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math_qa__j36VvdqthiKdOCB6

A square has a side 5 centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square Choose the correct choice from the following answers: A) 5 B) 6 C) 7 D) 8 E) 9

<gadget id="calculator">5 ** 2</gadget> <output>25</output> <gadget id="calculator">25 ** (1/2)</gadget> <output>5</output> <result>A</result>

A

A square has a side 5 centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square

square_edge_by_area(square_area(5))

square_area(n0)|square_edge_by_area(#0)

let x be the side of the smaller square and y be the side of the larger square . the statement ` ` a square has a side 5 centimeters shorter than the side of a second square ' ' may be formulated by x = y - 5 the area of the smaller square is equal to x 2 = ( y - 5 ) 2 and the area of the larger square is equal to y 2 the statement ` ` the area of the larger square is four times the area of the smaller square ' ' may be formulated by y 2 = 4 ( y - 5 ) 2 write the above equation so that the right side is equal to 0 y 2 - 4 ( y - 5 ) 2 = 0 the left side is made up of the difference of two squares and can be easily factored as follows [ y - 2 ( y - 5 ) ] [ y + 2 ( y - 5 ) ] = 0 solve for y to find y = 10 and y = 10 / 3 . we now use the equation x = y - 5 to find x y = 10 and x = 5 for the second solution y = 10 / 3 , x is negative and can not be accepted as the length of the side of a square must be positive . answer a

physics

math_qa__XtYswJ0VANded4u4

The ratio of the present age of Sandy to that of Molly is 7:2. Sixteen years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago? Choose the correct choice from the following. A) 66 B) 70 C) 74 D) 78 E) 82

<gadget id="calculator">10 + 6</gadget> <output>16</output> <gadget id="calculator">5 * 16</gadget> <output>80</output> <gadget id="calculator">2 * 16</gadget> <output>32</output> <gadget id="calculator">80 - 32</gadget> <output>48</output> <gadget id="calculator">48 * 7</gadget> <output>336</output> <gadget id="calculator">2 + 2</gadget> <output>4</output> <gadget id="calculator">336 / 4</gadget> <output>84</output> <gadget id="calculator">84 - 6</gadget> <output>78</output> <result>D</result>

D

The ratio of the present age of Sandy to that of Molly is 7:2. Sixteen years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?

subtract(divide(multiply(subtract(multiply(5, add(const_10, 6)), multiply(2, add(const_10, 6))), 7), add(2, 2)), 6)

add(n4,const_10)|add(n1,n1)|multiply(n2,#0)|multiply(n1,#0)|subtract(#2,#3)|multiply(n0,#4)|divide(#5,#1)|subtract(#6,n4)

let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 16 ) / ( 2 x + 16 ) = 5 / 2 4 x = 48 x = 12 six years ago , sandy ' s age was 7 ( 12 ) - 6 = 78 the answer is d .

general

math_qa__YliJVFuQtepa9stF

A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated? Pick: A) 28 % B) 30 % C) 32 % D) 34 % E) 40 %

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 400</gadget> <output>80</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">100 * (3/5)</gadget> <output>60</output> <gadget id="calculator">80 + 60</gadget> <output>140</output> <gadget id="calculator">400 + 100</gadget> <output>500</output> <gadget id="calculator">140 / 500</gadget> <output>7/25 = around 0.28</output> <gadget id="calculator">(7/25) * 100</gadget> <output>28</output> <result>A</result>

A

A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

multiply(divide(add(multiply(divide(20, 100), 400), multiply(100, divide(60, 100))), add(400, 100)), 100)

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

"1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 140 pounds of decaffeinated out of 500 pounds , that means 140 / 500 * 100 % = 28 % . the correct answer is a ."

gain

math_qa__f1nT7tLFTJiJUiMg

At what rate percent per annum will a sum of money double in 8 years. Select. A) 12.5 % B) 12.9 % C) 18.5 % D) 11.5 % E) 12.3 %

<gadget id="calculator">100 / 8</gadget> <output>25/2 = around 12.5</output> <result>A</result>

A

At what rate percent per annum will a sum of money double in 8 years.

divide(const_100, 8)

divide(const_100,n0)|

"explanation : let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 12.5 % per annum . answer : a ) 12.5 %"

gain

math_qa__azUe5tDGlVBmnqaw

Paper charge is Rs. 60 per kg. How much expenditure would be there to cover a cube of edge 10m with a paper, if one kg of paper covers 20 sq.m. area? Choose one: A) rs . 2250 B) rs . 3600 C) rs . 2700 D) rs . 1800 E) none of these

<gadget id="calculator">60 / 10</gadget> <output>6</output> <gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">6 * 100</gadget> <output>600</output> <gadget id="calculator">600 / 20</gadget> <output>30</output> <gadget id="calculator">30 * 60</gadget> <output>1_800</output> <result>D</result>

D

Paper charge is Rs. 60 per kg. How much expenditure would be there to cover a cube of edge 10m with a paper, if one kg of paper covers 20 sq.m. area?

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

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

explanation : total surface area of the cube = 6 x ( 10 ) 2 = 600 sq . m 1 kg covers 20 sq . m area , for 600 we need = 600 / 20 = 30 kg paper . expenditure = rate x quantity = rs . 60 x 30 kg = rs . 1800 answer is d

geometry

math_qa__uYqKX9MnR5doM9za

A shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight. What is his profit percentage? Choose the correct choice from the following options: A) 25 % B) 18 % C) 20 % D) 40 % E) 45 %

<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 + 5</gadget> <output>10</output> <gadget id="calculator">10 * 100</gadget> <output>1_000</output> <gadget id="calculator">1_000 - 800</gadget> <output>200</output> <gadget id="calculator">200 / 800</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * 100</gadget> <output>25</output> <result>A</result>

A

A shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight. What is his profit percentage?

multiply(divide(subtract(multiply(add(add(const_4, const_1), add(const_4, const_1)), const_100), 800), 800), const_100)

add(const_1,const_4)|add(#0,#0)|multiply(#1,const_100)|subtract(#2,n0)|divide(#3,n0)|multiply(#4,const_100)|

"100 ( 1000 - 800 ) / 800 = 25 % profit percentage = 25 % answer a"

gain

math_qa__msXPbtD53EfE2YRm

By selling 18 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 35%? Choose the correct choice from the following choices: A) 11 B) 13 C) 15 D) 18 E) 12

<gadget id="calculator">100 + 35</gadget> <output>135</output> <gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">1 / 90</gadget> <output>1/90 = around 0.011111</output> <gadget id="calculator">135 * (1/90)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">1 / (3/2)</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(2/3) * 18</gadget> <output>12</output> <result>E</result>

E

By selling 18 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 35%?

multiply(divide(const_1, multiply(add(const_100, 35), divide(const_1, subtract(const_100, 10)))), 18)

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

90 % - - - 18 135 % - - - ? 90 / 135 * 18 = 12 answer : e

gain

math_qa__zMBVsn5fGRfEAcUR

How many pieces of 0.35 meteres can be cut from a rod 12.5 meteres long Choose the correct choice from the following. A) 30 B) 40 C) 35 D) 60 E) 70

<gadget id="calculator">12.5 / 0.35</gadget> <output>35.714286</output> <result>C</result>

C

How many pieces of 0.35 meteres can be cut from a rod 12.5 meteres long

divide(12.5, 0.35)

divide(n1,n0)|

"explanation : we need so simple divide 42.5 / 0.85 , = ( 1250 / 35 ) = 35 option c"

physics

math_qa__EkT0NpHVGXtYZPvv

In a class,7 students like to play Basketball and 5 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? Select the correct option A) 12 B) 15 C) 16 D) 9 E) 22

<gadget id="calculator">7 + 5</gadget> <output>12</output> <gadget id="calculator">12 - 3</gadget> <output>9</output> <result>D</result>

D

In a class,7 students like to play Basketball and 5 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?

subtract(add(7, 5), 3)

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

"draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 5 - 3 = 9 d )"

other

math_qa__knvHKyWBViWOmG1E

8 men can dig a pit in 20 days.If a men work half as much again as a boy,then 4 men and 9 boys can dig a similar pit.Fint the days for 15 boys can dig? Choose one A) 17 B) 10 C) 15 D) 20 E) 16

<gadget id="calculator">15 - 9</gadget> <output>6</output> <gadget id="calculator">6 / 4</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">8 * (3/2)</gadget> <output>12</output> <gadget id="calculator">12 * 20</gadget> <output>240</output> <gadget id="calculator">240 / 15</gadget> <output>16</output> <result>E</result>

E

8 men can dig a pit in 20 days.If a men work half as much again as a boy,then 4 men and 9 boys can dig a similar pit.Fint the days for 15 boys can dig?

divide(multiply(multiply(8, divide(subtract(15, 9), 4)), 20), 15)

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

1 man = 3 / 2 boys ( 4 men + 9 boys ) = 15 boys 8 men = [ ( 3 / 2 ) + 8 ] = 12 boys now , 12 boys can dig the pit in 20 days . 15 boys can dig = 16 days . answer is option e

physics

math_qa__CgjTc6WdolmYHz9Y

A man invests in a 16% stock at 128. The interest obtained by him is Pick. A) 22.5 % B) 42.5 % C) 12.5 % D) 62.5 % E) 82.5 %

<gadget id="calculator">16 / 128</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/8) * 100</gadget> <output>25/2 = around 12.5</output> <result>C</result>

C

A man invests in a 16% stock at 128. The interest obtained by him is

multiply(divide(16, 128), const_100)

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

by investing rs 128 , income derived = rs . 16 by investing rs . 100 , income derived = = rs . 12.5 interest obtained = 12.5 % answer : c

gain

math_qa__A2wgiiaiVjwIW4uZ

In what ratio must tea at Rs.60 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.63 per Kg? Choose the correct choice from the following choices A) 3 : 1 B) 3 : 2 C) 4 : 3 D) 7 : 3 E) none

<gadget id="calculator">70 - 63</gadget> <output>7</output> <gadget id="calculator">63 - 60</gadget> <output>3</output> <gadget id="calculator">7 / 3</gadget> <output>7/3 = around 2.333333</output> <result>D</result>

D

In what ratio must tea at Rs.60 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.63 per Kg?

divide(subtract(70, 63), subtract(63, 60))

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

"required ratio = 700 : 300 = 7 : 3 answer d"

other

math_qa__a0s5XPEKhFZotyjy

How many pounds of salt at 80 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb? Choose the correct answer: A) 5 B) 15 C) 40 D) 50 E) 25

<gadget id="calculator">48 * 40</gadget> <output>1_920</output> <gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">120 / 100</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">35 * 40</gadget> <output>1_400</output> <gadget id="calculator">(6/5) * 1_400</gadget> <output>1_680</output> <gadget id="calculator">1_920 - 1_680</gadget> <output>240</output> <gadget id="calculator">80 * (6/5)</gadget> <output>96</output> <gadget id="calculator">96 - 48</gadget> <output>48</output> <gadget id="calculator">240 / 48</gadget> <output>5</output> <result>A</result>

A

How many pounds of salt at 80 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?

