / projected * 100 = 75 / 125 * 100 = 60 % . answer : c ."

general

math_qa__lgU86bMsiWLAlhpD

Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 900 then loss of Pyarelal? Pick: A) 610 B) 710 C) 810 D) 900 E) 1000

<gadget id="calculator">9 * 900</gadget> <output>8_100</output> <gadget id="calculator">1 + 9</gadget> <output>10</output> <gadget id="calculator">8_100 / 10</gadget> <output>810</output> <result>C</result>

C

Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 900 then loss of Pyarelal?

divide(multiply(9, 900), add(1, 9))

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

"let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 900 , loss of pyarelal = 900 * 9 x / 10 x = 810 answer : c"

gain

math_qa__p8MjYMh9QLekQdYx

At what rate percent on simple interest will Rs.750 amount to Rs.975 in 5 years? Choose the correct answer. A) 2 B) 3 C) 4 D) 5 E) 6

<gadget id="calculator">975 - 750</gadget> <output>225</output> <gadget id="calculator">225 / 750</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) / 5</gadget> <output>3/50 = around 0.06</output> <gadget id="calculator">(3/50) * 100</gadget> <output>6</output> <result>E</result>

E

At what rate percent on simple interest will Rs.750 amount to Rs.975 in 5 years?

multiply(divide(divide(subtract(975, 750), 750), 5), const_100)

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

"225 = ( 750 * 5 * r ) / 100 r = 6 % . answer : e"

gain

math_qa__fWoDN1QKoZrBOiAl

A container holds 4 quarts of diesel and 4 quarts of petrol. How many quarts of water must be added to the container to create a mixture that is 3 parts dieselto 5 parts water by petrol? Choices A) 4 / 3 B) 5 / 3 C) 7 / 3 D) 8 / 3 E) 10 / 3

<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 4</gadget> <output>12/5 = around 2.4</output> <gadget id="calculator">4 - (12/5)</gadget> <output>8/5 = around 1.6</output> <gadget id="calculator">(8/5) / (3/5)</gadget> <output>8/3 = around 2.666667</output> <result>D</result>

D

A container holds 4 quarts of diesel and 4 quarts of petrol. How many quarts of water must be added to the container to create a mixture that is 3 parts dieselto 5 parts water by petrol?

divide(subtract(4, multiply(divide(3, 5), 4)), divide(3, 5))

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

an alternate to the alligation method is the more direct / algebraic method : let x be the amount of petrol to be added . new total amount of water = 4 + x total amount of diesel = 4 new total = 4 + 4 + x = 8 + x final ratio required ( for petrol ) = 5 / ( 5 + 3 ) = 5 / 8 thus , ( 4 + x ) / ( 8 + x ) = 5 / 8 - - > solving for x you get x = 8 / 3 . d is thus the correct answer .

general

math_qa__FFQIxOVykkxwjcQ7

At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.5 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day? Choose the correct choice from the following answers A) 7 B) 8 C) 9 D) 10 E) 11

<gadget id="calculator">12.8 - 0.5</gadget> <output>12.3</output> <gadget id="calculator">12.3 / 1.5</gadget> <output>8.2</output> <result>B</result>

B

At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.5 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?

divide(subtract(12.80, 0.50), 1.5)

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

"after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 1.5 < 9 = ~ 8 . answer : b ."

physics

math_qa__1W2aUooVK1ShBZmE

Tough and Tricky questions: Number Properties. What is the smallest positive integer x such that 1512x is the cube of a positive integer? Select: A) 7 B) 14 C) 28 D) 35 E) 49

<gadget id="calculator">1_512 / 2</gadget> <output>756</output> <gadget id="calculator">756 / 2</gadget> <output>378</output> <gadget id="calculator">378 / 2</gadget> <output>189</output> <gadget id="calculator">189 / 3</gadget> <output>63</output> <gadget id="calculator">63 / 3</gadget> <output>21</output> <gadget id="calculator">21 / 3</gadget> <output>7</output> <gadget id="calculator">7 ** 2</gadget> <output>49</output> <result>E</result>

E

Tough and Tricky questions: Number Properties. What is the smallest positive integer x such that 1512x is the cube of a positive integer?

power(divide(divide(divide(divide(divide(divide(1512, const_2), const_2), const_2), const_3), const_3), const_3), const_2)

divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_3)|divide(#3,const_3)|divide(#4,const_3)|power(#5,const_2)

we want to know the smallest x that will make 1512 x a cube of some number . let ' s call that number y . let ' s first figure out what we ' re working with . the prime factorization of 450 can be visualized : . . . . . . . . . 1512 . . . . . . . . / . . . . . . . \ . . . . . . 216 . . . . . . 7 . . . . . / . . \ . . . . . . . 36 . . . . 6 . . . . . . / . \ . . . . / . \ . . . . 6 … . 6 … 2 … 3 . / . \ . . / \ 2 . . 3 2 … 3 so , we have 2 * 2 * 2 * 3 * 3 * 3 * 7 that can be multiplied together to get 1512 . now we need to figure out what we need to make 1512 * x into a cube of y ( y ^ 3 = 1512 * x ) . we have two 5 s , two 3 s , and one 2 . to arrange these numbers in identical triples ( 2 , 3,7 ) , we need at least one more 5 , one 3 , and two 2 ' s . each of these triples will give us the value of y ( 2 * 3 * 7 = 42 ) , which , multiplied by itself three times , gives us 1512 * x . looking at the factors we need to complete the triples , we get 7 * 7 = 49 . we know this is the smallest number possible because prime factors by definition can not be broken down any further . therefore , we can go with answer choice d . if time permits , we can do a sanity check . we calculated that y should be 2 * 3 * 7 , or 42 . 42 * 42 * 42 = 74088 . also , 1512 * 49 = 74088 . answer : e

geometry

math_qa__gOc2XKeXd06N5bes

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days? Choose the most appropriate option A) 4 B) 16 C) 8 D) 1 E) 2

<gadget id="calculator">8 / 4</gadget> <output>2</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">8 * 2</gadget> <output>16</output> <result>B</result>

B

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

multiply(multiply(4, divide(8, 4)), divide(8, 4))

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

explanation : let the required number of mats be x more mat - weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) hence we can write as ( mat - weavers ) 4 : 8 ( days ) 4 : 8 } : : 4 : x ⇒ 4 × 4 × x = 8 × 8 × 4 ⇒ x = 2 × 2 × 4 = 16 answer : option b

gain

math_qa__Yojdm8o64zLtxaRN

If x+y=-4, and x=6/y, what is the value of x^2+y^2? Choices: A) 10 B) 15 C) 6 D) 4 E) 5

<gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">2 * 6</gadget> <output>12</output> <gadget id="calculator">16 - 12</gadget> <output>4</output> <result>D</result>

D

If x+y=-4, and x=6/y, what is the value of x^2+y^2?

subtract(power(4, const_2), multiply(2, 6))

multiply(n1,n2)|power(n0,const_2)|subtract(#1,#0)

x ^ 2 + y ^ 2 should make you think of these formulas : ( x + y ) ( x + y ) = x ^ 2 + y ^ 2 + 2 xy we already know ( x + y ) = - 4 and x * y = 6 ( x + y ) ( x + y ) = ( - 4 ) ( - 4 ) = x ^ 2 + y ^ 2 + 2 * ( 6 ) x ^ 2 + y ^ 2 = 16 - 12 = 4 answer : d

general

math_qa__YaBOUXdMZGbAt5MW

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days then the fraction of the work that is left is? Choose the correct choice from the following options. A) 1 / 4 B) 1 / 10 C) 7 / 15 D) 8 / 15 E) 9 / 13

<gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">1 / 20</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/15) + (1/20)</gadget> <output>7/60 = around 0.116667</output> <gadget id="calculator">(7/60) * 4</gadget> <output>7/15 = around 0.466667</output> <gadget id="calculator">1 - (7/15)</gadget> <output>8/15 = around 0.533333</output> <result>D</result>

D

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days then the fraction of the work that is left is?

subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 4))

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

"explanation : a ’ s one day work = 1 / 15 b ’ s one day work = 1 / 20 ( a + b ) ’ s one day work is = 1 / 15 + 1 / 20 = 7 / 60 their 4 days work = 4 x 7 / 60 = 7 / 15 remaining work = 8 / 15 answer : option d"

physics

math_qa__3NEFaOC9jMlyhSRh

The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 22. What is the cost price of the article? Choose the most appropriate option: A) rs . 40 B) rs . 50 C) rs . 49 D) rs . 59 E) rs . 44

