Question: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 15 more transactions than cal . how much transactions did jade handled ?

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">10 + 100</gadget>
<output>110</output>

<gadget id="calculator">(9/10) * 110</gadget>
<output>99</output>

<gadget id="calculator">99 * 2</gadget>
<output>198</output>

<gadget id="calculator">198 / 3</gadget>
<output>66</output>

<gadget id="calculator">66 + 15</gadget>
<output>81</output>
<result>81</result>

Choices:
A. 80
B. 81
C. 82
D. 83
E. 84

add(divide(multiply(multiply(divide(90, const_100), add(10, const_100)), 2), const_3), 15)

Explanation: solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 15 more transactions than cal . jade = 66 + 15 = 81 jade handled = 81 transactions . answer : b


Question: peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 850 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?

<gadget id="calculator">850 - 815</gadget>
<output>35</output>

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>

<gadget id="calculator">(1/25) - (3/100)</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">35 / (1/100)</gadget>
<output>3_500</output>

<gadget id="calculator">3_500 * (3/100)</gadget>
<output>105</output>

<gadget id="calculator">815 - 105</gadget>
<output>710</output>
<result>710</result>

Choices:
A. 670
B. 664
C. 698
D. 744
E. 710

subtract(815, multiply(divide(subtract(850, 815), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100)))

Explanation: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 850 - 815 = 35 interest earned for 3 years = 35 * 3 = 105 amount invested = 815 - 105 = 710 answer : e"


Question: the sector of a circle has perimeter 83 cm and central angle 225 o . find its radius ?

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">20 + 2</gadget>
<output>22</output>

<gadget id="calculator">4 + 3</gadget>
<output>7</output>

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">2 * (22/7)</gadget>
<output>44/7 = around 6.285714</output>

<gadget id="calculator">(44/7) * 225</gadget>
<output>9_900/7 = around 1_414.285714</output>

<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>

<gadget id="calculator">(9_900/7) / 360</gadget>
<output>55/14 = around 3.928571</output>

<gadget id="calculator">(55/14) + 2</gadget>
<output>83/14 = around 5.928571</output>

<gadget id="calculator">83 / (83/14)</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 21 cm
B. 15 cm
C. 14 cm
D. 24 cm
E. 28 cm

divide(83, add(divide(multiply(multiply(const_2, divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), 225), divide(const_3600, const_10)), const_2))

Explanation: let radius = x cm perimeter of the sector = length of the arc + 2 ( radius ) 83 = ( 225 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 83 = 55 x / 14 + 2 x 83 = 83 x / 14 1162 = 83 x x = 14 answer : c


Question: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses at the restaurant ? ( assume that all boxes are filled to capacity . )

<gadget id="calculator">16 * 2</gadget>
<output>32</output>

<gadget id="calculator">32 * 15</gadget>
<output>480</output>
<result>480</result>

Choices:
A. 96
B. 240
C. 56
D. 384
E. 480

Explanation: "1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can just ` ` add 28 s ' ' until we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"


Question: in a certain alphabet , 9 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?

<gadget id="calculator">9 + 24</gadget>
<output>33</output>

<gadget id="calculator">40 - 33</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 8
C. 14
D. 20
E. 28

Explanation: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 9 + 24 = 33 ; next , we find the total # of letters without line : 40 - 33 = 7 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 7 - 0 = 7 . a"


Question: if a train , travelling at a speed of 90 kmph , crosses a pole in 4 sec , then the length of train is ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>

<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 281
B. 125
C. 288
D. 100
E. 121

Explanation: "d = 90 * 5 / 18 * 4 = 100 m answer : d"


Question: john ' s bank ' s saving amount is decreased 20 % due to loan payment and current balance is rs . 24000 . find the actual balance before deduction ?