divide(subtract(multiply(48, 40), multiply(divide(add(const_100, 20), const_100), multiply(35, 40))), subtract(multiply(80, divide(add(const_100, 20), const_100)), 48))

add(n3,const_100)|multiply(n1,n4)|multiply(n1,n2)|divide(#0,const_100)|multiply(#3,#2)|multiply(n0,#3)|subtract(#1,#4)|subtract(#5,n4)|divide(#6,#7)|

"selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 80 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 80 - 40 ) / ( 40 - 35 ) = 8 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 5 lbs . answer ( a )"

gain

math_qa__2q92jXeFg4PGaDXA

How long does a train 120 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length? Select the correct option: A) 33 B) 72 C) 52 D) 82 E) 62

<gadget id="calculator">120 + 660</gadget> <output>780</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">54 * (5/18)</gadget> <output>15</output> <gadget id="calculator">780 / 15</gadget> <output>52</output> <result>C</result>

C

How long does a train 120 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?

divide(add(120, 660), multiply(54, const_0_2778))

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

explanation : t = ( 660 + 120 ) / 54 * 18 / 5 t = 52 answer : option c

physics

math_qa__5W7M3KO0NoObMRkg

If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10? A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit Choose the correct choice from the following options: A) 8 / 2652 B) 18 / 2652 C) 1 / 2652 D) 12 / 2652 E) 16 / 2652

<gadget id="calculator">4 - 1</gadget> <output>3</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">9 * 2</gadget> <output>18</output> <gadget id="calculator">52 - 1</gadget> <output>51</output> <gadget id="calculator">52 * 51</gadget> <output>2_652</output> <gadget id="calculator">18 / 2_652</gadget> <output>3/442 = around 0.006787</output> <result>B</result>

B

If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10? A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit

divide(multiply(multiply(subtract(4, const_1), subtract(4, const_1)), const_2), multiply(52, subtract(52, const_1)))

subtract(n4,const_1)|subtract(n1,const_1)|multiply(#0,#0)|multiply(n1,#1)|multiply(#2,const_2)|divide(#4,#3)

2 possible cases : king - 10 or 10 - king ( 4 kings and 4 10 ) . either way , the total probability = 2 ( king - 10 ) = 2 ( 4 / 52 * 4 / 51 ) = 18 / 2652 . b is the correct answer .

probability

math_qa__qloDftllHvkakYXB

A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 10 multiples of 14, how many multiples of 7 are there in Q? Pick A) 20 B) 19 C) 18 D) 17 E) 16

<gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">20 - 1</gadget> <output>19</output> <result>B</result>

B

A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 10 multiples of 14, how many multiples of 7 are there in Q?

subtract(multiply(10, const_2), const_1)

multiply(n1,const_2)|subtract(#0,const_1)|

"halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 10 + 9 = 19 . the answer is b ."

physics

math_qa__06rQpF6B1yPc27cB

60 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple? Choose the correct choice: A) 47 B) 46 C) 54 D) 58 E) 67

<gadget id="calculator">60 - 4</gadget> <output>56</output> <gadget id="calculator">56 + 7</gadget> <output>63</output> <gadget id="calculator">10 - 7</gadget> <output>3</output> <gadget id="calculator">63 + 3</gadget> <output>66</output> <result>E</result>

E

60 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple?

add(add(subtract(60, 4), 7), subtract(10, 7))

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

"orange + mango - apple = 7 mango + apple - orange = 10 apple = 60 orange + mango + apple = 4 60 + 10 + 4 - 7 = 67 like apple answer : e"

general

math_qa__BTlBz2hjLJvIMCid

Bhanu spends 30% of his income on petrol on scooter 20% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent? Choose the correct choice: A) 2287 B) 140 C) 128 D) 797 E) 123

<gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">300 / (3/10)</gadget> <output>1_000</output> <gadget id="calculator">1_000 - 300</gadget> <output>700</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">700 * (1/5)</gadget> <output>140</output> <result>B</result>

B

Bhanu spends 30% of his income on petrol on scooter 20% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?

multiply(subtract(divide(300, divide(30, const_100)), 300), divide(20, const_100))

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

"given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 20 % ( 700 ) = rs . 140 answer : b"

gain

math_qa__Cr91Zd5Gkk51NxOw

the average of the first 5 multiples of 9 is : Answers: A) 20 B) 27 C) 28 D) 30 E) none of these

<gadget id="calculator">9 * 2</gadget> <output>18</output> <gadget id="calculator">9 + 18</gadget> <output>27</output> <gadget id="calculator">9 * 3</gadget> <output>27</output> <gadget id="calculator">27 + 27</gadget> <output>54</output> <gadget id="calculator">9 * 4</gadget> <output>36</output> <gadget id="calculator">54 + 36</gadget> <output>90</output> <gadget id="calculator">9 * 5</gadget> <output>45</output> <gadget id="calculator">90 + 45</gadget> <output>135</output> <gadget id="calculator">135 / 5</gadget> <output>27</output> <result>B</result>

B

the average of the first 5 multiples of 9 is :

divide(add(add(add(add(9, multiply(9, const_2)), multiply(9, const_3)), multiply(9, const_4)), multiply(9, 5)), 5)

multiply(n1,const_2)|multiply(n1,const_3)|multiply(n1,const_4)|multiply(n0,n1)|add(n1,#0)|add(#4,#1)|add(#5,#2)|add(#6,#3)|divide(#7,n0)

solution : required average = ( total sum of multiple of 9 ) / 5 = ( 9 + 18 + 27 + 36 + 45 ) / 5 = 27 note that , average of 9 and 45 is also 27 . and average of 18 and 36 is also 27 . answer : option b

general

math_qa__PJtdjm2XYw0Pijj9

13 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type? Pick: A) 80 B) 160 C) 720 D) 1100 E) 2184

<gadget id="calculator">factorial(13)</gadget> <output>6_227_020_800</output> <gadget id="calculator">13 - 2</gadget> <output>11</output> <gadget id="calculator">factorial(11)</gadget> <output>39_916_800</output> <gadget id="calculator">6_227_020_800 / 39_916_800</gadget> <output>156</output> <gadget id="calculator">156 / 2</gadget> <output>78</output> <gadget id="calculator">factorial(8)</gadget> <output>40_320</output> <gadget id="calculator">8 - 2</gadget> <output>6</output> <gadget id="calculator">factorial(6)</gadget> <output>720</output> <gadget id="calculator">40_320 / 720</gadget> <output>56</output> <gadget id="calculator">56 / 2</gadget> <output>28</output> <gadget id="calculator">78 * 28</gadget> <output>2_184</output> <result>E</result>

E

13 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?

multiply(divide(divide(factorial(13), factorial(subtract(13, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2))

factorial(n0)|factorial(n1)|subtract(n0,n2)|subtract(n1,n2)|factorial(#2)|factorial(#3)|divide(#0,#4)|divide(#1,#5)|divide(#6,n2)|divide(#7,n2)|multiply(#8,#9)|

"no . of ways of picking 2 biology books ( from 13 books ) = 13 c 2 = ( 13 * 12 ) / 2 = 78 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 78 * 28 = 2184 ( option e )"

other

math_qa__8KY3AFwbWaQiPLCA

Calculate the share of Y , if Rs. 690 is divided among X, Y and Z in the ratio 5 : 7 : 11? Select. A) 190 B) 160 C) 120 D) 151 E) 150

<gadget id="calculator">5 + 7</gadget> <output>12</output> <gadget id="calculator">12 + 11</gadget> <output>23</output> <gadget id="calculator">690 / 23</gadget> <output>30</output> <gadget id="calculator">30 * 5</gadget> <output>150</output> <result>E</result>

E

Calculate the share of Y , if Rs. 690 is divided among X, Y and Z in the ratio 5 : 7 : 11?

multiply(divide(690, add(add(5, 7), 11)), 5)

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

"5 + 7 + 11 = 23 690 / 23 = 30 so y ' s share = 5 * 30 = 150 answer : e"

general

math_qa__7ZOC1D4OJK5Nkyt8

You hold some gold in a vault as an investment. Over the past year the price of gold increases by 52%. In order to keep your gold in the vault, you must pay 6% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year. Select the correct option A) 42.88 $ B) 43 % C) 45 % D) 45.5 % E) 46.3 %

<gadget id="calculator">52 / 6</gadget> <output>26/3 = around 8.666667</output> <gadget id="calculator">52 - (26/3)</gadget> <output>130/3 = around 43.333333</output> <result>A</result>

A

You hold some gold in a vault as an investment. Over the past year the price of gold increases by 52%. In order to keep your gold in the vault, you must pay 6% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year.

subtract(52, divide(52, 6))

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

( 100 % + 52 % ) * ( 100 % - 6 % ) = 152 * 0.94 = 142.88 % an increase of 42.88 % your gold holdings have increased in value by 42.88 % . the answer is a

gain

math_qa__fd88BGwNLjPCTshH

A sum fetched a total simple interest of Rs. 750 at the rate of 6 p.c.p.a. in 5 years. What is the sum? Choose one: A) 2600 B) 2500 C) 2900 D) 2800 E) 2700

<gadget id="calculator">750 * 100</gadget> <output>75_000</output> <gadget id="calculator">75_000 / 6</gadget> <output>12_500</output> <gadget id="calculator">12_500 / 5</gadget> <output>2_500</output> <result>B</result>

B

A sum fetched a total simple interest of Rs. 750 at the rate of 6 p.c.p.a. in 5 years. What is the sum?

divide(divide(multiply(750, const_100), 6), 5)

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

"sol . principal = rs . [ 100 * 750 / 6 * 5 ] = rs . [ 75000 / 30 ] = rs . 2500 . answer b"

gain

math_qa__FS9DTdTuJ9LhwcmQ

Robert ate 12 chocolates, Nickel ate 3 chocolates. How many more chocolates did Robert ate than nickel? Choose one A) 4 B) 7 C) 9 D) 5 E) 2

<gadget id="calculator">12 - 3</gadget> <output>9</output> <result>C</result>

C

Robert ate 12 chocolates, Nickel ate 3 chocolates. How many more chocolates did Robert ate than nickel?

subtract(12, 3)

subtract(n0,n1)|

12 - 3 = 9 . answer is c

general

math_qa__zVG7bC54bKorOrxt

In what time will a train 140 meters long cross an electric pole, if its speed is 210 km/hr Choose the correct choice from the following choices. A) 5 seconds B) 4.5 seconds C) 3 seconds D) 2.4 seconds E) none of these

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">210 * (5/18)</gadget> <output>175/3 = around 58.333333</output> <gadget id="calculator">140 / (175/3)</gadget> <output>12/5 = around 2.4</output> <result>D</result>

D

In what time will a train 140 meters long cross an electric pole, if its speed is 210 km/hr

divide(140, multiply(210, const_0_2778))

multiply(n1,const_0_2778)|divide(n0,#0)|

"explanation : first convert speed into m / sec speed = 210 * ( 5 / 18 ) = 58 m / sec time = distance / speed = 140 / 58 = 2.4 seconds option d"

physics

math_qa__kKUFHWowEiDHvYv9

There are two cars. One is 300 miles north of the other. Simultaneously, the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour. How many miles apart are the cars after 5 hours? Choose the correct choice from the following answers. A) 300 B) 360 C) 400 D) 450 E) 500