<gadget id="calculator">66 + 22</gadget> <output>88</output> <gadget id="calculator">88 / 2</gadget> <output>44</output> <result>E</result>

E

The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 22. What is the cost price of the article?

divide(add(66, 22), const_2)

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

s . p 1 - c . p = c . p – s . p 2 66 - c . p = c . p - 22 2 c . p = 66 + 22 ; c . p = 88 / 2 = 44 answer : e

gain

math_qa__9kTM9eGOBwusQcPG

An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share? Pick. A) 1266 B) 3000 C) 2866 D) 2999 E) 2678

<gadget id="calculator">12 - 7</gadget> <output>5</output> <gadget id="calculator">7 - 3</gadget> <output>4</output> <gadget id="calculator">2_400 / 4</gadget> <output>600</output> <gadget id="calculator">5 * 600</gadget> <output>3_000</output> <result>B</result>

B

An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?

multiply(subtract(12, 7), divide(2400, subtract(7, 3)))

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

"4 - - - 2000 5 - - - ? = > 3000 answer : b :"

general

math_qa__VFsjIIJXCiQyOSjK

If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.65 then sum is Choose the correct choice A) s . 5000 B) s . 6500 C) s . 5800 D) s . 6000 E) s . 6200

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/10) * (1/10)</gadget> <output>1/100 = around 0.01</output> <gadget id="calculator">65 / (1/100)</gadget> <output>6_500</output> <result>B</result>

B

If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.65 then sum is

divide(65, multiply(divide(10, const_100), divide(10, const_100)))

divide(n0,const_100)|multiply(#0,#0)|divide(n2,#1)|

"p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 65 6500 answer : b"

gain

math_qa__JTiddjSDCm1kFMfH

A volunteer organization is recruiting new members. In the fall they manage to increase their number by 4%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? Choose the correct choice from the following choices A) 16.16 % B) 15.76 % C) 14.14 % D) 13.13 % E) 12.12 %

<gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 + (1/25)</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">19 / 100</gadget> <output>19/100 = around 0.19</output> <gadget id="calculator">1 - (19/100)</gadget> <output>81/100 = around 0.81</output> <gadget id="calculator">(26/25) * (81/100)</gadget> <output>1_053/1_250 = around 0.8424</output> <gadget id="calculator">(1_053/1_250) * 100</gadget> <output>2_106/25 = around 84.24</output> <gadget id="calculator">100 - (2_106/25)</gadget> <output>394/25 = around 15.76</output> <result>B</result>

B

A volunteer organization is recruiting new members. In the fall they manage to increase their number by 4%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?

subtract(const_100, multiply(multiply(add(const_1, divide(4, const_100)), subtract(const_1, divide(19, const_100))), const_100))

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

"( 100 % + 4 % ) * ( 100 % - 19 % ) = 1.04 * . 81 = 0.8424 . 1 - 0.8424 = 15.76 % lost = - 15.76 % the answer is b the organization has lost 15.76 % of its total volunteers from fall to spring ."

general

math_qa__XYCzs7C7a5aIvTln

Find the value of (√1.21)/(√0.81) + (√0.81)/(√0.49) is Select: A) 195 / 63 B) 2.5 C) 155 / 63 D) 125 / 63 E) 185 / 63

<gadget id="calculator">1.21 ** (1/2)</gadget> <output>1.1</output> <gadget id="calculator">0.81 ** (1/2)</gadget> <output>0.9</output> <gadget id="calculator">1.1 / 0.9</gadget> <output>1.222222</output> <gadget id="calculator">0.49 ** (1/2)</gadget> <output>0.7</output> <gadget id="calculator">0.9 / 0.7</gadget> <output>1.285714</output> <gadget id="calculator">1.222222 + 1.285714</gadget> <output>2.507936</output> <result>B</result>

B

Find the value of (√1.21)/(√0.81) + (√0.81)/(√0.49) is

add(divide(sqrt(1.21), sqrt(0.81)), divide(sqrt(0.81), sqrt(0.49)))

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

"( √ 1.21 ) / ( √ 0.81 ) + ( √ 0.81 ) / ( √ 0.49 ) 11 / 9 + 9 / 7 = > 2.50 answer is b"

general

math_qa__HKID25UeWCA73Vfm

There are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning? Options. A) 12 B) 9 C) 8 D) 7 E) 6

<gadget id="calculator">18 - 3</gadget> <output>15</output> <gadget id="calculator">15 / 5</gadget> <output>3</output> <gadget id="calculator">3 + 3</gadget> <output>6</output> <result>E</result>

E

There are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?

add(divide(subtract(18, 3), 5), 3)

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

there are 18 balls in a jar . you take out 3 blue balls without putting 3 blue balls + 15 / 5 = 6 answer : e

probability

math_qa__JPNO8p42kFDKjG8r

Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 45% nuts, what percent of the combined mixture is dried fruit? Choose the correct choice from the following choices: A) 25 % B) 30 % C) 35 % D) 40 % E) 45 %

<gadget id="calculator">100 * 2</gadget> <output>200</output> <gadget id="calculator">70 / 200</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">(7/20) * 100</gadget> <output>35</output> <result>C</result>

C

Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 45% nuts, what percent of the combined mixture is dried fruit?

multiply(divide(70, multiply(const_100, const_2)), const_100)

multiply(const_100,const_2)|divide(n1,#0)|multiply(#1,const_100)

45 % is 15 % - points above 30 % and 15 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 1 : 1 . 1 / 2 * 70 % = 35 % the answer is c .

gain

math_qa__AugaDpLrsPp0WP7X

In August,a cricket team that played 120 matches won 20% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average? Pick one: A) 40 B) 52 C) 68 D) 80 E) 98

<gadget id="calculator">52 / 100</gadget> <output>13/25 = around 0.52</output> <gadget id="calculator">(13/25) * 120</gadget> <output>312/5 = around 62.4</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 120</gadget> <output>24</output> <gadget id="calculator">(312/5) - 24</gadget> <output>192/5 = around 38.4</output> <gadget id="calculator">1 - (13/25)</gadget> <output>12/25 = around 0.48</output> <gadget id="calculator">(192/5) / (12/25)</gadget> <output>80</output> <result>D</result>

D

In August,a cricket team that played 120 matches won 20% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?

divide(subtract(multiply(divide(52, const_100), 120), multiply(divide(20, const_100), 120)), subtract(const_1, divide(52, const_100)))

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

"let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 24 + x by solving we get x = 80 answer : d"

general

math_qa__BIt2TR4BbemMPmxd

Dacid obtained 72, 45, 72, 77 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Choices A) 67 B) 68 C) 87 D) 26 E) 75

<gadget id="calculator">72 + 45</gadget> <output>117</output> <gadget id="calculator">117 + 72</gadget> <output>189</output> <gadget id="calculator">189 + 77</gadget> <output>266</output> <gadget id="calculator">266 + 75</gadget> <output>341</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">341 / 5</gadget> <output>341/5 = around 68.2</output> <result>B</result>

B

Dacid obtained 72, 45, 72, 77 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?

divide(add(add(add(add(72, 45), 72), 77), 75), divide(const_10, const_2))

add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|

"average = ( 72 + 45 + 72 + 77 + 75 ) / 5 = 341 / 5 = 68 . answer : b"

general

math_qa__50Jx3g1UEhTo5k64

Find the area of a parallelogram with base 24 cm and height 16 cm. Select: A) 379 B) 384 C) 345 D) 342 E) 376

<gadget id="calculator">24 * 16</gadget> <output>384</output> <result>B</result>

B

Find the area of a parallelogram with base 24 cm and height 16 cm.

multiply(24, 16)

multiply(n0,n1)|

"area of a parallelogram = base * height = 24 * 16 = 384 cm 2 area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : option b"

geometry

math_qa__sPDwElxBrlMcrzJe

Two pipes A and B can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Choose the correct choice: A) 18 hours B) 15 hours C) 10 hours D) 12 hours E) 8 hours

<gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">1 / 45</gadget> <output>1/45 = around 0.022222</output> <gadget id="calculator">(1/30) + (1/45)</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">1 / (1/18)</gadget> <output>18</output> <result>A</result>

A

Two pipes A and B can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

divide(const_1, add(divide(const_1, 30), divide(const_1, 45)))

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

"part filled by a in 1 hour = 1 / 30 part filled by b in 1 hour = 1 / 45 part filled by ( a + b ) in 1 hour = 1 / 30 + 1 / 45 = 5 / 90 = 1 / 18 both the pipes together fill the tank in 18 hours answer is a"

physics

math_qa__jyeDEA5KVsFjunR0

A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price D per t-shirt that the vendor paid for these purchases? Pick: A) $ 12.20 B) $ 12.50 C) $ 12.55 D) $ 12.70 E) $ 13.00