<gadget id="calculator">24_000 * 20</gadget>
<output>480_000</output>

<gadget id="calculator">480_000 / 100</gadget>
<output>4_800</output>

<gadget id="calculator">4_800 + 24_000</gadget>
<output>28_800</output>
<result>28_800</result>

Choices:
A. 8000
B. 8500
C. 9000
D. 9500
E. 30000

Explanation: "20 % decreased 80 % balance = 24000 100 % = 24000 / 80 * 100 = 30000 answer : e"


Question: two employees x and y are paid a total of rs . 700 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

<gadget id="calculator">1 + 4</gadget>
<output>5</output>

<gadget id="calculator">5 * 2</gadget>
<output>10</output>

<gadget id="calculator">700 * 10</gadget>
<output>7_000</output>

<gadget id="calculator">10 + 1</gadget>
<output>11</output>

<gadget id="calculator">11 * 2</gadget>
<output>22</output>

<gadget id="calculator">7_000 / 22</gadget>
<output>3_500/11 = around 318.181818</output>
<result>3_500/11 = around 318.181818</result>

Choices:
A. s . 200.18
B. s . 240.18
C. s . 290.18
D. s . 300.18
E. s . 318.18

divide(multiply(700, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 700 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 700 ⇒ y [ 12 / 10 + 1 ] = 700 ⇒ 22 y / 10 = 700 ⇒ 22 y = 7000 ⇒ y = 7000 / 22 = rs . 318.18 e )"


Question: james took a 3 - hour bike ride . in the second hour he travlled 12 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?

<gadget id="calculator">1 * 100</gadget>
<output>100</output>

<gadget id="calculator">100 * 12</gadget>
<output>1_200</output>

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">1_200 / 120</gadget>
<output>10</output>

<gadget id="calculator">25 * 12</gadget>
<output>300</output>

<gadget id="calculator">300 / 20</gadget>
<output>15</output>

<gadget id="calculator">10 + 15</gadget>
<output>25</output>

<gadget id="calculator">25 + 12</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 54.0
B. 54.9
C. 55.5
D. 37.0
E. 63.0

add(add(divide(multiply(multiply(const_1, const_100), 12), add(multiply(const_1, const_100), 20)), divide(multiply(25, 12), 20)), 12)

Explanation: "let the distance travelled in the first hour be x . thus , 1.2 x = 12 , x = 10 . now , the distance travelled in the 3 rd hour = 12 + 1 / 4 â ˆ — 12 = 15 therefore 12 + 15 + 10 = 37 answer : d"


Question: in a group of 100 cars , 47 cars do not have air conditioning . if at least 53 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?

<gadget id="calculator">100 - 53</gadget>
<output>47</output>
<result>47</result>

Choices:
A. 45
B. 47
C. 49
D. 51
E. 53

Explanation: "lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 53 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 53 . . we have to assign atleast 6 tocars with ac and racing stripes . hence ac = 53 - 6 = 47 . the answer is b"


Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions ?

<gadget id="calculator">3 + 4</gadget>
<output>7</output>

<gadget id="calculator">7 * 3</gadget>
<output>21</output>

<gadget id="calculator">21 + 1</gadget>
<output>22</output>

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>

<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>

<gadget id="calculator">140.8 * 600</gadget>
<output>84_480</output>

<gadget id="calculator">84_480 / 100</gadget>
<output>4_224/5 = around 844.8</output>
<result>4_224/5 = around 844.8</result>

Choices:
A. 844.8 m
B. 704 m
C. 774 m
D. 714 m
E. 744 m

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 600), const_100)

Explanation: in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84480 cm = 844.8 m answer : a


Question: mr . depak has $ 449774 in his bank account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among her 6 best friends ? options :

<gadget id="calculator">449_774 + 1</gadget>
<output>449_775</output>

<gadget id="calculator">449_775 - 449_774</gadget>
<output>1</output>
<result>1</result>

Choices:
A. $ 1
B. $ 2
C. $ 3
D. $ 4
E. $ 6

Explanation: to find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends , he needs to make the total divisible by 6 simply add the individual digits of the total = 4 + 4 + 9 + 7 + 7 + 4 = 35 if you add 1 , the number is divisible by 6 ( 35 + 1 ) correct option : a


Question: the ages of two person differ by 12 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">12 - 5</gadget>
<output>7</output>

<gadget id="calculator">25 + 7</gadget>
<output>32</output>

<gadget id="calculator">5 - 1</gadget>
<output>4</output>

<gadget id="calculator">32 / 4</gadget>
<output>8</output>

<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 30 , 10
B. 25 , 5
C. 29 , 9
D. 50 , 30
E. 20 , 8

add(divide(add(multiply(5, 5), subtract(12, 5)), subtract(5, const_1)), 12)

Explanation: "let their ages be x and ( x + 12 ) years . then , 5 ( x - 5 ) = ( x + 12 - 5 ) = > 4 x = 32 = > x = 8 their present ages are 20 years and 8 year . answer : e"


Question: a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 200 , $ 600 . then his average income is ?