<gadget id="calculator">60 * 5</gadget> <output>300</output> <gadget id="calculator">20 * 5</gadget> <output>100</output> <gadget id="calculator">300 + 100</gadget> <output>400</output> <gadget id="calculator">400 ** 2</gadget> <output>160_000</output> <gadget id="calculator">300 ** 2</gadget> <output>90_000</output> <gadget id="calculator">160_000 + 90_000</gadget> <output>250_000</output> <gadget id="calculator">250_000 ** (1/2)</gadget> <output>500</output> <result>E</result>

E

There are two cars. One is 300 miles north of the other. Simultaneously, the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour. How many miles apart are the cars after 5 hours?

sqrt(add(power(add(multiply(60, 5), multiply(20, 5)), const_2), power(multiply(60, 5), const_2)))

multiply(n2,n3)|multiply(n1,n3)|add(#0,#1)|power(#0,const_2)|power(#2,const_2)|add(#4,#3)|sqrt(#5)

here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 400 and a height of 300 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 300 lines up with the ' 3 ' and the 400 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 100 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 300 / 400 / 500 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : e

physics

math_qa__CG1sCaNfryDQOsPp

An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value? Choose the correct choice from the following choices: A) 3 B) 4 C) 6 D) 9 E) 12

<gadget id="calculator">log(3)</gadget> <output>log(3) = around 1.098612</output> <gadget id="calculator">34.1 / 100</gadget> <output>0.341</output> <gadget id="calculator">1 + 0.341</gadget> <output>1.341</output> <gadget id="calculator">log(1.341)</gadget> <output>0.293416</output> <gadget id="calculator">log(3) / 0.293416</gadget> <output>3.40813043596805*log(3) = around 3.744214</output> <gadget id="calculator">floor(3.40813043596805*log(3))</gadget> <output>3</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <result>B</result>

B

An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?

add(floor(divide(log(const_3), log(add(const_1, divide(34.1, const_100))))), const_1)

divide(n0,const_100)|log(const_3)|add(#0,const_1)|log(#2)|divide(#1,#3)|floor(#4)|add(#5,const_1)

assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 34.1 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x ; or in other words n = 4 answer : b

gain

math_qa__fGUf9bUEriV4FBAB

The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross-section is 630 square meters, what is the depth of the channel (in meters)? Choose the correct choice from the following choices: A) 50 B) 60 C) 70 D) 80 E) 90

<gadget id="calculator">12 + 6</gadget> <output>18</output> <gadget id="calculator">18 / 2</gadget> <output>9</output> <gadget id="calculator">630 / 9</gadget> <output>70</output> <result>C</result>

C

The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross-section is 630 square meters, what is the depth of the channel (in meters)?

divide(630, divide(add(12, 6), const_2))

add(n0,n1)|divide(#0,const_2)|divide(n2,#1)|

"1 / 2 * d * ( 12 + 6 ) = 630 d = 70 the answer is c ."

physics

math_qa__IqHkEfGDgmnL3Npz

A bicycle wheel has a diameter of 0.51m. How many complete revolutions does it make in 1km? Choose the correct choice. A) 246 B) 448 C) 1408 D) 710 E) 624

<gadget id="calculator">1_000 * 1</gadget> <output>1_000</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 + 2</gadget> <output>14</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">8 + 2</gadget> <output>10</output> <gadget id="calculator">10 ** 2</gadget> <output>100</output> <gadget id="calculator">14 / 100</gadget> <output>7/50 = around 0.14</output> <gadget id="calculator">3 + (7/50)</gadget> <output>157/50 = around 3.14</output> <gadget id="calculator">(157/50) * 0.51</gadget> <output>1.6014</output> <gadget id="calculator">1_000 / 1.6014</gadget> <output>624.453603</output> <result>E</result>

E

A bicycle wheel has a diameter of 0.51m. How many complete revolutions does it make in 1km?

divide(multiply(const_1000, 1), multiply(add(const_3, divide(add(multiply(const_3, const_4), const_2), power(add(multiply(const_4, const_2), const_2), const_2))), 0.51))

multiply(n1,const_1000)|multiply(const_3,const_4)|multiply(const_2,const_4)|add(#1,const_2)|add(#2,const_2)|power(#4,const_2)|divide(#3,#5)|add(#6,const_3)|multiply(n0,#7)|divide(#0,#8)

1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.51 m ) = 624.5 . hence 624 complete revolutions . answer e

physics

math_qa__z3AMU1TMmFd2ZMkk

Triangle ATriangle B are similar triangles with areas 1536 units square and 1734 units square respectively. The ratio of there corresponding height would be Choose one A) 9 : 10 B) 17 : 19 C) 23 : 27 D) 16 : 17 E) 15 : 23

<gadget id="calculator">1_536 / 1_734</gadget> <output>256/289 = around 0.885813</output> <gadget id="calculator">(256/289) ** (1/2)</gadget> <output>16/17 = around 0.941176</output> <result>D</result>

D

Triangle ATriangle B are similar triangles with areas 1536 units square and 1734 units square respectively. The ratio of there corresponding height would be

sqrt(divide(1536, 1734))

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

"let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1536 / 1734 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 6 ) / ( 17 * 17 * 7 ) ( x ^ 2 / y ^ 2 ) = 16 ^ 2 / 17 ^ 2 x / y = 16 / 17 ans = d"

geometry

math_qa__PFGingoPMI7vBhGf

X can finish a work in 20 days. Y can finish the same work in 16 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work? Choose the correct choice from the following: A) 2 B) 3 C) 9 D) 5 E) 8

<gadget id="calculator">1 / 16</gadget> <output>1/16 = around 0.0625</output> <gadget id="calculator">12 * (1/16)</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 / 20</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/4) / (1/20)</gadget> <output>5</output> <result>D</result>

D

X can finish a work in 20 days. Y can finish the same work in 16 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?

divide(subtract(const_1, multiply(12, divide(const_1, 16))), divide(const_1, 20))

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

"work done by x in 1 day = 1 / 20 work done by y in 1 day = 1 / 16 work done by y in 12 days = 12 / 16 = 3 / 4 remaining work = 1 – 3 / 4 = 1 / 4 number of days in which x can finish the remaining work = ( 1 / 4 ) / ( 1 / 20 ) = 5 d"

physics

math_qa__TSQ3YKNUtIjQQB0y

If the Average of 10 consecutive integers is 20.5 then the 10th integer is :- Choose one: A) 15 B) 20 C) 23 D) 24 E) 25

<gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">20.5 - 20</gadget> <output>0.5</output> <gadget id="calculator">0.5 * 10</gadget> <output>5</output> <gadget id="calculator">20 + 5</gadget> <output>25</output> <result>E</result>

E

If the Average of 10 consecutive integers is 20.5 then the 10th integer is :-

add(multiply(10, const_2), multiply(subtract(20.5, multiply(10, const_2)), 10))

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

the average falls between the 5 th and 6 th integers , integer 5 = 20 , integer 6 = 21 . counting up to the tenth integer we get 25 . answer : e

general

math_qa__atQ7aS7HKAqjf7j1

Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 55 marks. How many sums did Sandy get correct? Choose the correct choice: A) 19 B) 21 C) 23 D) 25 E) 27

<gadget id="calculator">2 * 30</gadget> <output>60</output> <gadget id="calculator">60 + 55</gadget> <output>115</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">115 / 5</gadget> <output>23</output> <result>C</result>

C

Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 55 marks. How many sums did Sandy get correct?

divide(add(multiply(2, 30), 55), add(2, 3))

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

"let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 55 5 x = 115 x = 23 the answer is c ."

general

math_qa__TsGlG24sG8yaczYA

A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money M did Bob receive? Choose the correct choice from the following answers. A) 20 B) 22 C) 24 D) 26 E) 52

<gadget id="calculator">32 * 2</gadget> <output>64</output> <gadget id="calculator">64 / 3</gadget> <output>64/3 = around 21.333333</output> <result>B</result>

B

A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money M did Bob receive?

divide(multiply(32, const_2), const_3)

multiply(n2,const_2)|divide(#0,const_3)|

"notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ m = 20 answer : b"

general

math_qa__e6OnxgzCChCpOPct

Last year Elaine spent 10% of her annual earnings on rent. This year she earned 15% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year? Select. A) 252.5 B) 364.5 C) 367.5 D) 375 E) 345

<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">(3/20) + 1</gadget> <output>23/20 = around 1.15</output> <gadget id="calculator">(23/20) * 30</gadget> <output>69/2 = around 34.5</output> <gadget id="calculator">(69/2) / 10</gadget> <output>69/20 = around 3.45</output> <gadget id="calculator">(69/20) * 100</gadget> <output>345</output> <result>E</result>

E

Last year Elaine spent 10% of her annual earnings on rent. This year she earned 15% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?

multiply(divide(multiply(add(divide(15, const_100), const_1), 30), 10), const_100)

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

"for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 10 of this on rent . this year she earned 15 % more , or $ 115 . she would ' ve spent 30 % of this on rent , or $ 34.5 do $ 34.5 / $ 10 this will give you 345 % e is the correct answer ."

gain

math_qa__AICgEapXBMb2I5q0

When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x? Choose the correct choice from the following choices: A) - 4 B) - 2 C) 5 D) 13 E) 22

<gadget id="calculator">16 + 4</gadget> <output>20</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">20 / 4</gadget> <output>5</output> <result>C</result>

C

When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x?

divide(add(16, 4), add(3, const_1))

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

"the equation that can be formed is : 3 x - 4 = 16 - x or , 4 x = 20 or , x = 5 . answer : c"

general

math_qa__txX6yTxuilkAJOFp

In a certain school, 25% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 36. What is the total number of students in the school? Choose the correct choice from the following choices: A) 72 B) 80 C) 120 D) 150 E) 100

<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">36 * (2/3)</gadget> <output>24</output> <gadget id="calculator">36 + 24</gadget> <output>60</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 - (1/4)</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">60 / (3/4)</gadget> <output>80</output> <result>B</result>

B

In a certain school, 25% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 36. What is the total number of students in the school?

divide(add(36, multiply(36, divide(2, 3))), subtract(const_1, divide(25, const_100)))

divide(n3,n4)|divide(n0,const_100)|multiply(n6,#0)|subtract(const_1,#1)|add(n6,#2)|divide(#4,#3)|

"explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 25 ) % of x = 75 % of x . 75 % of x = 36 + 2 / 3 of 36 75 / 100 x = 60 x = 80 . answer : option b"

general

math_qa__XYHiUyugAV0HhMVJ

How many seconds will a 600 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? Choose the correct choice from the following: A) 48 B) 36 C) 26 D) 11 E) 18

<gadget id="calculator">63 - 3</gadget> <output>60</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">600 / (50/3)</gadget> <output>36</output> <result>B</result>

B

How many seconds will a 600 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?

divide(600, multiply(subtract(63, 3), const_0_2778))