<gadget id="calculator">10 + 14</gadget> <output>24</output> <gadget id="calculator">24 / 2</gadget> <output>12</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) + (1/4)</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">12 + (1/2)</gadget> <output>25/2 = around 12.5</output> <result>A</result>

A

A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price D per t-shirt that the vendor paid for these purchases?

add(divide(add(10, 14), const_2), add(const_0_25, const_0_25))

add(const_0_25,const_0_25)|add(n0,n1)|divide(#1,const_2)|add(#0,#2)|

"correct answer : a explanation : the relevant formula for this problem is average d = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."

general

math_qa__za3aikrUyEwrEIAZ

There are 20 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12th pole . How much time will it take to reach the last pole? Choose the correct choice from the following answers. A) 25.25 s B) 17.45 s C) 35.75 s D) 41.45 s E) none of these

<gadget id="calculator">24 / 12</gadget> <output>2</output> <gadget id="calculator">2 * 20</gadget> <output>40</output> <result>D</result>

D

There are 20 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12th pole . How much time will it take to reach the last pole?

multiply(divide(24, 12), 20)

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

let the distance between each pole be x m . then , the distance up to 12 th pole = 11 xm speed = 11 x ⁄ 24 m / s time taken to covers the total distance of 19 x = 19 x × 24 / 11 x = 41.45 s answer d

physics

math_qa__BqNTfVB4aKAScQSv

In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 57 students are taking History or Statistics or both, then how many students are taking History but not Statistics? Answers. A) 9 B) 19 C) 25 D) 27 E) 31

<gadget id="calculator">36 + 32</gadget> <output>68</output> <gadget id="calculator">68 - 57</gadget> <output>11</output> <gadget id="calculator">36 - 11</gadget> <output>25</output> <result>C</result>

C

In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 57 students are taking History or Statistics or both, then how many students are taking History but not Statistics?

subtract(36, subtract(add(36, 32), 57))

add(n1,n2)|subtract(#0,n3)|subtract(n1,#1)

number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 57 number of students taking neither history nor statistics = n = 90 - 57 = 33 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 32 + 33 - x or x = 11 now , number of students taking only history will be h - x or 36 - 11 = 25 answer : - c

other

math_qa__u0FmfklmGhEExDLk

If a - b = 4 and a2 + b2 = 18, find the value of ab. Options: A) 9 B) 1 C) 2 D) 18 E) 19

<gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">18 - 16</gadget> <output>2</output> <gadget id="calculator">2 / 2</gadget> <output>1</output> <result>B</result>

B

If a - b = 4 and a2 + b2 = 18, find the value of ab.

divide(subtract(18, power(4, 2)), 2)

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

"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 18 - 16 = 2 ab = 1 . answer : b"

general

math_qa__djnBJA1fbmQPAfh0

A batsman makes a score of 88 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning? Choose the correct answer: A) 19 B) 29 C) 40 D) 49 E) 59

<gadget id="calculator">17 * 3</gadget> <output>51</output> <gadget id="calculator">88 - 51</gadget> <output>37</output> <gadget id="calculator">37 + 3</gadget> <output>40</output> <result>C</result>

C

A batsman makes a score of 88 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?

add(subtract(88, multiply(17, 3)), 3)

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

"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 88 = 17 x therefore x = 40 answer : c"

general

math_qa__lNf3me0rOD9ES3vP

Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 2 days? Options: A) 2 / 5 B) 1 / 6 C) 1 / 4 D) 1 / 9 E) 2 / 6

<gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">1 / 45</gadget> <output>1/45 = around 0.022222</output> <gadget id="calculator">(1/30) + (1/45)</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">2 * (1/18)</gadget> <output>1/9 = around 0.111111</output> <result>D</result>

D

Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 2 days?

multiply(2, add(divide(const_1, 30), divide(const_1, 45)))

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

"a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 2 days = 2 ( 1 / 18 ) = 1 / 9 . answer d"

physics

math_qa__WrGdUHQn9GEYaQmn

Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time? Choose the correct choice from the following choices. A) 9 B) 8 C) 10 D) 8.5 E) 21

<gadget id="calculator">63 / 3</gadget> <output>21</output> <result>E</result>

E

Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time?

divide(63, 3)

divide(n0,n1)|

"63 / 3 = 21 answer : e"

physics

math_qa__40OZ1sANcswGKN6X

John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? Choose the correct choice from the following: A) 90 % B) 30 % C) 40 % D) 70 % E) 80 %

<gadget id="calculator">100 - 10</gadget> <output>90</output> <result>A</result>

A

John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease?

subtract(100, 10)

subtract(n0,n1)|

"the is always the difference between our starting and ending points . in this case , it ’ s 100 – 10 = 90 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 90 / 100 ) * 100 = ( 0.9 ) * 100 = 90 % . a"

general

math_qa__6HdkaZArZRFwEvoR

A river 2m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is? Choose the correct answer: A) 3000 m 3 B) 4580 m 3 C) 18500 m 3 D) 4900 m 3 E) 4700 m 3

<gadget id="calculator">2 * 45</gadget> <output>90</output> <gadget id="calculator">2 * 1_000</gadget> <output>2_000</output> <gadget id="calculator">90 * 2_000</gadget> <output>180_000</output> <gadget id="calculator">1 * 60</gadget> <output>60</output> <gadget id="calculator">180_000 / 60</gadget> <output>3_000</output> <result>A</result>

A

A river 2m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?

divide(multiply(multiply(2, 45), multiply(2, const_1000)), multiply(const_1, const_60))

multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)|

"explanation : ( 2000 * 2 * 45 ) / 60 = 3000 m 3 answer : option a"

physics

math_qa__iBA1HlkUDnEnr1sB

The sale price sarees listed for Rs.400 after successive discount is 20% and 5% is? Choose the correct choice from the following answers: A) 338 B) 277 C) 342 D) 882 E) 304

<gadget id="calculator">400 * 20</gadget> <output>8_000</output> <gadget id="calculator">8_000 / 100</gadget> <output>80</output> <gadget id="calculator">400 - 80</gadget> <output>320</output> <gadget id="calculator">320 * 5</gadget> <output>1_600</output> <gadget id="calculator">1_600 / 100</gadget> <output>16</output> <gadget id="calculator">320 - 16</gadget> <output>304</output> <result>E</result>

E

The sale price sarees listed for Rs.400 after successive discount is 20% and 5% is?

subtract(subtract(400, divide(multiply(400, 20), const_100)), divide(multiply(subtract(400, divide(multiply(400, 20), const_100)), 5), const_100))

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

"400 * ( 80 / 100 ) * ( 95 / 100 ) = 304 answer : e"

gain

math_qa__MDgtwQQMpJXQHQt1

Calculate how many seconds it eill take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 5, 8, 11 and 15 seconds. ? Answers A) 1310 B) 1320 C) 1322 D) 1323 E) 1312

<gadget id="calculator">5 * 8</gadget> <output>40</output> <gadget id="calculator">11 * 40</gadget> <output>440</output> <gadget id="calculator">3 * 440</gadget> <output>1_320</output> <result>B</result>

B

Calculate how many seconds it eill take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 5, 8, 11 and 15 seconds. ?

multiply(const_3, multiply(11, multiply(5, 8)))

multiply(n1,n2)|multiply(n3,#0)|multiply(#1,const_3)

lcm of 5 , 8 , 11 and 15 is 1320 lcm = 1320 answer : b

gain

math_qa__fxeMkzf045uXHsfa

The price of 3 pants and 6 t-shirts is Rs. 2250. With the same money one can buy 1 pant and 12 t-shirts. If one wants to buy 8 t-shirts, how much shall she have to pay ? Choose the correct option: A) 1300 B) 1100 C) 1000 D) 1200 E) 800

<gadget id="calculator">12 - 6</gadget> <output>6</output> <gadget id="calculator">3 - 1</gadget> <output>2</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">9 + 6</gadget> <output>15</output> <gadget id="calculator">2_250 / 15</gadget> <output>150</output> <gadget id="calculator">150 * 8</gadget> <output>1_200</output> <result>D</result>

D

The price of 3 pants and 6 t-shirts is Rs. 2250. With the same money one can buy 1 pant and 12 t-shirts. If one wants to buy 8 t-shirts, how much shall she have to pay ?

multiply(divide(2250, add(multiply(divide(subtract(12, 6), subtract(3, 1)), 3), 6)), 8)