<gadget id="calculator">300 + 150</gadget>
<output>450</output>

<gadget id="calculator">450 + 750</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 + 200</gadget>
<output>1_400</output>

<gadget id="calculator">1_400 + 600</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 / 5</gadget>
<output>400</output>
<result>400</result>

Choices:
A. $ 350
B. $ 375
C. $ 400
D. $ 425
E. $ 450

Explanation: "avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 200 + 600 ) / 5 = 400 answer is c"


Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 4 men and 2 women will do that task .

<gadget id="calculator">8 - 2</gadget>
<output>6</output>

<gadget id="calculator">6 - 3</gadget>
<output>3</output>

<gadget id="calculator">6 / 3</gadget>
<output>2</output>

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

<gadget id="calculator">8 + 2</gadget>
<output>10</output>

<gadget id="calculator">6 * 2</gadget>
<output>12</output>

<gadget id="calculator">12 + 2</gadget>
<output>14</output>

<gadget id="calculator">10 / 14</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>

Choices:
A. 5 / 7
B. 3 / 10
C. 5 / 18
D. 5 / 16
E. 5 / 11

divide(add(multiply(divide(subtract(8, 2), subtract(6, 3)), 4), 2), add(multiply(6, divide(subtract(8, 2), subtract(6, 3))), 2))

Explanation: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 4 m + 2 w = 10 w answer is 10 / 14 = 5 / 7 answer : a"


Question: a trained covered x km at 90 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .

<gadget id="calculator">90 * 3</gadget>
<output>270</output>

<gadget id="calculator">90 / 90</gadget>
<output>1</output>

<gadget id="calculator">2 * 90</gadget>
<output>180</output>

<gadget id="calculator">180 / 20</gadget>
<output>9</output>

<gadget id="calculator">1 + 9</gadget>
<output>10</output>

<gadget id="calculator">270 / 10</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 22
B. 99
C. 27
D. 66
E. 887

divide(multiply(90, const_3), add(divide(90, 90), divide(multiply(const_2, 90), 20)))

Explanation: total time taken = x / 90 + 2 x / 20 hours = x / 9 hours average speed = 3 x / ( x / 9 ) = 27 kmph answer : c


Question: sachin is younger than rahul by 4 years . if the ratio of their ages is 7 : 9 , find the age of sachin

<gadget id="calculator">9 - 7</gadget>
<output>2</output>

<gadget id="calculator">4 / 2</gadget>
<output>2</output>

<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 24.58
B. 24.5
C. 24.3
D. 24.9
E. 14

Explanation: "if rahul age is x , then sachin age is x - 4 , so ( x - 4 ) / x = 7 / 9 = > 9 x - 36 = 7 x = > 2 x = 36 = > x = 18 so sachin age is 18 - 4 = 14 answer : e"


Question: a triangle and a parallelogram are constructed on the same base such that their areas are equal . if the altitude of the parallelogram is 100 m , then the altitude of the triangle is .

<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 10 √ 2 m
B. 100 m
C. 100 √ 2 m
D. 200 m
E. none

Explanation: solution let the altitude of the triangle be h ï and base of each be b . then , ( ½ × b × h 1 ) where h 2 = 100 m . = h 1 = 2 h 2 = ( 2 x 100 ) m = 200 m . answer d


Question: a man buys an item at rs . 1200 and sells it at the loss of 20 percent . then what is the selling price of that item

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">1_200 * (4/5)</gadget>
<output>960</output>
<result>960</result>

Choices:
A. rs . 660
B. rs . 760
C. rs . 860
D. rs . 960
E. none of these

multiply(1200, subtract(const_1, divide(20, const_100)))

Explanation: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 1200 = 80 / 100 * 1200 = 960 option d"


Question: a man rows his boat 110 km downstream and 90 km upstream , taking 3 hours each time . find the speed of the stream ?

<gadget id="calculator">110 / 3</gadget>
<output>110/3 = around 36.666667</output>

<gadget id="calculator">90 / 3</gadget>
<output>30</output>

<gadget id="calculator">(110/3) - 30</gadget>
<output>20/3 = around 6.666667</output>

<gadget id="calculator">(20/3) / 2</gadget>
<output>10/3 = around 3.333333</output>
<result>10/3 = around 3.333333</result>

Choices:
A. 6
B. 5
C. 7.5
D. 3.5
E. 2.5

divide(subtract(divide(110, 3), divide(90, 3)), const_2)

Explanation: "speed downstream = d / t = 110 / ( 3 ) = 37 kmph speed upstream = d / t = 90 / ( 3 ) = 30 kmph the speed of the stream = ( 37 - 30 ) / 2 = 3.5 kmph answer : d"


Question: five women can do a work in ten days . 7 men can complete the same work in 5 days . what is the ratio between the capacity of a man and a woman ?