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

"explanation : here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 36 sec . answer : b"

physics

math_qa__5ifAlfLWHR4uRWSa

The radius of a cylindrical vessel is 7cm and height is 1cm. Find the whole surface of the cylinder? Choose the correct choice from the following answers. A) 352 B) 771 C) 440 D) 767 E) 1981

<gadget id="calculator">2 * pi * 7 * (7 + 1)</gadget> <output>112*pi = around 351.858377</output> <result>A</result>

A

The radius of a cylindrical vessel is 7cm and height is 1cm. Find the whole surface of the cylinder?

surface_cylinder(7, 1)

surface_cylinder(n0,n1)|

"r = 7 h = 1 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 8 ) = 352 answer : a"

geometry

math_qa__BbEYaTMRi2Hbatyn

Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 5600 envelopes. Pick one. A) 2 B) 3 C) 4 D) 6 E) 60 / 7

<gadget id="calculator">6_000 / 2.5</gadget> <output>2_400</output> <gadget id="calculator">3_000 / 1</gadget> <output>3_000</output> <gadget id="calculator">6_000 / 3</gadget> <output>2_000</output> <gadget id="calculator">3_000 - 2_000</gadget> <output>1_000</output> <gadget id="calculator">2_400 - 1_000</gadget> <output>1_400</output> <gadget id="calculator">5_600 / 1_400</gadget> <output>4</output> <result>C</result>

C

Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 5600 envelopes.

divide(5600, subtract(divide(6000, 2.5), subtract(divide(3000, 1), divide(6000, 3))))

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

"you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 5600 envelopes b will take 5600 / 1400 hrs = 4 hrs so the answer is choice c"

physics

math_qa__GbQ6MHcbkYhikr2P

What is the difference between the place value and face value of 4 in the numeral 46? Answers: A) 36 B) 45 C) 52 D) 44 E) 39

<gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">40 - 4</gadget> <output>36</output> <result>A</result>

A

What is the difference between the place value and face value of 4 in the numeral 46?

subtract(multiply(4, const_10), 4)

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

difference between the place value and face value of 4 = 40 - 4 = 36 answer is a

general

math_qa__PXSC5DHrFXjcPRL5

A person travels from P to Q a speed of 30 km/hr and returns by increasing his speed by 30%. What is his average speed for both the trips? Choose the correct choice: A) 33 B) 77 C) 48 D) 99 E) 34.5

<gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">1 + (3/10)</gadget> <output>13/10 = around 1.3</output> <gadget id="calculator">30 * (13/10)</gadget> <output>39</output> <gadget id="calculator">39 + 30</gadget> <output>69</output> <gadget id="calculator">69 / 2</gadget> <output>69/2 = around 34.5</output> <result>E</result>

E

A person travels from P to Q a speed of 30 km/hr and returns by increasing his speed by 30%. What is his average speed for both the trips?

divide(add(multiply(30, add(const_1, divide(30, const_100))), 30), const_2)

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

"speed on return trip = 130 % of 30 = 39 km / hr . average speed of trip = 30 + 39 / 2 = 69 / 2 = 34.5 km / hr answer : e"

general

math_qa__RFieCaXeEGrqh7SH

The sum of all the integers f such that -26 < f < 24 is Choose the correct option A) 0 B) - 2 C) - 25 D) - 49 E) - 51

<gadget id="calculator">-26</gadget> <output>-26</output> <gadget id="calculator">(-26) + 1</gadget> <output>-25</output> <gadget id="calculator">(-25) + 1</gadget> <output>-24</output> <gadget id="calculator">(-25) + (-24)</gadget> <output>-49</output> <result>D</result>

D

The sum of all the integers f such that -26 < f < 24 is

add(add(negate(26), const_1), add(add(negate(26), const_1), const_1))

negate(n0)|add(#0,const_1)|add(#1,const_1)|add(#1,#2)|

"easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 f = - 49 . d is the answer ."

general

math_qa__uSuKzWQrkUhe5H9Q

The average expenditure of a labourer for 6 months was 70 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i Choose one A) 69 B) 72 C) 75 D) 78 E) 80

<gadget id="calculator">70 * 6</gadget> <output>420</output> <gadget id="calculator">60 * 4</gadget> <output>240</output> <gadget id="calculator">420 + 240</gadget> <output>660</output> <gadget id="calculator">660 + 30</gadget> <output>690</output> <gadget id="calculator">6 + 4</gadget> <output>10</output> <gadget id="calculator">690 / 10</gadget> <output>69</output> <result>A</result>

A

The average expenditure of a labourer for 6 months was 70 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i

divide(add(add(multiply(70, 6), multiply(60, 4)), 30), add(6, 4))

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

"income of 6 months = ( 6 × 70 ) – debt = 420 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 690 average monthly income = 690 ÷ 10 = 69 answer a"

general

math_qa__inFBz3bRGup7ooFt

A student chose a number, multiplied it by 8, then subtracted 138 from the result and got 102. What was the number he chose? Choose the correct choice: A) 30 B) 120 C) 130 D) 140 E) 150

<gadget id="calculator">102 + 138</gadget> <output>240</output> <gadget id="calculator">240 / 8</gadget> <output>30</output> <result>A</result>

A

A student chose a number, multiplied it by 8, then subtracted 138 from the result and got 102. What was the number he chose?

divide(add(102, 138), 8)

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

"solution : let xx be the number he chose , then 8 ⋅ x − 138 = 102 8 x = 240 x = 30 answer a"

general

math_qa__a3jMbvIDkD4XDQS3

a man has rs . 192 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ? Pick: A) 37 B) 36 C) 22 D) 90 E) 28

<gadget id="calculator">1 + 5</gadget> <output>6</output> <gadget id="calculator">6 + 10</gadget> <output>16</output> <gadget id="calculator">192 / 16</gadget> <output>12</output> <gadget id="calculator">12 + 12</gadget> <output>24</output> <gadget id="calculator">24 + 12</gadget> <output>36</output> <result>B</result>

B

a man has rs . 192 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?

add(add(divide(192, add(add(const_1, 5), 10)), divide(192, add(add(const_1, 5), 10))), divide(192, add(add(const_1, 5), 10)))

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

let number of notes of each denomination be x . then , x + 5 x + 10 x = 192 16 x = 192 x = 12 . hence , total number of notes = 3 x = 36 . answer : b

general

math_qa__UyIS3s365eVLxLop

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat? Answers: A) 6 B) 12 C) 14 D) 16 E) 28

<gadget id="calculator">40 - 20</gadget> <output>20</output> <gadget id="calculator">20 * 8</gadget> <output>160</output> <gadget id="calculator">160 / 10</gadget> <output>16</output> <result>D</result>

D

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat?

divide(multiply(subtract(40, 20), 8), 10)

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

"equate the fat : 0.1 x + 0.4 * 8 = 0.2 ( x + 8 ) - - > x = 16 . answer : d ."

general

math_qa__7E5kjvpoRdBbRKJf

The price of lunch for 15 people was $211.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? Pick: A) $ 11.73 B) $ 12.78 C) $ 13.80 D) $ 14.00 E) $ 15.87

<gadget id="calculator">100 + 15</gadget> <output>115</output> <gadget id="calculator">211 / 115</gadget> <output>211/115 = around 1.834783</output> <gadget id="calculator">(211/115) * 100</gadget> <output>4_220/23 = around 183.478261</output> <gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">(4_220/23) * (1/15)</gadget> <output>844/69 = around 12.231884</output> <result>B</result>

B

The price of lunch for 15 people was $211.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?

multiply(multiply(divide(211.00, add(const_100, 15)), const_100), divide(const_1, 15))

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

"take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 211 is for 115 then we have to calculate for 100 for 115 211 for 100 x so by cross multiplication we get 115 x = 100 * 211 = > x = 100 * 211 / 110 by simplifying we get x as 191.81 which is the price of lunch before gratuity so the gratuity is 19.19 so as the question ask the average price person excluding gratuity is 191.81 / 15 = 12.78 so our answer is b )"

general

math_qa__dusZ4gOSt7lL7S4t

A part-time employee’s hourly wage was increased by 20%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased? Pick one. A) 9 % B) 17 % C) 25 % D) 50 % E) 100 %

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">20 + 100</gadget> <output>120</output> <gadget id="calculator">120 / 100</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">(1/5) / (6/5)</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/6) * 100</gadget> <output>50/3 = around 16.666667</output> <result>B</result>

B

A part-time employee’s hourly wage was increased by 20%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?

multiply(divide(divide(20, const_100), divide(add(20, const_100), const_100)), const_100)

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

"let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 20 % wage increase , the employee makes $ 1.20 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.20 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.20 to get : new # of hours = 100 / 1.20 ≈ 83 hours so , the number of hours decreases from 100 hours to ( approximately ) 83 hours . this represents a 17 % decrease ( approximately ) . answer : b"

general

math_qa__R97e5a8lg75m9fRq

The ratio of three numbers is 1:2:4 and the sum of their squares is 4725. The sum of the numbers is? Options A) 10 B) 12 C) 15 D) 14 E) 9

<gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">1 ** 2</gadget> <output>1</output> <gadget id="calculator">2 ** 2</gadget> <output>4</output> <gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">16 + 5</gadget> <output>21</output> <gadget id="calculator">4_725 / 21</gadget> <output>225</output> <gadget id="calculator">225 ** (1/2)</gadget> <output>15</output> <result>C</result>

C

The ratio of three numbers is 1:2:4 and the sum of their squares is 4725. The sum of the numbers is?

sqrt(divide(4725, add(power(4, const_2), add(power(1, const_2), power(2, const_2)))))

power(n0,const_2)|power(n1,const_2)|power(n2,const_2)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)

let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 4725 21 x ^ 2 = 4725 x ^ 2 = 225 x = 15 answer is c

other

math_qa__cBbTAjunbOW7vE6Q

Madhav ranks seventeenth in a class of thirtyone. What is his rank from the last? Choose the correct answer: A) 13 B) 14 C) 15 D) 16 E) 17

<gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 + 4</gadget> <output>16</output> <gadget id="calculator">1 + 16</gadget> <output>17</output> <gadget id="calculator">12 + 17</gadget> <output>29</output> <gadget id="calculator">29 + 2</gadget> <output>31</output> <gadget id="calculator">31 - 17</gadget> <output>14</output> <gadget id="calculator">14 + 1</gadget> <output>15</output> <result>C</result>

C

Madhav ranks seventeenth in a class of thirtyone. What is his rank from the last?

add(subtract(add(add(multiply(const_3, const_4), add(const_1, add(multiply(const_3, const_4), const_4))), const_2), add(const_1, add(multiply(const_3, const_4), const_4))), const_1)

multiply(const_3,const_4)|add(#0,const_4)|add(#1,const_1)|add(#2,#0)|add(#3,const_2)|subtract(#4,#2)|add(#5,const_1)

( rank from top ) + ( rank from bottom ) - 1 = total students 17 + x - 1 = 31 x = 15 answer : c

other

math_qa__wQyO05S3T4Pc4mmv

What positive number, when squared, is equal to the cube of the positive square root of 17? Select A) 64 B) 32 C) 8 D) 4 E) 2