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

"let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 2250 . . . . ( i ) and x + 12 y = 2250 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 750 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 2250 ( - ) x + 2 y = 750 - - - - - - - - - - - - - - - - 10 y = 1500 - - - - - - - - - - - - - - - - y = 150 cost of 8 t - shirts = 8 * 150 = 1200 answer : d"

general

math_qa__7ipgU3NARn8TtxQA

A train running at the speed of 30 km/hr crosses a pole in 24 seconds. What is the length of the train? Choose the correct choice from the following: A) 200 m B) 250 m C) 300 m D) 350 m E) 400 m

<gadget id="calculator">30 * 1_000</gadget> <output>30_000</output> <gadget id="calculator">30_000 / 3_600</gadget> <output>25/3 = around 8.333333</output> <gadget id="calculator">(25/3) * 24</gadget> <output>200</output> <result>A</result>

A

A train running at the speed of 30 km/hr crosses a pole in 24 seconds. What is the length of the train?

multiply(divide(multiply(30, const_1000), const_3600), 24)

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

"speed = ( 30 * 5 / 18 ) m / sec = ( 25 / 3 ) m / sec length of the train = ( speed x time ) = ( 25 / 3 * 24 ) m = 200 m . answer : a"

physics

math_qa__Ha1vfHSZrP5FyjwQ

----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 190 students answered yes only for subject M, how many of the students did not answer yes for either subject? Answers A) 100 B) 210 C) 300 D) 400 E) 500

<gadget id="calculator">500 - 190</gadget> <output>310</output> <gadget id="calculator">190 + 310</gadget> <output>500</output> <gadget id="calculator">400 - 310</gadget> <output>90</output> <gadget id="calculator">500 + 90</gadget> <output>590</output> <gadget id="calculator">800 - 590</gadget> <output>210</output> <result>B</result>

B

----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 190 students answered yes only for subject M, how many of the students did not answer yes for either subject?

subtract(800, add(add(190, subtract(500, 190)), subtract(400, subtract(500, 190))))

subtract(n0,n7)|add(n7,#0)|subtract(n3,#0)|add(#1,#2)|subtract(n6,#3)|

"since 190 students answered yes only for subject m , then the remaining 310 students who answered yes for subject m , also answered yes for subject r . so , 310 students answered yes for both subjects . if 310 students answered yes for both subjects , then 400 - 310 = 90 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 90 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 90 + 300 ) = 210 students did not answer yes for either subject . answer : b ."

general

math_qa__vSlc1SYaQuk2rgGt

The length of a bridge in meters, which a train 100-meters long and traveling at 45 km/hr can cross in 30 seconds is? Choose the correct answer: A) 225 B) 245 C) 275 D) 325 E) 375

<gadget id="calculator">45 * 1_000</gadget> <output>45_000</output> <gadget id="calculator">45_000 / 3_600</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">(25/2) * 30</gadget> <output>375</output> <gadget id="calculator">375 - 100</gadget> <output>275</output> <result>C</result>

C

The length of a bridge in meters, which a train 100-meters long and traveling at 45 km/hr can cross in 30 seconds is?

subtract(multiply(divide(multiply(45, const_1000), const_3600), 30), 100)

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

"45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 100 = 375 meters x = 275 meters the answer is c ."

physics

math_qa__mgsaTBJE8BTIhLds

Reema took a loan of Rs 800 with simple interest for as many years as the rate of interest. If she paid Rs. 632 as interest at the end of the loan period, what was the rate of interest. Choose the correct answer. A) 8.62 % B) 8.88 % C) 8.32 % D) 8 % E) 9 %

<gadget id="calculator">800 / 100</gadget> <output>8</output> <gadget id="calculator">632 / 8</gadget> <output>79</output> <gadget id="calculator">79 ** (1/2)</gadget> <output>sqrt(79) = around 8.888194</output> <result>B</result>

B

Reema took a loan of Rs 800 with simple interest for as many years as the rate of interest. If she paid Rs. 632 as interest at the end of the loan period, what was the rate of interest.

sqrt(divide(632, divide(800, const_100)))

divide(n0,const_100)|divide(n1,#0)|sqrt(#1)|

"explanation : let rate = r % then time = r years . = > 800 ∗ r ∗ r / 100 = 632 = > r 2 = 79 = > r = 8.88 % option b"

gain

math_qa__4jgALQdrgzrHCnCh

Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 3 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow? Choose the correct choice from the following answers: A) 4 minutes B) 32 / 7 minutes C) 192 / 7 minutes D) 224 / 7 minutes E) 32 / 5 minutes

<gadget id="calculator">1 / 32</gadget> <output>1/32 = around 0.03125</output> <gadget id="calculator">3 / 32</gadget> <output>3/32 = around 0.09375</output> <gadget id="calculator">(1/32) + (3/32)</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/32) + (1/8)</gadget> <output>5/32 = around 0.15625</output> <gadget id="calculator">1 / (5/32)</gadget> <output>32/5 = around 6.4</output> <result>E</result>

E

Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 3 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?

inverse(add(divide(const_1, 32), add(divide(const_1, 32), divide(3, 32))))

divide(const_1,n0)|divide(n1,n0)|add(#0,#1)|add(#2,#0)|inverse(#3)

pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 3 times fasterthan pipe a - - > the rate of b = 1 / 32 + 3 / 32 = 4 / 32 tank / minute . their combined rate = 1 / 32 + 4 / 32 = 5 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 5 minutes . answer : e

physics

math_qa__sdoqpfzT32XUw9ET

The positive number z is divisible by 4. What is the remainder of dividing z(2+4+z)+3 by 2? Answers: A) 0 B) 1 C) 2 D) 3 E) 4

<gadget id="calculator">3 % 2</gadget> <output>1</output> <result>B</result>

B

The positive number z is divisible by 4. What is the remainder of dividing z(2+4+z)+3 by 2?

reminder(3, 2)

reminder(n3,n1)

when we solve any of these equations : 28 + 3 ( z = 4 ) or 56 + 3 ( z = 8 ) we end up with numbers to which we have to subtract 1 to end up with a number that is exactly divisible by 2 . this is why we know that every result we get is going to have 1 as a remainder . hence answer is b .

general

math_qa__QZb5l9ZAWcKnSUm0

The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? Pick one. A) 10000 B) 12000 C) 13000 D) 10860 E) 14400

<gadget id="calculator">18 / 100</gadget> <output>9/50 = around 0.18</output> <gadget id="calculator">1 + (9/50)</gadget> <output>59/50 = around 1.18</output> <gadget id="calculator">(59/50) ** 2</gadget> <output>3_481/2_500 = around 1.3924</output> <gadget id="calculator">7_800 * (3_481/2_500)</gadget> <output>271_518/25 = around 10_860.72</output> <result>D</result>

D

The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years?

multiply(7800, power(add(const_1, divide(18, const_100)), 2))

divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)|

"formula : ( after = 100 denominator ago = 100 numerator ) 7800 × 118 / 100 × 118 / 100 = 10860 d"

gain

math_qa__clJi7llS1ne0QckS

Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 168 and for 36kgs of Apples is 186 then the cost of first 20 kgs of Apples is Choose the correct choice from the following answers: A) 3.69 B) 3.66 C) 3.6 D) 100 E) 3.61

<gadget id="calculator">33 - 30</gadget> <output>3</output> <gadget id="calculator">186 - 168</gadget> <output>18</output> <gadget id="calculator">36 - 33</gadget> <output>3</output> <gadget id="calculator">18 / 3</gadget> <output>6</output> <gadget id="calculator">3 * 6</gadget> <output>18</output> <gadget id="calculator">168 - 18</gadget> <output>150</output> <gadget id="calculator">150 / 30</gadget> <output>5</output> <gadget id="calculator">5 * 20</gadget> <output>100</output> <result>D</result>

D

Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 168 and for 36kgs of Apples is 186 then the cost of first 20 kgs of Apples is

multiply(divide(subtract(168, multiply(subtract(33, 30), divide(subtract(186, 168), subtract(36, 33)))), 30), 20)

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

"ans : by framing equations we get 30 l + 3 q = 168 30 l + 6 q = 186 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 30 l = 150 = > l = 5 then we get l = 5 cost of 20 kgs of apples = 20 x 5 = 100 answer : d"

other

math_qa__iMwNcew4nGyHiqQX

Two trains 200m and 160m long run at the speed of 68kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is? Choose the correct choice from the following answers: A) 5.6 sec B) 8.9 sec C) 10.8 sec D) 12 sec E) 15 sec