<gadget id="calculator">7 * 5</gadget>
<output>35</output>

<gadget id="calculator">1 / 35</gadget>
<output>1/35 = around 0.028571</output>

<gadget id="calculator">5 * 10</gadget>
<output>50</output>

<gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">(1/35) / (1/50)</gadget>
<output>10/7 = around 1.428571</output>
<result>10/7 = around 1.428571</result>

Choices:
A. 10 : 7
B. 11 : 10
C. 2 : 3
D. 3 : 2
E. none of these

divide(divide(const_1, multiply(7, 5)), divide(const_1, multiply(5, const_10)))

Explanation: explanation : ( 50 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 50 ( 7 ã — 5 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 35 so , required ratio = 1 / 50 : 1 / 35 = 10 : 7 answer : a


Question: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 340 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?

<gadget id="calculator">12 * 340</gadget>
<output>4_080</output>

<gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>

<gadget id="calculator">3 * 100</gadget>
<output>300</output>

<gadget id="calculator">3_000 + 300</gadget>
<output>3_300</output>

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">3_300 + 20</gadget>
<output>3_320</output>

<gadget id="calculator">4_080 - 3_320</gadget>
<output>760</output>

<gadget id="calculator">12 - 8</gadget>
<output>4</output>

<gadget id="calculator">760 / 4</gadget>
<output>190</output>

<gadget id="calculator">340 - 190</gadget>
<output>150</output>

<gadget id="calculator">190 - 150</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40
B. 110
C. 120
D. 130
E. 220

subtract(divide(subtract(multiply(12, 340), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)), subtract(340, divide(subtract(multiply(12, 340), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8))))

Explanation: "orchestra seats - a balcony seats - b a + b = 340 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 340 = 3320 - 2720 = 600 i . e . a = 150 and b = 340 - 150 = 190 more seats in balcony than orchestra = b - a = 190 - 150 = 40 answer : option a"


Question: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 8 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?

<gadget id="calculator">8 - 1</gadget>
<output>7</output>

<gadget id="calculator">8 * 7</gadget>
<output>56</output>

<gadget id="calculator">9 * 8</gadget>
<output>72</output>

<gadget id="calculator">56 * 72</gadget>
<output>4_032</output>
<result>4_032</result>

Choices:
A. 54
B. 4032
C. 2,160
D. 2,916
E. 148,824

multiply(multiply(8, subtract(8, const_1)), multiply(9, 8))

Explanation: we have the rectangle with dimensions 9 * 8 ( 9 horizontal dots and 8 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 8 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 7 c 1 , ( 8 - 1 = 7 as 1 vertical dot is already occupied by a ) . 9 c 1 * 8 c * 8 c 1 * 7 c 1 = 4032 . answer : b .


Question: there are 8 stores in town that had a total of 22 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?

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

<gadget id="calculator">22 - 16</gadget>
<output>6</output>

<gadget id="calculator">12 - 8</gadget>
<output>4</output>

<gadget id="calculator">4 - 1</gadget>
<output>3</output>

<gadget id="calculator">6 - 3</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 2
B. 3
C. 4
D. 5
E. 6

subtract(subtract(22, multiply(8, const_2)), subtract(subtract(12, 8), const_1))

Explanation: 8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 22 - 16 - 3 = 3 , which is the maximum that one person could have visited . the answer is b .


Question: it takes avery 3 hours to build a brick wall while tom can do it in 3 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) + (1/3)</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) / (1/3)</gadget>
<output>1</output>

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 20
B. 60
C. 30
D. 40
E. 50

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

Explanation: "avery takes 3 hours tom takes 3 hours efficiency of avery is 1 / 3 units / hr efficiency of tom is 1 / 3 units / hr combined efficiency of tom and avery is 1 / 3 + 1 / 3 = 2 / 3 units / hr since they worked for 1 hour they completed 2 / 3 units of work and 1 / 3 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 3 / 1 / 3 hours = > 1 * 60 = 60 minutes . . . answer will be ( b )"


Question: a student got 70 % in one subject , 80 % in other . to get overall 75 % how much he should get in third subject .