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">17 ** (1/2)</gadget> <output>sqrt(17) = around 4.123106</output> <gadget id="calculator">(sqrt(17)) ** 3</gadget> <output>17*sqrt(17) = around 70.092796</output> <gadget id="calculator">(17*sqrt(17)) ** (1/2)</gadget> <output>17**(3/4) = around 8.372144</output> <result>C</result>

C

What positive number, when squared, is equal to the cube of the positive square root of 17?

sqrt(power(power(17, divide(const_1, const_2)), const_3))

divide(const_1,const_2)|power(n0,#0)|power(#1,const_3)|sqrt(#2)

let the positive number be x x ^ 2 = ( ( 17 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c

geometry

math_qa__lq29CgmrhI7te1bJ

The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is: Select the correct option A) rs . 72 B) rs . 60 C) rs . 75 D) rs . 76 E) none

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 + (1/5)</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">75 * (6/5)</gadget> <output>90</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">90 * (4/5)</gadget> <output>72</output> <result>A</result>

A

The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

multiply(multiply(75, add(const_1, divide(20, const_100))), subtract(const_1, divide(20, const_100)))

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

solution : initial cost = rs . 75 after 20 % increase in the cost , it becomes , ( 75 + 20 % of 75 ) = rs . 90 now , cost is decreased by 20 % , so cost will become , ( 90 - 20 % of 90 ) = rs . 72 . so , present cost is rs . 72 . mind calculation method : 75 - - - - - 20 % ↑ - - → 90 - - - - - 20 % ↓ - - - - - → 72 . answer : option a

gain

math_qa__KeLZyP73MW3uLHXp

Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 100 km and the other at the rate of 120 kmph. In what time will they be completely clear of each other from the moment they meet? Choices A) 4.85 B) 7.85 C) 4.51 D) 5.85 E) 6.15

<gadget id="calculator">111 + 165</gadget> <output>276</output> <gadget id="calculator">100 + 120</gadget> <output>220</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">220 * (5/18)</gadget> <output>550/9 = around 61.111111</output> <gadget id="calculator">276 / (550/9)</gadget> <output>1_242/275 = around 4.516364</output> <result>C</result>

C

Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 100 km and the other at the rate of 120 kmph. In what time will they be completely clear of each other from the moment they meet?

divide(add(111, 165), multiply(add(100, 120), const_0_2778))

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

"t = ( 111 + 165 ) / ( 100 + 120 ) * 18 / 5 t = 4.51 answer : c"

physics

math_qa__cXqtROEnR7tTk5ns

In how many years will a sum of money be doubled given that the annual interest on it is 10%? Choose the correct choice from the following answers A) 11 B) 14 C) 13 D) 15 E) 10

<gadget id="calculator">100 / 10</gadget> <output>10</output> <result>E</result>

E

In how many years will a sum of money be doubled given that the annual interest on it is 10%?

divide(const_100, 10)

divide(const_100,n0)

p = ( p * 10 * r ) / 100 r = 10 % answer : e

gain

math_qa__aSQNuh0CHPsSuS9E

Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=2/5, what is the ratio of rectangle A’s area to rectangle B’s area? Options: A) 2 / 5 B) 2 / 25 C) 5 / 2 D) 5 / 4 E) 4 / 25

<gadget id="calculator">2 ** 2</gadget> <output>4</output> <gadget id="calculator">5 ** 2</gadget> <output>25</output> <gadget id="calculator">4 / 25</gadget> <output>4/25 = around 0.16</output> <result>E</result>

E

Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=2/5, what is the ratio of rectangle A’s area to rectangle B’s area?

divide(power(2, const_2), power(5, const_2))

power(n0,const_2)|power(n1,const_2)|divide(#0,#1)|

"the area of rectangle a is ab . c = 5 a / 2 and d = 5 b / 2 . the area of rectangle b is cd = 25 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 4 ) = 4 / 25 . the answer is e ."

geometry

math_qa__rHYl1K4Eu5QPwN7V

If a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours, what is the speed of the boat and the river? Pick one: A) 21 , 21 B) 9 , 21 C) 21 , 9 D) 9 , 9 E) 20 , 8

<gadget id="calculator">48 / 4</gadget> <output>12</output> <gadget id="calculator">600 / 20</gadget> <output>30</output> <gadget id="calculator">12 + 30</gadget> <output>42</output> <gadget id="calculator">42 / 2</gadget> <output>21</output> <result>C</result>

C

If a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours, what is the speed of the boat and the river?

divide(add(divide(48, 4), divide(600, 20)), const_2)

divide(n2,n3)|divide(n0,n1)|add(#0,#1)|divide(#2,const_2)|

"explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 30 ; us = 12 x = ( 30 + 12 ) / 2 = 42 / 2 = 21 km / hr y = ( 30 - 12 ) / 2 = 18 / 2 = 9 km / hr answer : c"

physics

math_qa__qQI0jkNlMZ72mTuD

A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? Select: A) 333 sec B) 190 sec C) 176 sec D) 2687 sec E) 1876 sec

<gadget id="calculator">1_200 + 700</gadget> <output>1_900</output> <gadget id="calculator">1_200 / 120</gadget> <output>10</output> <gadget id="calculator">1_900 / 10</gadget> <output>190</output> <result>B</result>

B

A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?

divide(add(1200, 700), divide(1200, 120))

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

"l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1900 m t = d / s t = 1900 / 10 t = 190 sec answer : b"

physics

math_qa__PVS9TYkzAB8Prygc

Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a even number written on it? Choose the correct choice from the following answers: A) 1 / 12 B) 1 / 10 C) 1 / 8 D) 1 / 42 E) 5 / 9

<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">9 + 1</gadget> <output>10</output> <gadget id="calculator">5 / 10</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">5 - 1</gadget> <output>4</output> <gadget id="calculator">10 - 1</gadget> <output>9</output> <gadget id="calculator">4 / 9</gadget> <output>4/9 = around 0.444444</output> <gadget id="calculator">(1/2) * (4/9)</gadget> <output>2/9 = around 0.222222</output> <gadget id="calculator">4 - 1</gadget> <output>3</output> <gadget id="calculator">9 - 1</gadget> <output>8</output> <gadget id="calculator">3 / 8</gadget> <output>3/8 = around 0.375</output> <gadget id="calculator">(2/9) * (3/8)</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">3 - 1</gadget> <output>2</output> <gadget id="calculator">8 - 1</gadget> <output>7</output> <gadget id="calculator">2 / 7</gadget> <output>2/7 = around 0.285714</output> <gadget id="calculator">(1/12) * (2/7)</gadget> <output>1/42 = around 0.02381</output> <result>D</result>

D

Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a even number written on it?

multiply(multiply(multiply(divide(add(const_4, const_1), add(9, const_1)), divide(subtract(add(const_4, const_1), const_1), subtract(add(9, const_1), const_1))), divide(subtract(subtract(add(const_4, const_1), const_1), const_1), subtract(subtract(add(9, const_1), const_1), const_1))), divide(subtract(subtract(subtract(add(const_4, const_1), const_1), const_1), const_1), subtract(subtract(subtract(add(9, const_1), const_1), const_1), const_1)))

add(const_1,const_4)|add(n1,const_1)|divide(#0,#1)|subtract(#0,const_1)|subtract(#1,const_1)|divide(#3,#4)|subtract(#3,const_1)|subtract(#4,const_1)|divide(#6,#7)|multiply(#2,#5)|subtract(#6,const_1)|subtract(#7,const_1)|divide(#10,#11)|multiply(#8,#9)|multiply(#12,#13)

key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 = 1 / 42 d

gain

math_qa__qL6SWFA1dKUYm7Bw

Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 70 km more than the other. What is the distance between the two stations? Choose the correct choice from the following answers: A) 630 km B) 540 km C) 276 km D) 178 km E) 176 km

<gadget id="calculator">20 + 25</gadget> <output>45</output> <gadget id="calculator">25 - 20</gadget> <output>5</output> <gadget id="calculator">70 / 5</gadget> <output>14</output> <gadget id="calculator">45 * 14</gadget> <output>630</output> <result>A</result>

A

Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 70 km more than the other. What is the distance between the two stations?

multiply(add(20, 25), divide(70, subtract(25, 20)))

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

"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 70 km more than the other , 25 x â € “ 20 x = 70 5 x = 70 x = 14 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 14 = 630 km . answer : a"

general

math_qa__k1QiKDuMoP9oToCo

The average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women? Choose the correct choice A) 21 B) 32 C) 30 D) 41 E) 37

<gadget id="calculator">10 + 12</gadget> <output>22</output> <gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">22 + 20</gadget> <output>42</output> <gadget id="calculator">42 / 2</gadget> <output>21</output> <result>A</result>

A

The average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women?

divide(add(add(10, 12), multiply(10, 2)), const_2)

add(n2,n3)|multiply(n0,n1)|add(#0,#1)|divide(#2,const_2)|

"10 + 12 + 10 * 2 = 42 / 2 = 21 answer : a"

general

math_qa__5L6XFBb7Owzdj4oP

a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives : Choose the correct choice from the following answers: A) 8400 B) 14703 C) 37798 D) 13777 E) 14778

<gadget id="calculator">4_000 + 5_000</gadget> <output>9_000</output> <gadget id="calculator">9_000 + 5_000</gadget> <output>14_000</output> <gadget id="calculator">50_000 - 14_000</gadget> <output>36_000</output> <gadget id="calculator">36_000 / 3</gadget> <output>12_000</output> <gadget id="calculator">12_000 / 50_000</gadget> <output>6/25 = around 0.24</output> <gadget id="calculator">35_000 * (6/25)</gadget> <output>8_400</output> <result>A</result>

A

a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives :

multiply(35000, divide(divide(subtract(50000, add(add(4000, 5000), 5000)), const_3), 50000))

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

explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 * 12 / 50 ) = rs . 8,400 . answer : a )

general

math_qa__gmoZDdxq9N5uJ1yD

Due to construction, the speed limit along an 6-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? Pick one: A) 4 B) 8 C) 10 D) 15 E) 24

<gadget id="calculator">55 + 6</gadget> <output>61</output> <gadget id="calculator">61 - 1</gadget> <output>60</output> <gadget id="calculator">6 / 35</gadget> <output>6/35 = around 0.171429</output> <gadget id="calculator">6 / 55</gadget> <output>6/55 = around 0.109091</output> <gadget id="calculator">(6/35) - (6/55)</gadget> <output>24/385 = around 0.062338</output> <gadget id="calculator">60 * (24/385)</gadget> <output>288/77 = around 3.74026</output> <gadget id="calculator">max(288/77, 4)</gadget> <output>4</output> <result>A</result>

A

Due to construction, the speed limit along an 6-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?

max(multiply(subtract(add(55, 6), const_1), subtract(divide(6, 35), divide(6, 55))), const_4)

add(n0,n1)|divide(n0,n2)|divide(n0,n1)|subtract(#0,const_1)|subtract(#1,#2)|multiply(#3,#4)|max(#5,const_4)