<gadget id="calculator">200 + 160</gadget> <output>360</output> <gadget id="calculator">68 + 40</gadget> <output>108</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">108 * (5/18)</gadget> <output>30</output> <gadget id="calculator">360 / 30</gadget> <output>12</output> <result>D</result>

D

Two trains 200m and 160m long run at the speed of 68kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is?

divide(add(200, 160), multiply(add(68, 40), const_0_2778))

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

"relative speed = 68 + 40 = 108 kmph * 5 / 18 = 30 m / s distance covered in crossing each other = 200 + 160 = 360 m required time = 360 * 1 / 30 = 12 sec answer is d"

physics

math_qa__gfUnnCKLtlOB8syJ

The total age of A and B is 11 years more than the total age of B and C. C is how many years younger than A.? Pick one: A) 16 B) 12 C) 11 D) 20 E) 10

<gadget id="calculator">11 * 1</gadget> <output>11</output> <result>C</result>

C

The total age of A and B is 11 years more than the total age of B and C. C is how many years younger than A.?

multiply(11, const_1)

multiply(n0,const_1)|

"( a + b ) - ( b - c ) = 11 a - c = 11 answer is c"

general

math_qa__Cynp8oHoerk2vkgA

Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,44,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is: Choose the correct choice from the following answers. A) 0.23255 B) 0.14544 C) 0.25632 D) 0.35466 E) 0.63435

<gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">480 / (3/5)</gadget> <output>800</output> <gadget id="calculator">3 * 100</gadget> <output>300</output> <gadget id="calculator">300 * 1_000</gadget> <output>300_000</output> <gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">40 + 4</gadget> <output>44</output> <gadget id="calculator">44 * 1_000</gadget> <output>44_000</output> <gadget id="calculator">300_000 + 44_000</gadget> <output>344_000</output> <gadget id="calculator">800 / 344_000</gadget> <output>1/430 = around 0.002326</output> <gadget id="calculator">(1/430) * 100</gadget> <output>10/43 = around 0.232558</output> <result>A</result>

A

Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,44,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:

multiply(divide(divide(480, divide(60, const_100)), add(multiply(multiply(3, const_100), const_1000), multiply(add(multiply(const_4, const_10), const_4), const_1000))), const_100)

divide(n0,const_100)|multiply(n1,const_100)|multiply(const_10,const_4)|add(#2,const_4)|divide(n3,#0)|multiply(#1,const_1000)|multiply(#3,const_1000)|add(#5,#6)|divide(#4,#7)|multiply(#8,const_100)

total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a

general

math_qa__DbfjmfMceMRoSYw9

S = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set S and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? Options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33

<gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">4 / 20</gadget> <output>1/5 = around 0.2</output> <result>B</result>

B

S = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set S and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

divide(const_4, multiply(const_4, 5))

multiply(n3,const_4)|divide(const_4,#0)

the total number of pairs s , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .

general

math_qa__1SiFeRrOX5GGhErC

Given that 100.48 = x, 100.70 = y and xz = y², then the value of z is close to Choose one: A) 1.2 B) 1.45 C) 2.2 D) 2.9 E) none

<gadget id="calculator">100.7 - 100</gadget> <output>0.7</output> <gadget id="calculator">0.7 * 2</gadget> <output>1.4</output> <gadget id="calculator">100.48 - 100</gadget> <output>0.48</output> <gadget id="calculator">1.4 / 0.48</gadget> <output>2.916667</output> <result>D</result>

D

Given that 100.48 = x, 100.70 = y and xz = y², then the value of z is close to

divide(multiply(subtract(100.7, const_100), const_2), subtract(100.48, const_100))

subtract(n1,const_100)|subtract(n0,const_100)|multiply(#0,const_2)|divide(#2,#1)

sol . xz = y ² ⇔ ( 10 0.48 ) z ( 100.70 ) 2 ( 10 0.48 z ) = 10 ( 2 × 0.70 ) = 101.40 ⇔ 0.48 z = 1.40 ⇔ z = 140 / 48 = 35 / 12 = 2.9 ( approx ) . answer d

general

math_qa__ttV6OjtbjSbMNpfY

The number of stamps that P and Q had were in the ratio of 7:4 respectively. After P gave Q 8 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 6:5. As a result of the gift, P had how many more stamps than Q? Select. A) 4 B) 8 C) 12 D) 16 E) 20

<gadget id="calculator">8 * 6</gadget> <output>48</output> <gadget id="calculator">8 * 5</gadget> <output>40</output> <gadget id="calculator">48 + 40</gadget> <output>88</output> <gadget id="calculator">6 + 5</gadget> <output>11</output> <gadget id="calculator">88 / 11</gadget> <output>8</output> <result>B</result>

B

The number of stamps that P and Q had were in the ratio of 7:4 respectively. After P gave Q 8 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 6:5. As a result of the gift, P had how many more stamps than Q?

divide(add(multiply(8, 6), multiply(8, 5)), add(6, 5))

add(n3,n4)|multiply(n2,n3)|multiply(n2,n4)|add(#1,#2)|divide(#3,#0)

p started with 7 k stamps and q started with 4 k stamps . ( 7 k - 8 ) / ( 4 k + 8 ) = 6 / 5 35 k - 24 k = 48 + 40 11 k = 88 k = 8 p has 7 ( 8 ) - 8 = 48 stamps and q has 4 ( 8 ) + 8 = 40 stamps . the answer is b .

other

math_qa__JBhl3CVasFkDxzeg

A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 20 miles per gallon, and from Town B to Town C, the car averaged 25 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? Choose the correct choice from the following answers A) 20 B) 18 C) 21.4 D) 16 E) 10

<gadget id="calculator">25 * 10</gadget> <output>250</output> <gadget id="calculator">250 / 2</gadget> <output>125</output> <gadget id="calculator">250 + 125</gadget> <output>375</output> <gadget id="calculator">250 / 20</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">125 / 25</gadget> <output>5</output> <gadget id="calculator">(25/2) + 5</gadget> <output>35/2 = around 17.5</output> <gadget id="calculator">375 / (35/2)</gadget> <output>150/7 = around 21.428571</output> <result>C</result>

C

A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 20 miles per gallon, and from Town B to Town C, the car averaged 25 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

divide(add(multiply(25, const_10), divide(multiply(25, const_10), const_2)), add(divide(multiply(25, const_10), 20), divide(divide(multiply(25, const_10), const_2), 25)))

multiply(n1,const_10)|divide(#0,const_2)|divide(#0,n0)|add(#1,#0)|divide(#1,n1)|add(#2,#4)|divide(#3,#5)|

"step 1 ) took lcm of 20 and 25 . . came as 100 . step 2 ) 100 distance between b to c . . . do 100 / 25 hence 4 gallons used step 3 ) twice distance . . hence 100 * 2 = 200 . . . do as above . . 200 / 20 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 100 + 200 = 300 miles hence . . average of whole journey = 300 / 14 which comes to 21.4 answer : c"

general

math_qa__cRXAXSaE0uC29Ve9

Sum of the squares of 3 no.'s is 267 and the sum of their products taken two at a time is 131. Find the sum? Choose the correct choice from the following options. A) 20 B) 24 C) 26 D) 23 E) 30

<gadget id="calculator">131 * 2</gadget> <output>262</output> <gadget id="calculator">262 + 267</gadget> <output>529</output> <gadget id="calculator">529 ** (1/2)</gadget> <output>23</output> <result>D</result>

D

Sum of the squares of 3 no.'s is 267 and the sum of their products taken two at a time is 131. Find the sum?

sqrt(add(multiply(131, const_2), 267))

multiply(n2,const_2)|add(n1,#0)|sqrt(#1)|

"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 267 + 2 * 131 a + b + c = √ 529 = 23 d"

general

math_qa__I1TuncmK0AOSemG2

The average age of 10 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher. Choose the correct answer: A) 30 B) 26 C) 28 D) 29 E) 45

<gadget id="calculator">10 * 15</gadget> <output>150</output> <gadget id="calculator">150 + 16</gadget> <output>166</output> <gadget id="calculator">166 + 10</gadget> <output>176</output> <gadget id="calculator">176 - 150</gadget> <output>26</output> <result>B</result>

B

The average age of 10 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.

subtract(add(add(multiply(10, 15), 16), 10), multiply(10, 15))

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

"explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 10 ) = 26 years answer : b"

general

math_qa__qMdr7XvjejlBKNU8

The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability W that the next couple the maitre 'd seats will not order dessert? Choose the most appropriate option: A) 20 % B) 25 % C) 40 % D) 60 % E) 75 %

<gadget id="calculator">2 * 5</gadget> <output>10</output> <gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(3/5) / (4/5)</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 - (3/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * 100</gadget> <output>25</output> <result>B</result>