<gadget id="calculator">70 + 80</gadget>
<output>150</output>

<gadget id="calculator">150 + 75</gadget>
<output>225</output>

<gadget id="calculator">225 / 3</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 65 %
B. 75 %
C. 85 %
D. 95 %
E. 88 %

Explanation: already average of two subjects is ( 70 + 80 ) / 2 = 75 % to maintain the percentage at 75 % , he shouls get 75 % marks in third subject answer : b


Question: 4 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>

<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 12
B. 144
C. 18
D. 21
E. 24

Explanation: the list should be wmwmw . hence , from women 3 ! and men 4 ! , we get ( 3 ! ) ( 4 ! ) = 144 . therefore , the correct answer is b .


Question: in a class , 10 students like to play basketball and 8 like to play cricket . 4 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?

<gadget id="calculator">10 + 8</gadget>
<output>18</output>

<gadget id="calculator">18 - 4</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 12
B. 15
C. 16
D. 18
E. 14

Explanation: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 10 + 8 - 4 = 14 e )"


Question: a box contains 9 apples , 8 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?

<gadget id="calculator">0.5 * 8</gadget>
<output>4</output>

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 3
B. 4
C. 5
D. 6
E. 7

Explanation: "p ( choosing a red apple 5 times in a row ) = 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 * 4 / 5 = 4 / 9 < 0.5 the answer is c ."


Question: the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>

<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>

<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>

<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>

<gadget id="calculator">375 - 130</gadget>
<output>245</output>
<result>245</result>

Choices:
A. 200 m
B. 225 m
C. 245 m
D. 250 m
E. none

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 130)

Explanation: "sol . speed = [ 45 x 5 / 18 ] m / sec = ( 25 / 2 ) m / sec ; time = 30 sec . let the length of bridge be x metres . then , 130 + x / 30 = 25 / 2 ⇔ 2 ( 130 + x ) = 750 ⇔ x = 245 m . answer c"


Question: the sum of the even numbers between 1 and n is 89 * 90 , where n is an odd number , then n = ?

<gadget id="calculator">89 * 2</gadget>
<output>178</output>

<gadget id="calculator">178 + 1</gadget>
<output>179</output>
<result>179</result>

Choices:
A. 167
B. 173
C. 179
D. 185
E. 193

Explanation: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 89 * 90 then a = 89 and n = 179 . the answer is c ."


Question: a person distributed 10 % of his income to his 2 children each . he deposited 20 % of his income to his wife ' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 500 . find his total income ?

<gadget id="calculator">10 * 2</gadget>
<output>20</output>

<gadget id="calculator">20 + 20</gadget>
<output>40</output>

<gadget id="calculator">40 + 10</gadget>
<output>50</output>

<gadget id="calculator">100 - 50</gadget>
<output>50</output>

<gadget id="calculator">500 / 50</gadget>
<output>10</output>

<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. $ 900
B. $ 1000
C. $ 1200
D. $ 1150
E. $ 1500

multiply(divide(500, subtract(const_100, add(add(multiply(10, 2), 20), 10))), const_100)

Explanation: "2 children got = 2 * 10 % = 20 % wife got = 20 % orphan house = 10 % total = 20 + 20 + 10 = 50 % remaining = 100 - 50 = 50 % 50 % = 500 100 % = 500 * 100 / 50 = $ 1000 answer is b"


Question: the average weight of 8 persons increases by 5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?

<gadget id="calculator">8 * 5</gadget>
<output>40</output>

<gadget id="calculator">65 + 40</gadget>
<output>105</output>
<result>105</result>

Choices:
A. 75 kg
B. 65 kg
C. 55 kg
D. 85 kg
E. 105 kg

Explanation: "total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 65 + 40 ) kg = 105 kg . answer : e"


Question: two cubes of their volumes in the ratio 64 : 343 . the ratio of their surface area is :

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>

<gadget id="calculator">343 ** (1/3)</gadget>
<output>7</output>

<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>
<result>4/7 = around 0.571429</result>

Choices:
A. 1.5 : 5
B. 2 : 5
C. 3 : 5
D. 1 : 5
E. 4 : 7

divide(power(64, const_0_33), power(343, const_0_33))

Explanation: "the ratio of their surface area is 64 : 343 4 : 7 answer is e ."