6 / 35 - 6 / 55 = 6 / 5 * ( 11 - 7 ) / 77 = 6 / 5 * 4 / 77 * 60 min = 6 * 12 * 4 / 77 = 288 / 77 ~ 3.7 answer - a

physics

math_qa__L0CqU4WzYk5rIK2p

A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 21 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store? Choose the correct choice from the following: A) 36 B) 42 C) 45 D) 48 E) 51

<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (1/3)</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(2/3) * 21</gadget> <output>14</output> <gadget id="calculator">1 - (2/3)</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">14 / (1/3)</gadget> <output>42</output> <result>B</result>

B

A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 21 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?

divide(multiply(subtract(1, divide(1, 3)), 21), subtract(1, subtract(1, divide(1, 3))))

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

"let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 21 r / 2 = 21 r = 42 the answer is b ."

general

math_qa__a7tRyQ6luwo1sJON

Find a number such that when 15 is subtracted from 7 times the number, the Result is 10 more than twice the number. Choose the correct choice from the following answers: A) 1 B) 4 C) 5 D) 0 E) 3

<gadget id="calculator">15 + 10</gadget> <output>25</output> <gadget id="calculator">7 - 2</gadget> <output>5</output> <gadget id="calculator">25 / 5</gadget> <output>5</output> <result>C</result>

C

Find a number such that when 15 is subtracted from 7 times the number, the Result is 10 more than twice the number.

divide(add(15, 10), subtract(7, const_2))

add(n0,n2)|subtract(n1,const_2)|divide(#0,#1)

let the number be x . then , 7 x - 15 = 2 x + 10 = > 5 x = 25 = > x = 5 . hence , the required number is 5 . answer is c .

general

math_qa__fo64R1spdEfRG9H4

Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper? Choose the correct choice from the following answers: A) 1000 B) 1055 C) 965 D) 1075 E) 1080

<gadget id="calculator">8 * 70</gadget> <output>560</output> <gadget id="calculator">9 * 45</gadget> <output>405</output> <gadget id="calculator">560 + 405</gadget> <output>965</output> <result>C</result>

C

Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper?

add(multiply(8, 70), multiply(9, 45))

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

"cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 45 × 9 = 405 . total cost he has to pay = 560 + 405 = 965 . c )"

gain

math_qa__AZGQ2avsku8Rex8I

The average monthly income of A and B is Rs. 4050. The average monthly income of B and C is Rs. 5250 and the average monthly income of A and C is Rs. 4200. What is the monthly income of A? Choose the correct option. A) 2000 B) 2500 C) 3000 D) 3500 E) 4000

<gadget id="calculator">2 * 4_050</gadget> <output>8_100</output> <gadget id="calculator">2 * 5_250</gadget> <output>10_500</output> <gadget id="calculator">2 * 4_200</gadget> <output>8_400</output> <gadget id="calculator">10_500 - 8_400</gadget> <output>2_100</output> <gadget id="calculator">8_100 + 2_100</gadget> <output>10_200</output> <gadget id="calculator">10_200 / 2</gadget> <output>5_100</output> <gadget id="calculator">8_100 - 5_100</gadget> <output>3_000</output> <result>C</result>

C

The average monthly income of A and B is Rs. 4050. The average monthly income of B and C is Rs. 5250 and the average monthly income of A and C is Rs. 4200. What is the monthly income of A?

subtract(multiply(const_2, 4050), divide(add(multiply(const_2, 4050), subtract(multiply(const_2, 5250), multiply(const_2, 4200))), const_2))

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

let monthly income of a = x monthly income of b = y monthly income of c = z x + y = 2 × 4050 . . . . ( equation 1 ) y + z = 2 × 5250 . . . . ( equation 2 ) z + x = 2 × 4200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > x + y + x + z - ( y + z ) = ( 2 × 4050 ) + ( 2 × 4200 ) - ( 2 × 5250 ) = > 2 x = 2 ( 4050 + 4200 - 5250 ) = > x = 3000 i . e . , monthly income of a = 3000 answer : c

general

math_qa__jZEKzswMbOl53mht

A merchant marks his goods up by 40% and then offers a discount of 15% on the marked price. What % profit does the merchant make after the discount? Pick one. A) 21 % B) 25 % C) 69 % D) 31 % E) 19 %

<gadget id="calculator">40 + 100</gadget> <output>140</output> <gadget id="calculator">140 * 15</gadget> <output>2_100</output> <gadget id="calculator">2_100 / 100</gadget> <output>21</output> <gadget id="calculator">140 - 21</gadget> <output>119</output> <gadget id="calculator">119 - 100</gadget> <output>19</output> <result>E</result>

E

A merchant marks his goods up by 40% and then offers a discount of 15% on the marked price. What % profit does the merchant make after the discount?

subtract(subtract(add(40, const_100), divide(multiply(add(40, const_100), 15), const_100)), const_100)

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

let the original price be 100 . after 40 % markup , price = 140 after 15 % discount on this marked - up price , price = 140 - ( 15 % of 140 ) = 140 - 21 = 119 final profit = ( ( 119 - 100 ) / 100 ) * 100 = 19 % option e

gain

math_qa__jyi4IPvP4XQgXFp5

A rectangular grassy plot 100 m. by 70 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 90 paise per sq. metre. Choose the most appropriate option. A) rs . 700 B) rs . 708.50 C) rs . 732.50 D) rs . 742.50 E) none of these

<gadget id="calculator">100 * 70</gadget> <output>7_000</output> <gadget id="calculator">2.5 * 2</gadget> <output>5</output> <gadget id="calculator">100 - 5</gadget> <output>95</output> <gadget id="calculator">70 - 5</gadget> <output>65</output> <gadget id="calculator">95 * 65</gadget> <output>6_175</output> <gadget id="calculator">7_000 - 6_175</gadget> <output>825</output> <gadget id="calculator">825 * 90</gadget> <output>74_250</output> <gadget id="calculator">74_250 / 100</gadget> <output>1_485/2 = around 742.5</output> <result>D</result>

D

A rectangular grassy plot 100 m. by 70 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 90 paise per sq. metre.

divide(multiply(subtract(multiply(100, 70), multiply(subtract(100, multiply(2.5, const_2)), subtract(70, multiply(2.5, const_2)))), 90), const_100)

multiply(n0,n1)|multiply(n2,const_2)|subtract(n0,#1)|subtract(n1,#1)|multiply(#2,#3)|subtract(#0,#4)|multiply(n3,#5)|divide(#6,const_100)|

"explanation : area of the plot = ( 100 x 70 ) m 2 = 7000 m 2 area of the plot excluding the path = [ ( 100 - 5 ) * ( 70 - 5 ) ] m 2 = 6175 m 2 . area of the path = ( 7000 - 6175 ) m 2 = 825 m 2 . cost of gravelling the path = rs . 825 * ( 90 / 100 ) = rs . 742.50 answer : option d"

physics

math_qa__qrPSslZukmya40xd

The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre. Choose the correct answer: A) rs . 15500 B) rs . 16500 C) rs . 17500 D) rs . 18500 E) rs . 19500

<gadget id="calculator">5.5 * 3.75</gadget> <output>20.625</output> <gadget id="calculator">800 * 20.625</gadget> <output>16_500</output> <result>B</result>

B

The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre.

multiply(800, multiply(5.5, 3.75))

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

"area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b"

physics

math_qa__2UeARNWHcLGW7IQ9

The product X of two prime numbers is between 15 and 70. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X = Choose the most appropriate option. A) 18 B) 29 C) 37 D) 44 E) 69

<gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">25 - 2</gadget> <output>23</output> <gadget id="calculator">3 * 23</gadget> <output>69</output> <result>E</result>

E

The product X of two prime numbers is between 15 and 70. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =

multiply(add(2, const_1), subtract(25, 2))

add(n2,const_1)|subtract(n5,n2)|multiply(#0,#1)

option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 69 = 3 * 23 > > answer answer = e

general

math_qa__tmwpNJyz7F0X2NvJ

We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value R of the ratio A/B? Pick one: A) 1 / 2 B) 1 / 3 C) 2 / 3 D) 1 / 4 E) 1 / 5

<gadget id="calculator">2_020 / 2_020</gadget> <output>1</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <result>A</result>

A

We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value R of the ratio A/B?

divide(divide(2020, 2020), add(divide(2020, 2020), divide(2020, 2020)))

divide(n6,n6)|add(#0,#0)|divide(#0,#1)|

"r - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."

general

math_qa__6q2hhTgvRDCOVDhW

A candidate got 40% of the votes polled and he lost to his rival by 5000 votes. How many votes were cast? Choose the correct option: A) 25000 B) 2028 C) 2775 D) 5496 E) 6851

<gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">1 - (2/5)</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) - (2/5)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">5_000 / (1/5)</gadget> <output>25_000</output> <result>A</result>

A

A candidate got 40% of the votes polled and he lost to his rival by 5000 votes. How many votes were cast?

divide(5000, subtract(subtract(const_1, divide(40, const_100)), divide(40, const_100)))

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

"40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 5000 100 % - - - - - - - - - ? = > 25000 answer : a"

gain

math_qa__6gj69LVgH4nTcXoH

Two employees A and B are paid a total of Rs. 560 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week? Choose the correct choice from the following answers A) s . 130 B) s . 140 C) s . 150 D) s . 224 E) s . 280

<gadget id="calculator">150 / 100</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) + 1</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">560 / (5/2)</gadget> <output>224</output> <result>D</result>

D

Two employees A and B are paid a total of Rs. 560 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?

divide(560, add(divide(150, const_100), const_1))

divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|

"let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 560 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 560 ⇒ y [ 15 / 10 + 1 ] = 560 ⇒ 25 y / 10 = 560 ⇒ 25 y = 5600 ⇒ y = 5600 / 25 = rs . 224 d )"

general

math_qa__hdVzBv5S52kol62C

Find the lowest common multiple of 10, 14 and 20. Choose the correct choice from the following answers: A) 360 B) 420 C) 510 D) 320 E) 140

<gadget id="calculator">lcm(10, 14)</gadget> <output>70</output> <gadget id="calculator">lcm(70, 20)</gadget> <output>140</output> <result>E</result>

E

Find the lowest common multiple of 10, 14 and 20.

lcm(lcm(10, 14), 20)

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

"lcm = 2 * 2 * 5 * 7 = 140 . answer is e"

general

math_qa__6qHvGBZAL0uxbHDF

3034 - (1002 / 200.4) = ? Choose the correct choice from the following options. A) 2984 B) 3029 C) 2982 D) 2981 E) none of these

<gadget id="calculator">1_002 / 200.4</gadget> <output>5</output> <gadget id="calculator">3_034 - 5</gadget> <output>3_029</output> <result>B</result>

B

3034 - (1002 / 200.4) = ?

subtract(3034, divide(1002, 200.4))

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

"3034 - 5 = 3029 answer : b"

general

math_qa__SGZQq39rZzYlz5je

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is: Select: A) 90 cm B) 6 dm C) 1 m D) 1.1 cm E) none of these

<gadget id="calculator">3.3 * 2.6</gadget> <output>8.58</output> <gadget id="calculator">8.58 * 1.6</gadget> <output>13.728</output> <gadget id="calculator">8_000 / 1_000</gadget> <output>8</output> <gadget id="calculator">13.728 - 8</gadget> <output>5.728</output> <result>B</result>