B

The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability W that the next couple the maitre 'd seats will not order dessert?

multiply(subtract(const_1, divide(divide(60, multiply(multiply(const_2, const_5), multiply(const_2, const_5))), subtract(const_1, divide(20, multiply(multiply(const_2, const_5), multiply(const_2, const_5)))))), multiply(multiply(const_2, const_5), multiply(const_2, const_5)))

multiply(const_2,const_5)|multiply(#0,#0)|divide(n0,#1)|divide(n1,#1)|subtract(const_1,#3)|divide(#2,#4)|subtract(const_1,#5)|multiply(#1,#6)|

"could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . w = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"

probability

math_qa__w3XqWBmxCyNwyHO9

Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "COW"? Pick one A) 120 B) 123 C) 126 D) 129 E) 132

<gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">20 - 2</gadget> <output>18</output> <gadget id="calculator">18 + 1</gadget> <output>19</output> <gadget id="calculator">19 + 20</gadget> <output>39</output> <gadget id="calculator">39 * 3</gadget> <output>117</output> <result>B</result>

B

Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "COW"?

multiply(add(add(subtract(multiply(2, const_10), 2), 1), multiply(2, const_10)), 3)

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

"` ` cow ' ' = ( 3 + 15 + 23 ) * 3 = 123 . the answer is b ."

general

math_qa__m3PpZNb9SoDZLDX4

A straight line in the xy- plane has y-intercept of 79 and slope of 6. On this line the y-coordinate of the point is 14, then what is the X-coordinate of the point? Select the correct option: A) 11 B) - 10.83 C) 71 D) 20.83 E) - 12

<gadget id="calculator">14 - 79</gadget> <output>-65</output> <gadget id="calculator">(-65) / 6</gadget> <output>-65/6 = around -10.833333</output> <result>B</result>

B

A straight line in the xy- plane has y-intercept of 79 and slope of 6. On this line the y-coordinate of the point is 14, then what is the X-coordinate of the point?

divide(subtract(14, 79), 6)

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

"eq of line = y = mx + c c = 79 m = 6 y = 14 substitute given : x = ( y - c ) / m = ( 14 - 79 ) / 6 = - 65 / 6 = - 10.83 correct option is b"

general

math_qa__PAhjuAAPNymqmhwp

A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads? Choose the correct choice from the following options: A) 400 B) 1550 C) 1575 D) 1600 E) 1625

<gadget id="calculator">200 * 5</gadget> <output>1_000</output> <gadget id="calculator">120 * 5</gadget> <output>600</output> <gadget id="calculator">1_000 + 600</gadget> <output>1_600</output> <result>C</result>

C

A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads?

add(rectangle_area(200, 5), rectangle_area(120, 5))

rectangle_area(n0,n2)|rectangle_area(n1,n2)|add(#0,#1)|

"area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads t = 1000 + 600 - 25 = 1575 answer : option c"

geometry

math_qa__MQYAZEYY80yRCeCZ

3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? Pick. A) 45 % B) 48 % C) 57 % D) 59 % E) 61 %

<gadget id="calculator">5_136 + 7_636</gadget> <output>12_772</output> <gadget id="calculator">12_772 + 11_628</gadget> <output>24_400</output> <gadget id="calculator">11_628 / 24_400</gadget> <output>2_907/6_100 = around 0.476557</output> <gadget id="calculator">(2_907/6_100) * 100</gadget> <output>2_907/61 = around 47.655738</output> <result>B</result>

B

3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?

multiply(divide(11628, add(add(5136, 7636), 11628)), const_100)

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

"total number of votes polled = ( 5136 + 7636 + 11628 ) = 24400 so , required percentage = 11628 / 24400 * 100 = 48 % b"

gain

math_qa__a9Ztr063UqX9efYl

3550 - (1002 / 20.04) = ? Select. A) 2984 B) 2983 C) 3500 D) 2981 E) none of these

<gadget id="calculator">1_002 / 20.04</gadget> <output>50</output> <gadget id="calculator">3_550 - 50</gadget> <output>3_500</output> <result>C</result>

C

3550 - (1002 / 20.04) = ?

subtract(3550, divide(1002, 20.04))

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

"3550 - 50 = 3500 answer : c"

general

math_qa__s1gByKpQgPQZXtQx

Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of z crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of z? Pick one A) z / 2 B) z C) 3 z / 2 D) 2 z E) 3 z

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 + (1/2)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">2 * (3/2)</gadget> <output>3</output> <result>E</result>

E

Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of z crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of z?

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

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

"lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( z ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"

general

math_qa__znxZHq3tfeSSJgDL

A waiter's salary consists of his salary and tips. During one week his tips were 3/4 of his salary. What fraction of his income came from tips ? Choose the correct choice from the following answers. A) 3 / 7 B) 5 / 4 C) 5 / 8 D) 5 / 9 E) 6 / 9

<gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) + 1</gadget> <output>7/4 = around 1.75</output> <gadget id="calculator">(3/4) / (7/4)</gadget> <output>3/7 = around 0.428571</output> <result>A</result>

A

A waiter's salary consists of his salary and tips. During one week his tips were 3/4 of his salary. What fraction of his income came from tips ?

divide(divide(3, 4), add(divide(3, 4), const_1))

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

"income = salary ( s ) + tips = s + s * 3 / 4 = s * 7 / 4 tips = s * 3 / 4 fraction of his income came from tips = ( s * 3 / 4 ) / ( s * 7 / 4 ) = 3 / 7 answer : a"

general

math_qa__tNNdox6SoDNCbFfy

The least number which must be subtracted from 509 to make it exactly divisible by 9 is: Select A) 2 B) 3 C) 5 D) 5 E) 6

<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 * 10</gadget> <output>50</output> <gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">50 + 6</gadget> <output>56</output> <gadget id="calculator">56 * 9</gadget> <output>504</output> <gadget id="calculator">509 - 504</gadget> <output>5</output> <result>C</result>

C

The least number which must be subtracted from 509 to make it exactly divisible by 9 is:

subtract(509, multiply(add(multiply(add(const_4, const_1), const_10), add(const_4, const_2)), 9))

add(const_2,const_4)|add(const_1,const_4)|multiply(#1,const_10)|add(#0,#2)|multiply(n1,#3)|subtract(n0,#4)

on dividing 509 by 9 , we get remainder = 5 therefore , required number to be subtracted = 5 answer : c

general

math_qa__Zp9k9rV5w9MpI0sz

A train 140 m long, running with a speed of 63 km/hr will pass a tree in? Select. A) 15 sec B) 16 sec C) 18 sec D) 11 sec E) 8 sec

<gadget id="calculator">63 * 1_000</gadget> <output>63_000</output> <gadget id="calculator">140 / 63_000</gadget> <output>1/450 = around 0.002222</output> <gadget id="calculator">(1/450) * 3_600</gadget> <output>8</output> <result>E</result>

E

A train 140 m long, running with a speed of 63 km/hr will pass a tree in?

multiply(divide(140, multiply(63, const_1000)), const_3600)

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

"speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 140 * 2 / 35 = 8 sec answer : e"

physics

math_qa__IQJkL795UAyV66LP

A person borrows Rs. 8000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year. Choose the correct choice from the following answers: A) 100 rs B) 150 rs C) 160 rs D) 180 rs E) 200 rs

<gadget id="calculator">8_000 * 6</gadget> <output>48_000</output> <gadget id="calculator">48_000 * 2</gadget> <output>96_000</output> <gadget id="calculator">96_000 / 100</gadget> <output>960</output> <gadget id="calculator">8_000 * 4</gadget> <output>32_000</output> <gadget id="calculator">32_000 * 2</gadget> <output>64_000</output> <gadget id="calculator">64_000 / 100</gadget> <output>640</output> <gadget id="calculator">960 - 640</gadget> <output>320</output> <gadget id="calculator">320 / 2</gadget> <output>160</output> <result>C</result>

C

A person borrows Rs. 8000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.

divide(subtract(divide(multiply(multiply(8000, 6), 2), const_100), divide(multiply(multiply(8000, 4), 2), const_100)), 2)

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

"gain in 2 years = [ ( 8000 * 6 * 2 ) / 100 ] - [ ( 8000 * 4 * 2 ) / 100 ] 960 - 640 = 320 gain in 1 year = ( 320 / 2 ) = 160 rs answer : c"

gain

math_qa__9HxK3SQIKCz3ADoD

In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 50 bricks in the wall, how many bricks does the bottom row contain ? Choose the most appropriate option: A) 12 B) 10 C) 9 D) 8 E) 11