Question: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 , then n =

<gadget id="calculator">28 * 2</gadget>
<output>56</output>

<gadget id="calculator">56 - 2</gadget>
<output>54</output>

<gadget id="calculator">54 / 2</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 3
B. 6
C. 12
D. 27
E. 24

Explanation: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 = > 4 x 2 ^ 2 n = 4 ^ 28 = 2 ^ 56 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 56 = > 2 ^ ( 2 n + 2 ) = 2 ^ 56 = > 2 n + 2 = 56 = > n = 27 so . answer will be d ."


Question: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order y ? ( 1 cubic meter = 1000 liters )

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1_000 ** (1/3)</gadget>
<output>10</output>

<gadget id="calculator">10 * 10</gadget>
<output>100</output>

<gadget id="calculator">100 * 12</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / 2</gadget>
<output>600</output>

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

<gadget id="calculator">600 / 8</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 92
B. 90
C. 82
D. 78
E. 75

divide(divide(multiply(multiply(power(1000, divide(1, const_3)), power(1000, divide(1, const_3))), const_12), const_2), multiply(4, 2))

Explanation: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . y = 12.5 * 6 = 75 . e


Question: if a / b = 4 / 3 , then ( 3 a + 2 b ) / ( 3 a - 2 b ) = ?

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">12 + 6</gadget>
<output>18</output>

<gadget id="calculator">12 - 6</gadget>
<output>6</output>

<gadget id="calculator">18 / 6</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 6
B. 3
C. 5
D. - 1
E. none

divide(add(multiply(3, 4), multiply(2, 3)), subtract(multiply(3, 4), multiply(2, 3)))

Explanation: answer dividing numerator as well as denominator by b , we get given exp . = ( 3 a + 2 b ) / ( 3 a - 2 b ) = ( 3 a / b + 2 ) / ( 3 a / b - 2 ) = [ ( 3 x 4 ) / 3 + 2 ] / [ ( 3 x 4 ) / 3 - 2 ] = ( 4 + 2 ) / ( 4 - 2 ) = 3 option : b


Question: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 15000 left with him . find salary . .

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(1/5) + (1/10)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/10) + (3/5)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">15_000 / (1/10)</gadget>
<output>150_000</output>
<result>150_000</result>

Choices:
A. $ 150000
B. $ 18000
C. $ 180000
D. $ 1800
E. none

divide(15000, subtract(const_1, add(add(divide(1, 5), divide(1, 10)), divide(3, 5))))

Explanation: [ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 15000 , = [ 1 - 9 / 10 ] * total salary = $ 15000 , total salary = $ 15000 * 10 = $ 150000 , correct answer ( a )


Question: how many cuboids of length 5 m , width 3 m and height 2 m can be farmed from a cuboid of 12 m length , 14 m width and 10 m height .

<gadget id="calculator">12 * 14</gadget>
<output>168</output>

<gadget id="calculator">168 * 10</gadget>
<output>1_680</output>

<gadget id="calculator">5 * 3</gadget>
<output>15</output>

<gadget id="calculator">15 * 2</gadget>
<output>30</output>

<gadget id="calculator">1_680 / 30</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 82
B. 56
C. 80
D. 56
E. 100

divide(multiply(multiply(12, 14), 10), multiply(multiply(5, 3), 2))

Explanation: "( 12 ã — 14 ã — 10 ) / ( 5 ã — 3 ã — 2 ) = 56 answer is b ."


Question: the length of the bridge , which a train 160 m long and traveling at 45 km / hr can cross in 30 sec is ?

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>

<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>

<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>

<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>

<gadget id="calculator">375 - 160</gadget>
<output>215</output>
<result>215</result>

Choices:
A. 377
B. 367
C. 237
D. 215
E. 267

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 160)

Explanation: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 x = 215 m . answer : d"


Question: car dealership x , the total profit from sales increased by 30 percent over the previous years , while the number of cars sold decreased by 30 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

<gadget id="calculator">10 - 3</gadget>
<output>7</output>

<gadget id="calculator">130 / 7</gadget>
<output>130/7 = around 18.571429</output>

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

<gadget id="calculator">(130/7) - 10</gadget>
<output>60/7 = around 8.571429</output>

<gadget id="calculator">(60/7) / 10</gadget>
<output>6/7 = around 0.857143</output>

<gadget id="calculator">(6/7) * 100</gadget>
<output>600/7 = around 85.714286</output>
<result>600/7 = around 85.714286</result>

Choices:
A. 18 %
B. 30 %
C. 52 %
D. 63 %
E. 85.71 %

multiply(divide(subtract(divide(add(const_100, 30), subtract(const_10, const_3)), divide(const_100, const_10)), divide(const_100, const_10)), const_100)

Explanation: let profit be x and cars sold be y originally profit / car = x / y now it is 1.3 x / 0.7 y = 13 / 7 ( x / y ) increase in profit per car = ( ( 6 / 7 ) ( x / y ) ) / ( x / y ) * 100 = 85.71 % answer = e


Question: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 30 days .