B

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is:

subtract(multiply(multiply(3.3, 2.6), 1.6), divide(8000, const_1000))

divide(n0,const_1000)|multiply(n1,n2)|multiply(n3,#1)|subtract(#2,#0)

explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 160 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 160 - x ) = 8000 × 1000 = > ( 160 - x ) = 8000 × 1000 / 320 = 100 = > x = 60 cm = 6 dm . answer : b

physics

math_qa__8x5mQlD9rG5ha45G

If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds? Choose the correct answer: A) 180 B) 184 C) 188 D) 192 E) 196

<gadget id="calculator">290 - 8</gadget> <output>282</output> <gadget id="calculator">282 / 3</gadget> <output>94</output> <gadget id="calculator">94 * 2</gadget> <output>188</output> <gadget id="calculator">188 + 8</gadget> <output>196</output> <result>E</result>

E

If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds?

add(multiply(divide(subtract(290, 8), const_3), const_2), 8)

subtract(n1,n0)|divide(#0,const_3)|multiply(#1,const_2)|add(n0,#2)|

"j + k = 290 and so k = 290 - j j - 8 = 2 k j - 8 = 2 ( 290 - j ) 3 j = 588 j = 196 the answer is e ."

general

math_qa__CvlVkNSnZcmCTCmR

In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent X of his family’s total income? Choose the most appropriate option: A) 15 % B) 17 % C) 24 % D) 30 % E) 33 %

<gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * (2/5)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(2/5) - (1/10)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">1 - (1/10)</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">(3/10) / (9/10)</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 100</gadget> <output>100/3 = around 33.333333</output> <result>E</result>

E

In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent X of his family’s total income?

multiply(divide(subtract(divide(40, const_100), multiply(divide(25, const_100), divide(40, const_100))), subtract(const_1, multiply(divide(25, const_100), divide(40, const_100)))), const_100)

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

"lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march x = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"

general

math_qa__CCLp9R83KReGFwY1

At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 16th highest price and the 23rd lowest price among the prices of the items sold, how many items were sold at the garage sale? Choose the correct choice from the following options: A) 35 B) 36 C) 37 D) 38 E) 39

<gadget id="calculator">23 + 16</gadget> <output>39</output> <gadget id="calculator">39 - 1</gadget> <output>38</output> <result>D</result>

D

At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 16th highest price and the 23rd lowest price among the prices of the items sold, how many items were sold at the garage sale?

subtract(add(23, 16), const_1)

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

"there were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio . including the radio , there were 15 + 22 + 1 = 38 items sold . the answer is d ."

other

math_qa__sjogfYBpn9YvLRH7

One hour after Yolanda started walking from X to Y, a distance of 52 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met? Select the correct option: A) 28 B) 23 C) 22 D) 21 E) 19.5

<gadget id="calculator">52 - 3</gadget> <output>49</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">49 / 7</gadget> <output>7</output> <gadget id="calculator">7 * 4</gadget> <output>28</output> <result>A</result>

A

One hour after Yolanda started walking from X to Y, a distance of 52 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?

multiply(divide(subtract(52, 3), add(3, 4)), 4)

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

"when b started walking y already has covered 3 miles out of 52 , hence the distance at that time between them was 52 - 3 = 49 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 49 / 7 = 7 hours . in 6 hours b walked 7 * 4 = 28 miles . answer : a ."

physics

math_qa__ixwuELibDYlBMgQH

Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.13 of money? Pick A) 1300 B) 1992 C) 9921 D) 2798 E) 2789

<gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">13 / 20</gadget> <output>13/20 = around 0.65</output> <gadget id="calculator">(13/20) * 100</gadget> <output>65</output> <gadget id="calculator">65 * 20</gadget> <output>1_300</output> <result>A</result>

A

Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.13 of money?

multiply(multiply(divide(13, multiply(10, 2)), const_100), multiply(10, 2))

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

"p = 13 ( 100 / 10 ) 2 = > p = 1300 answer : a"

general

math_qa__ONlqXQHqhGzfsbqV

30 men can do a work in 40 days. When should 10 men leave the work so that the entire work is completed in 40 days after they leave the work? Pick one A) 87 days B) 10 days C) 55 days D) 44 days E) 20 days

<gadget id="calculator">30 * 40</gadget> <output>1_200</output> <gadget id="calculator">40 * 10</gadget> <output>400</output> <gadget id="calculator">1_200 - 400</gadget> <output>800</output> <gadget id="calculator">800 / 40</gadget> <output>20</output> <result>E</result>

E

30 men can do a work in 40 days. When should 10 men leave the work so that the entire work is completed in 40 days after they leave the work?

divide(subtract(multiply(30, 40), multiply(40, 10)), 40)

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

"total work to be done = 30 * 40 = 1200 let 10 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 10 * 40 ) = 1200 40 p = 800 = > p = 20 days answer : e"

physics

math_qa__MjvNVD4f9CjkuSgV

Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Options. A) 16 sec B) 12 sec C) 17 sec D) 21 sec E) 23 sec

<gadget id="calculator">120 * 2</gadget> <output>240</output> <gadget id="calculator">120 / 15</gadget> <output>8</output> <gadget id="calculator">120 / 10</gadget> <output>12</output> <gadget id="calculator">8 + 12</gadget> <output>20</output> <gadget id="calculator">240 / 20</gadget> <output>12</output> <result>B</result>

B

Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?

divide(multiply(120, const_2), add(speed(120, 15), speed(120, 10)))

multiply(n2,const_2)|speed(n2,n1)|speed(n2,n0)|add(#1,#2)|divide(#0,#3)|

"speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 120 + 120 ) / 20 = 12 sec . answer : b"

physics

math_qa__r6TRjHoCfdEOfhRT

Jill's favorite number is even and has some repeating prime factors. John is guessing Jills favorite number, and the only hint she gives is that 7 is a prime factor. What is Johns best guess? Choose the most appropriate option. A) 84 B) 105 C) 54 D) 42 E) 70

<gadget id="calculator">2 ** 2</gadget> <output>4</output> <gadget id="calculator">7 * 3</gadget> <output>21</output> <gadget id="calculator">4 * 21</gadget> <output>84</output> <result>A</result>

A

Jill's favorite number is even and has some repeating prime factors. John is guessing Jills favorite number, and the only hint she gives is that 7 is a prime factor. What is Johns best guess?

multiply(power(const_2, const_2), multiply(7, const_3))

multiply(n0,const_3)|power(const_2,const_2)|multiply(#0,#1)

a 84 = 2 * 2 * 2 * 7 b 105 is odd c 54 = 2 * 3 * 3 d 42 = 2 * 3 * 7 e 70 = 2 * 5 * 7 the answer must meet three criteria : odd , have repeating prime factors , and 7 is a prime factor . a is the only answer that meets all criteria

other

math_qa__DSbXEPbBCfjC39TG

Kamal obtained 76, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Choose the correct option: A) 65 B) 69 C) 72 D) 75 E) none

<gadget id="calculator">76 + 65</gadget> <output>141</output> <gadget id="calculator">141 + 82</gadget> <output>223</output> <gadget id="calculator">223 + 67</gadget> <output>290</output> <gadget id="calculator">290 + 85</gadget> <output>375</output> <gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">375 / 5</gadget> <output>75</output> <result>D</result>

D

Kamal obtained 76, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?

divide(add(add(add(add(76, 65), 82), 67), 85), add(const_1, const_4))

add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|

"sol . average = 76 + 65 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 75 . answer d"

general

math_qa__rOKdgQnVv1XiHtkX

Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer? Choose the correct choice from the following answers: A) 1 B) 2 C) 3 D) 4 E) 6

<gadget id="calculator">180 / 3</gadget> <output>60</output> <gadget id="calculator">60 / 2</gadget> <output>30</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">30 / 5</gadget> <output>6</output> <result>E</result>

E

Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

divide(divide(divide(180, const_3), 2), add(const_3, const_2))

add(const_2,const_3)|divide(n0,const_3)|divide(#1,n2)|divide(#2,#0)

make sure to follow posting guidelines ( link in my signatures ) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors ( this is fine for this question as 180 is a relatively small number ) . number of factors of 180 ( = 2 ^ 2 * 3 ^ 2 * 5 ) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors ( = 2 , 610 , 1830 ) . you can stop here and mark 6 ( 6 th one = 90 ) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer .

general

math_qa__tKbDnNislqJ3NWjE

Every student of a certain school must play an instrument. In last year, 1/2 of the students picked a woodwind instrument, 2/5 of the students picked a brass instrument, and all of the other students took percussion. In this year, 1/2 of the students who play woodwind and 1/4 of the students who play brass instruments left school, other students did not leave, and no fresh student come in. What fraction of all students play either a woodwind or brass instrument? Options: A) 7 / 13 B) 4 / 5 C) 9 / 13 D) 11 / 13 E) 7 / 10

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 - (1/2)</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) / 2</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/2) - (1/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) / 4</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(2/5) - (1/10)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(1/4) + (3/10)</gadget> <output>11/20 = around 0.55</output> <gadget id="calculator">1 - (1/4)</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(1/2) - (2/5)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(3/4) - (1/10)</gadget> <output>13/20 = around 0.65</output> <gadget id="calculator">(11/20) / (13/20)</gadget> <output>11/13 = around 0.846154</output> <result>D</result>

D

Every student of a certain school must play an instrument. In last year, 1/2 of the students picked a woodwind instrument, 2/5 of the students picked a brass instrument, and all of the other students took percussion. In this year, 1/2 of the students who play woodwind and 1/4 of the students who play brass instruments left school, other students did not leave, and no fresh student come in. What fraction of all students play either a woodwind or brass instrument?

divide(add(subtract(subtract(1, divide(const_1, const_2)), divide(divide(const_1, const_2), 2)), subtract(divide(const_2, 5), divide(divide(const_2, 5), 4))), subtract(subtract(1, subtract(subtract(1, divide(const_1, const_2)), divide(divide(const_1, const_2), 2))), subtract(subtract(1, divide(const_1, const_2)), divide(const_2, 5))))

divide(const_1,const_2)|divide(const_2,n3)|divide(#0,n1)|divide(#1,n7)|subtract(n0,#0)|subtract(#4,#2)|subtract(#1,#3)|subtract(#4,#1)|add(#5,#6)|subtract(n0,#5)|subtract(#9,#7)|divide(#8,#10)

lets pick smart numbers . total number of students : 20 woodwind ( 1 / 2 ) : 10 brass ( 2 / 5 ) : 8 percussion ( 1 / 10 ) : 2 after leaving school woodwind : 5 brass : 6 percussion : 2 new total number of students : 13 woodwind and brass : 11 answer 11 / 13 or d

general

math_qa__SGw9ZSzE6snWwXBT

There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 16 days more? Choose the correct choice from the following answers: A) 122 B) 140 C) 199 D) 188 E) 190