<gadget id="calculator">50 - 1</gadget> <output>49</output> <gadget id="calculator">49 - 2</gadget> <output>47</output> <gadget id="calculator">47 - 3</gadget> <output>44</output> <gadget id="calculator">44 - 4</gadget> <output>40</output> <gadget id="calculator">40 / 5</gadget> <output>8</output> <result>D</result>

D

In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 50 bricks in the wall, how many bricks does the bottom row contain ?

divide(subtract(subtract(subtract(subtract(50, const_1), const_2), const_3), const_4), 5)

subtract(n1,const_1)|subtract(#0,const_2)|subtract(#1,const_3)|subtract(#2,const_4)|divide(#3,n0)

the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 50 5 x - 10 = 50 5 x = 40 x = 8 answer : d

general

math_qa__EPMmBk8oyvmZjQEQ

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot? Choose one A) $ 1.75 B) $ 1.85 C) $ 2.00 D) $ 2.15 E) $ 2.30

<gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">5 * 6</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <gadget id="calculator">15 * 0.15</gadget> <output>2.25</output> <gadget id="calculator">8.25 - 2.25</gadget> <output>6</output> <gadget id="calculator">6 / 6</gadget> <output>1</output> <gadget id="calculator">5 * 0.15</gadget> <output>0.75</output> <gadget id="calculator">1 + 0.75</gadget> <output>1.75</output> <result>A</result>

A

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

add(divide(subtract(8.25, multiply(divide(multiply(subtract(6, const_1), 6), const_2), 0.15)), 6), multiply(subtract(6, const_1), 0.15))

subtract(n0,const_1)|multiply(n0,#0)|multiply(n2,#0)|divide(#1,const_2)|multiply(n2,#3)|subtract(n1,#4)|divide(#5,n0)|add(#6,#2)|

"this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 15 - cent increment ) and the the difference in sequential prices of the pots is 15 cents , the largest pot probably has a price that is a 15 - cent increment . from the answer choices , i would then test answer a first if . . . . the largest pot = $ 1.75 1 1.15 1.3 1.45 1.6 1.75 total = $ 8.25 so this must be the answer . a"

general

math_qa__3NYeK1DDFNuwOEFH

A pipe can fill a cistern in 66 minutes. Find the time in which 1/11 part of the cistern will be filled? Choices A) 5 min B) 2 min C) 6 min D) 1 min E) 10 min

<gadget id="calculator">1 / 11</gadget> <output>1/11 = around 0.090909</output> <gadget id="calculator">66 * (1/11)</gadget> <output>6</output> <result>C</result>

C

A pipe can fill a cistern in 66 minutes. Find the time in which 1/11 part of the cistern will be filled?

multiply(66, divide(1, 11))

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

"full cistern filled in = 66 minutes 1 / 11 part filled in = 66 * 1 / 11 = 6 minutes answer is c"

physics

math_qa__3Dj5f4lbTSL6uDBS

A train crosses a platform of 160 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? Answers: A) 110 B) 887 C) 167 D) 197 E) 161

<gadget id="calculator">15 / 3</gadget> <output>5</output> <gadget id="calculator">15 / 5</gadget> <output>3</output> <gadget id="calculator">250 * 3</gadget> <output>750</output> <gadget id="calculator">20 / 5</gadget> <output>4</output> <gadget id="calculator">160 * 4</gadget> <output>640</output> <gadget id="calculator">750 - 640</gadget> <output>110</output> <result>A</result>

A

A train crosses a platform of 160 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?

subtract(multiply(250, divide(15, divide(15, const_3))), multiply(160, divide(20, divide(15, const_3))))

divide(n1,const_3)|divide(n1,#0)|divide(n3,#0)|multiply(n2,#1)|multiply(n0,#2)|subtract(#3,#4)|

"length of the train be ‘ x ’ x + 160 / 15 = x + 250 / 20 20 x + 3200 = 15 x + 3750 5 x = 550 x = 110 m answer : a"

physics

math_qa__ZdJ6kIF8wknJ9O7v

Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be Choose the correct choice from the following: A) rs . 169.50 B) rs . 1700 C) rs . 175.50 D) rs . 180 E) none

<gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 + 2</gadget> <output>4</output> <gadget id="calculator">153 * 4</gadget> <output>612</output> <gadget id="calculator">126 + 126</gadget> <output>252</output> <gadget id="calculator">612 - 252</gadget> <output>360</output> <gadget id="calculator">360 / 2</gadget> <output>180</output> <result>C</result>

C

Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be

divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 126)), 2)

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

"solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 = › x - 153 = 22.50 = › x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer c"

other

math_qa__1EMcXKZD9IfTzRM4

On dividing 23 by a number, the quotient is 4 and the remainder is 3. Find the divisor. Choose the correct choice from the following answers: A) 1 B) 2 C) 4 D) 5 E) 7

<gadget id="calculator">23 / 4</gadget> <output>23/4 = around 5.75</output> <gadget id="calculator">floor(23/4)</gadget> <output>5</output> <result>D</result>

D

On dividing 23 by a number, the quotient is 4 and the remainder is 3. Find the divisor.

floor(divide(23, 4))

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

"d = ( d - r ) / q = ( 23 - 3 ) / 4 = 20 / 4 = 5 d"

general

math_qa__d6UolIfTLyGhdUZa

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: Pick. A) 18 cm B) 28 cm C) 30 cm D) 38 cm E) 42 cm

<gadget id="calculator">2 * 20</gadget> <output>40</output> <gadget id="calculator">41 + 40</gadget> <output>81</output> <gadget id="calculator">81 ** (1/2)</gadget> <output>9</output> <gadget id="calculator">2 * 9</gadget> <output>18</output> <result>A</result>

A

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

multiply(const_2, sqrt(add(41, multiply(const_2, 20))))

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

l 2 + b 2 = 41 . also , lb = 20 . ( l + b ) 2 = ( l 2 + b 2 ) + 2 lb = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . a )

geometry

math_qa__7zn3WTLN4UuL12y9

After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.4 cubic inches, what is the original volume of the cubic ice, in cubic inches? Choose one: A) 2.5 B) 3.0 C) 4.0 D) 6.4 E) 8.0

<gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">0.4 / (1/4)</gadget> <output>1.6</output> <gadget id="calculator">1.6 / (1/4)</gadget> <output>6.4</output> <result>D</result>

D

After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.4 cubic inches, what is the original volume of the cubic ice, in cubic inches?

divide(divide(0.4, const_0_25), const_0_25)

divide(n4,const_0_25)|divide(#0,const_0_25)

let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.4 x = 6.4 alternate solution : try to backsolve . initial volume = 6.4 after one hour - - > ( 1 / 4 ) 6.4 = 1.6 after two hours - - > ( 1 / 4 ) 1.6 = 0.4 answer : d

physics

math_qa__FNbNV5cz6lYl7Ir8

The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car? Choose the most appropriate option. A) 79 kmph B) 85 kmph C) 35 kmph D) 23 kmph E) 14 kmph

<gadget id="calculator">10 + 60</gadget> <output>70</output> <gadget id="calculator">70 / 2</gadget> <output>35</output> <result>C</result>

C

The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car?

divide(add(10, 60), const_2)

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

"s = ( 10 + 60 ) / 2 = 35 kmph answer : c"

physics

math_qa__G63v6sxCk7iIfeA9

plaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ? Choose the correct choice from the following: A) 54 B) 72 C) 96 D) 144 E) 432

<gadget id="calculator">10 - 4</gadget> <output>6</output> <gadget id="calculator">6 * 9</gadget> <output>54</output> <result>A</result>

A

plaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?

multiply(subtract(const_10, 4), 9)

subtract(const_10,n0)|multiply(n2,#0)

plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a .

general

math_qa__T89IjNwtT7XgIwW4

In Town X, 64 percent of the population are employed, and 55 percent of the population are employed males. What percent of the employed people in Town X are females? Choose the correct choice from the following choices. A) 14 % B) 25 % C) 32 % D) 40 % E) 52 %

<gadget id="calculator">64 - 55</gadget> <output>9</output> <gadget id="calculator">9 / 64</gadget> <output>9/64 = around 0.140625</output> <gadget id="calculator">(9/64) * 100</gadget> <output>225/16 = around 14.0625</output> <result>A</result>

A

In Town X, 64 percent of the population are employed, and 55 percent of the population are employed males. What percent of the employed people in Town X are females?

multiply(divide(subtract(64, 55), 64), const_100)

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

"we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 55 are employed males , hence 9 % are employed females . ( employed females ) / ( total employed people ) = 9 / 64 = 14 % answer : a ."