<gadget id="calculator">22 - 2</gadget> <output>20</output> <gadget id="calculator">760 * 20</gadget> <output>15_200</output> <gadget id="calculator">15_200 / 16</gadget> <output>950</output> <gadget id="calculator">950 - 760</gadget> <output>190</output> <result>E</result>

E

There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 16 days more?

subtract(divide(multiply(760, subtract(22, const_2)), 16), 760)

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

"760 - - - - 22 760 - - - - 20 x - - - - - 16 x * 16 = 760 * 20 x = 950 760 - - - - - - - 190 answer : e"

physics

math_qa__iJjGJBZcowR5E2np

If W is the set of all the integers between 19 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers? Select the correct option A) 26 B) 32 C) 33 D) 34 E) 54

<gadget id="calculator">99 - 19</gadget> <output>80</output> <gadget id="calculator">80 / 3</gadget> <output>80/3 = around 26.666667</output> <gadget id="calculator">floor(80/3)</gadget> <output>26</output> <gadget id="calculator">80 / 2</gadget> <output>40</output> <gadget id="calculator">26 + 40</gadget> <output>66</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">80 / 6</gadget> <output>40/3 = around 13.333333</output> <gadget id="calculator">floor(40/3)</gadget> <output>13</output> <gadget id="calculator">66 - 13</gadget> <output>53</output> <result>E</result>

E

If W is the set of all the integers between 19 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?

subtract(add(floor(divide(subtract(99, 19), 3)), divide(subtract(99, 19), 2)), floor(divide(subtract(99, 19), multiply(2, 3))))

multiply(n3,n2)|subtract(n1,n0)|divide(#1,n3)|divide(#1,n2)|divide(#1,#0)|floor(#3)|floor(#4)|add(#2,#5)|subtract(#7,#6)|

"multiples of 2 from 19 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 18 = [ 99 / 2 ] - [ 18 / 2 ] = 49 - 9 = 40 multiples of 3 from 19 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 18 = [ 99 / 3 ] - [ 18 / 3 ] = 33 - 6 = 27 multiples of 2 and 3 bothi . e . 6 from 19 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 18 = [ 99 / 6 ] - [ 18 / 6 ] = 16 - 3 = 13 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 40 + 27 - 13 = 54 answer option e"

other

math_qa__FLIZUxyN59OU8hJR

Find the curved surface area, if the radius of a cone is 28 m and slant height is 30 m? Choose the correct choice from the following choices: A) 2550 B) 2640 C) 3960 D) 4280 E) 5490

<gadget id="calculator">28 * 30</gadget> <output>840</output> <gadget id="calculator">pi * 840</gadget> <output>840*pi = around 2_638.937829</output> <result>B</result>

B

Find the curved surface area, if the radius of a cone is 28 m and slant height is 30 m?

multiply(const_pi, multiply(28, 30))

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

"cone curved surface area = ï € rl 22 / 7 ã — 28 ã — 30 = 88 ã — 30 = 2640 m ( power 2 ) answer is b ."

geometry

math_qa__DnfhPUzOKB1afXz0

|16 - 5| - |5 - 12| = ? Answers A) 3 B) 2 C) 1 D) 0 E) 4

<gadget id="calculator">16 - 5</gadget> <output>11</output> <gadget id="calculator">12 - 5</gadget> <output>7</output> <gadget id="calculator">11 - 7</gadget> <output>4</output> <result>E</result>

E

|16 - 5| - |5 - 12| = ?

subtract(subtract(16, 5), subtract(12, 5))

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

"| 16 - 5 | - | 5 - 12 | = | 11 | - | - 7 | = 11 - 7 = 4 correct answer e"

general

math_qa__ZXgjmRYLiUGhvpIE

If two-third of a bucket is filled in 90 seconds then the time taken to fill the bucket completely will be . Choose the correct choice: A) 90 seconds B) 70 seconds C) 135 seconds D) 100 seconds E) 120 seconds

<gadget id="calculator">90 / 2</gadget> <output>45</output> <gadget id="calculator">45 * 3</gadget> <output>135</output> <result>C</result>

C

If two-third of a bucket is filled in 90 seconds then the time taken to fill the bucket completely will be .

multiply(divide(90, const_2), const_3)

divide(n0,const_2)|multiply(#0,const_3)|

"2 / 3 filled in 90 seconds 1 / 3 filled in 45 seconds then 2 / 3 + 1 / 3 = 90 + 45 seconds = 135 seconds answer : c"

physics

math_qa__6jIPLB2gY2lH2qo3

If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? Choose the correct option. A) 7 meters B) 9 meters C) 8 meters D) 5 meters E) 3 meters

<gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">60 * 400</gadget> <output>24_000</output> <gadget id="calculator">120 / 24_000</gadget> <output>1/200 = around 0.005</output> <gadget id="calculator">(1/200) * 1_000</gadget> <output>5</output> <result>D</result>

D

If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?

multiply(divide(120, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)

multiply(const_2,const_3)|multiply(#0,const_10)|multiply(n0,#1)|divide(n1,#2)|multiply(#3,const_1000)

400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 12,0000 m : c is the circumference c = 5 meters correct answer d

physics

math_qa__s1Sq3mxvvkafCACv

the population of a town increased from 1 , 75000 to 2 , 62500 in a decade . what is the average percent increase of population per year ? Choose the correct choice A) 4 % B) 6 % C) 5 % D) 50 % E) none of these

<gadget id="calculator">1_000 * 100</gadget> <output>100_000</output> <gadget id="calculator">62_500 / 100_000</gadget> <output>5/8 = around 0.625</output> <gadget id="calculator">2 + (5/8)</gadget> <output>21/8 = around 2.625</output> <gadget id="calculator">75_000 / 100_000</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 + (3/4)</gadget> <output>7/4 = around 1.75</output> <gadget id="calculator">(21/8) - (7/4)</gadget> <output>7/8 = around 0.875</output> <gadget id="calculator">(7/8) / 10</gadget> <output>7/80 = around 0.0875</output> <gadget id="calculator">(7/80) / (7/4)</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/20) * 100</gadget> <output>5</output> <result>C</result>

C

the population of a town increased from 1 , 75000 to 2 , 62500 in a decade . what is the average percent increase of population per year ?

multiply(divide(divide(subtract(add(2, divide(62500, multiply(const_1000, const_100))), add(1, divide(75000, multiply(const_1000, const_100)))), const_10), add(1, divide(75000, multiply(const_1000, const_100)))), const_100)

multiply(const_100,const_1000)|divide(n3,#0)|divide(n1,#0)|add(n2,#1)|add(n0,#2)|subtract(#3,#4)|divide(#5,const_10)|divide(#6,#4)|multiply(#7,const_100)

explanation : increase in the population in 10 years = 2 , 62500 - 1 , 75000 = 87500 % ncrease in the population in 10 years = ( 87500 / 175000 ) × 100 = 8750 / 175 = 50 % average % increase of population per year = 50 % / 10 = 5 % answer : option c

general

math_qa__KYoJNrc3yAajq30J

10 men do a work in 10days. How many men are needed to finish the work in 2days? Choose the correct choice from the following answers: A) 50 B) 20 C) 30 D) 10 E) 15

<gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">100 / 2</gadget> <output>50</output> <result>A</result>

A

10 men do a work in 10days. How many men are needed to finish the work in 2days?

divide(multiply(10, 10), 2)

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

"men required to finish the work in 2 days = 10 * 10 / 2 = 50 answer is a"

physics

math_qa__yLwrIvUwqko49Nxm

A man can row 8 Kmph in still water. If the velocity of the current is 2 Kmph and it takes him 2 hours to row to a place and come back. How far is the place? Choose the correct choice from the following options: A) 5.5 B) 8.5 C) 6.5 D) 9.5 E) 7.5

<gadget id="calculator">8 - 2</gadget> <output>6</output> <gadget id="calculator">8 + 2</gadget> <output>10</output> <gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">60 * 2</gadget> <output>120</output> <gadget id="calculator">10 + 6</gadget> <output>16</output> <gadget id="calculator">120 / 16</gadget> <output>15/2 = around 7.5</output> <result>E</result>

E

A man can row 8 Kmph in still water. If the velocity of the current is 2 Kmph and it takes him 2 hours to row to a place and come back. How far is the place?

divide(multiply(multiply(subtract(8, 2), add(8, 2)), 2), add(add(8, 2), subtract(8, 2)))

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

man ' s rate down stream = 8 + 2 = 10 kmph man ' s rate upstream = 8 - 2 = 6 kmph let the required distance be x km then x / 10 + x / 6 = 2 3 x + 5 x = 60 8 x = 60 x = 7.5 km answer is e .

physics

math_qa__yNQt2SdIjM3ENqNX

If x is equal to the sum of the integers from 20 to 40, inclusive, and y is the number of even integers from 20 to 40, inclusive, what is the value of x + y? Choose the correct choice A) 601 B) 611 C) 621 D) 631 E) 641

<gadget id="calculator">20 + 40</gadget> <output>60</output> <gadget id="calculator">60 / 2</gadget> <output>30</output> <gadget id="calculator">40 - 20</gadget> <output>20</output> <gadget id="calculator">20 + 1</gadget> <output>21</output> <gadget id="calculator">30 * 21</gadget> <output>630</output> <gadget id="calculator">20 / 2</gadget> <output>10</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">630 + 11</gadget> <output>641</output> <result>E</result>

E

If x is equal to the sum of the integers from 20 to 40, inclusive, and y is the number of even integers from 20 to 40, inclusive, what is the value of x + y?

add(multiply(divide(add(20, 40), const_2), add(subtract(40, 20), const_1)), add(divide(subtract(40, 20), const_2), const_1))

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

"x = 20 + 21 + . . . + 40 = 21 ( 30 ) = 630 y = 11 x + y = 641 the answer is e ."

general

math_qa__wttkEwItFPu9Bize

the hiker walking at a constant rate of 5 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? Choose the correct choice from the following: A) 15 B) 10 C) 20 D) 30 E) 35

<gadget id="calculator">20 - 5</gadget> <output>15</output> <gadget id="calculator">5 / 60</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">15 * (1/12)</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(5/4) / 5</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * 60</gadget> <output>15</output> <result>A</result>

A

the hiker walking at a constant rate of 5 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?

multiply(divide(multiply(subtract(20, 5), divide(5, const_60)), 5), const_60)

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

"after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 5 / 12 miles . so the hiker still has to cover 15 / 12 miles to meet the waiting cyclist . the hiker will need 1 / 4 hours or 15 mins to cover the remaining 15 / 12 miles . so the answer is a ."

physics

math_qa__DavjOrNIOT6BvTCX

A 90 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? Choose the correct choice from the following: A) 220 meter B) 225 meter C) 230 meter D) 410 meter E) none of these

<gadget id="calculator">120 + 80</gadget> <output>200</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">200 * (5/18)</gadget> <output>500/9 = around 55.555556</output> <gadget id="calculator">(500/9) * 9</gadget> <output>500</output> <gadget id="calculator">500 - 90</gadget> <output>410</output> <result>D</result>

D

A 90 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 90)

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

"explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 90 / 9 = 500 / 9 = > x + 90 = 500 = > x = 410 so the length of the train is 410 meters option d"

physics