gain

math_qa__2IpkzZwkLBUfBiox

For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? Pick one: A) 12 % B) 26 % C) 29 % D) 32 % E) 60 %

<gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 300</gadget> <output>90</output> <gadget id="calculator">35 / 100</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">(7/20) * 200</gadget> <output>70</output> <gadget id="calculator">90 + 70</gadget> <output>160</output> <gadget id="calculator">300 + 200</gadget> <output>500</output> <gadget id="calculator">160 / 500</gadget> <output>8/25 = around 0.32</output> <gadget id="calculator">(8/25) * 100</gadget> <output>32</output> <result>D</result>

D

For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?

multiply(divide(add(multiply(divide(30, const_100), 300), multiply(divide(35, const_100), 200)), add(300, 200)), const_100)

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

"in the first plot 30 % of 300 seeds germinated , so 0.3 x 300 = 90 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 160 / 500 ) x 100 % , or 32 % . answer : d ."

general

math_qa__wpUitd9afG8ftpmS

A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? Pick one. A) 35 kmph B) 48 kmph C) 52 kmph D) 54 kmph E) 60 kmph

<gadget id="calculator">6 * 3</gadget> <output>18</output> <gadget id="calculator">18 / 2</gadget> <output>9</output> <gadget id="calculator">540 / 9</gadget> <output>60</output> <result>E</result>

E

A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?

divide(540, divide(multiply(6, 3), 2))

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

"time = 6 distance = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph e )"

physics

math_qa__dn3XXz3diB9Y0ZFx

How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 12km/hr? Choose the correct choice: A) 52 sec B) 45 sec C) 60 sec D) 25 sec E) 39 sec

<gadget id="calculator">50 * 4</gadget> <output>200</output> <gadget id="calculator">1_000 / 3_600</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">12 * (5/18)</gadget> <output>10/3 = around 3.333333</output> <gadget id="calculator">200 / (10/3)</gadget> <output>60</output> <result>C</result>

C

How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 12km/hr?

divide(multiply(50, const_4), multiply(12, divide(const_1000, const_3600)))

divide(const_1000,const_3600)|multiply(n0,const_4)|multiply(n1,#0)|divide(#1,#2)|

"speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 50 * 4 = 200 m time taken = 200 * 3 / 10 = 60 sec answer is c"

gain

math_qa__HDA5lKmmyXMBlUiB

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings? Choose the correct choice from the following answers. A) 28 B) 27 C) 12 D) 37 E) 01

<gadget id="calculator">17 * 3</gadget> <output>51</output> <gadget id="calculator">85 - 51</gadget> <output>34</output> <gadget id="calculator">34 + 3</gadget> <output>37</output> <result>D</result>

D

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?

add(subtract(85, multiply(17, 3)), 3)

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

"explanation : 16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"

general

math_qa__9Ow991e8dz6Agjvw

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 5 such machines produce in 4 minutes? Choose the most appropriate option: A) 900 B) 1,800 C) 2,700 D) 10,800 E) 64,800

<gadget id="calculator">270 / 6</gadget> <output>45</output> <gadget id="calculator">45 * 4</gadget> <output>180</output> <gadget id="calculator">180 * 5</gadget> <output>900</output> <result>A</result>

A

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 5 such machines produce in 4 minutes?

multiply(multiply(divide(270, 6), 4), 5)

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

"6 machines produce 270 bottles per minute ; 1 machine produces 270 / 6 = 45 bottles per minute ; 5 machines produce 45 * 5 = 225 bottles per minute ; in 4 minutes 10 machines produce 225 * 4 = 900 bottles . answer : a ."

gain

math_qa__w3DBca2jc7UopIPe

P, Q and R have $9000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R? Choices: A) 2400 B) 3600 C) 3998 D) 2539 E) 1930

<gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">9_000 * 4</gadget> <output>36_000</output> <gadget id="calculator">4 / 3</gadget> <output>4/3 = around 1.333333</output> <gadget id="calculator">(4/3) * 3</gadget> <output>4</output> <gadget id="calculator">1 * 3</gadget> <output>3</output> <gadget id="calculator">4 + 3</gadget> <output>7</output> <gadget id="calculator">7 + 3</gadget> <output>10</output> <gadget id="calculator">36_000 / 10</gadget> <output>3_600</output> <result>B</result>

B

P, Q and R have $9000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?

divide(multiply(9000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))

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

"b 3600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 9000 - r ) = > 3 r = 18000 - 2 r = > 5 r = 18000 = > r = 3600 ."

general

math_qa__WoWwk33Un2rpCTji

How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 340 m in length? Choices: A) 18.9 sec B) 88.9 sec C) 22.9 sec D) 27.00 sec E) 72.0 sec

<gadget id="calculator">110 + 340</gadget> <output>450</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">60 * (5/18)</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">450 / (50/3)</gadget> <output>27</output> <result>D</result>

D

How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 340 m in length?

divide(add(110, 340), multiply(60, const_0_2778))

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

"d = 110 + 340 = 450 m s = 60 * 5 / 18 = 50 / 3 t = 450 * 3 / 50 = 27.00 sec answer : d"

physics

math_qa__t2UHzn9o1kutDOTT

The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, what is x? Options: A) 18 B) 20 C) 22 D) 24 E) 26

<gadget id="calculator">30 * 4</gadget> <output>120</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">120 / 5</gadget> <output>24</output> <result>D</result>

D

The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, what is x?

divide(multiply(30, const_4), add(const_4, const_1))

add(const_1,const_4)|multiply(n0,const_4)|divide(#1,#0)

let the cost price = y the cost price of 30 articles = 30 y the selling price of x articles = 1.25 y * x 1.25 y * x = 30 y x = 30 / 1.25 = 24 the answer is d .

gain

math_qa__FPy3j7FTMJz3SVZW

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 42, the how old is B? Choose the most appropriate option. A) 16 B) 9 C) 8 D) 11 E) 10

<gadget id="calculator">42 - 2</gadget> <output>40</output> <gadget id="calculator">40 * 2</gadget> <output>80</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">80 / 5</gadget> <output>16</output> <result>A</result>

A

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 42, the how old is B?

divide(multiply(subtract(42, const_2), const_2), add(const_4, const_1))

add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)|

"explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 ⇒ 5 x = 40 ⇒ x = 8 . hence , b ' s age = 2 x = 16 years . answer : a"

general

math_qa__qeoOa1Ik0oK6k9wT

Calculate the ratio between x and y if 15% of x equal to 50% of y? Select the correct option A) 3 : 5 B) 3 : 7 C) 3 : 8 D) 3 : 10 E) 3 : 9

<gadget id="calculator">15 / 50</gadget> <output>3/10 = around 0.3</output> <result>D</result>

D

Calculate the ratio between x and y if 15% of x equal to 50% of y?

divide(15, 50)

divide(n0,n1)|

"explanation : 15 x = 50 y x : y = 15 : 50 = 3 : 10 answer : d"

general

math_qa__C3JeXiD5hzgjMC7O

If 0.8 of a number is equal to 0.09 of another number, the ratio of the numbers i Choose the most appropriate option. A) 2 : 3 B) 3 : 4 C) 9 : 80 D) 20 : 3 E) none

<gadget id="calculator">0.09 * 100</gadget> <output>9</output> <gadget id="calculator">0.8 * 100</gadget> <output>80</output> <gadget id="calculator">9 / 80</gadget> <output>9/80 = around 0.1125</output> <result>C</result>

C

If 0.8 of a number is equal to 0.09 of another number, the ratio of the numbers i

divide(multiply(0.09, const_100), multiply(0.8, const_100))

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

"sol . 0.8 a = 0.09 b â ‡ ” a / b = 0.09 / 0.8 = 9 / 80 = . â ˆ ´ a : b = 9 : 80 . answer c"

other

math_qa__idTsitTJkRy6dBOl

the product of 3 consecutive numbers is 210 . then the sum of the smallest two numbers is ? Choose the correct choice from the following answers A) 11 B) 15 C) 20 D) 38 E) 56

<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">210 ** (1/3)</gadget> <output>210**(1/3) = around 5.943922</output> <gadget id="calculator">floor(210**(1/3))</gadget> <output>5</output> <gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 + 5</gadget> <output>11</output> <result>A</result>

A

the product of 3 consecutive numbers is 210 . then the sum of the smallest two numbers is ?

add(add(floor(power(210, const_0_33)), const_1), floor(power(210, const_0_33)))

power(n1,const_0_33)|floor(#0)|add(#1,const_1)|add(#2,#1)

product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a

general