<gadget id="calculator">30 / 10</gadget>
<output>3</output>

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">30 - 12</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 16 days .
B. 17 days .
C. 18 days .
D. 19 days .
E. 20 days .

subtract(30, multiply(divide(30, 10), 4))

Explanation: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 30 * 6 / 10 = 18 days . answer : c"


Question: 10 men and 15 women together can complete a work in 8 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?

<gadget id="calculator">1 * 100</gadget>
<output>100</output>

<gadget id="calculator">10 * 8</gadget>
<output>80</output>

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

<gadget id="calculator">100 / 20</gadget>
<output>5</output>

<gadget id="calculator">15 * 8</gadget>
<output>120</output>

<gadget id="calculator">5 * 120</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 127 days
B. 667 days
C. 177 days
D. 187 days
E. 600 days

multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 8))), multiply(15, 8))

Explanation: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 8 15 women ' s 1 day work = ( 1 / 8 - 10 / 100 ) = 1 / 40 1 woman ' s 1 day work = 1 / 600 1 woman alone can complete the work in 600 days . answer : e"


Question: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same sum at the rate and for the same time ?

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) * 2</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">50 / (1/10)</gadget>
<output>500</output>

<gadget id="calculator">500 * 5</gadget>
<output>2_500</output>

<gadget id="calculator">2_500 / 100</gadget>
<output>25</output>

<gadget id="calculator">25 + 500</gadget>
<output>525</output>

<gadget id="calculator">525 * 5</gadget>
<output>2_625</output>

<gadget id="calculator">2_625 / 100</gadget>
<output>105/4 = around 26.25</output>

<gadget id="calculator">525 + (105/4)</gadget>
<output>2_205/4 = around 551.25</output>

<gadget id="calculator">(2_205/4) - 500</gadget>
<output>205/4 = around 51.25</output>
<result>205/4 = around 51.25</result>

Choices:
A. rs . 51.25
B. rs . 51.27
C. rs . 51.79
D. rs . 51.8
E. rs . 51.93

subtract(add(add(divide(multiply(divide(50, multiply(divide(5, const_100), 2)), 5), const_100), divide(50, multiply(divide(5, const_100), 2))), divide(multiply(add(divide(multiply(divide(50, multiply(divide(5, const_100), 2)), 5), const_100), divide(50, multiply(divide(5, const_100), 2))), 5), const_100)), divide(50, multiply(divide(5, const_100), 2)))

Explanation: "sum = ( 50 * 100 ) / ( 2 * 5 ) = rs . 500 amount = [ 500 * ( 1 + 5 / 100 ) 2 ] = rs . 551.25 c . i . = ( 551.25 - 500 ) = rs . 51.25 . answer : a"


Question: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 6.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?

<gadget id="calculator">6.8 - 3.2</gadget>
<output>3.6</output>

<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>

<gadget id="calculator">(sqrt(2)) - 1</gadget>
<output>-1 + sqrt(2) = around 0.414214</output>

<gadget id="calculator">5 + (-1 + sqrt(2))</gadget>
<output>sqrt(2) + 4 = around 5.414214</output>

<gadget id="calculator">3.6 / (sqrt(2) + 4)</gadget>
<output>3.6/(sqrt(2) + 4) = around 0.664917</output>

<gadget id="calculator">(3.6/(sqrt(2) + 4)) * 5</gadget>
<output>18.0/(sqrt(2) + 4) = around 3.324583</output>

<gadget id="calculator">3.2 + (18.0/(sqrt(2) + 4))</gadget>
<output>3.2 + 18.0/(sqrt(2) + 4) = around 6.524583</output>
<result>3.2 + 18.0/(sqrt(2) + 4) = around 6.524583</result>

Choices:
A. $ 4.50
B. $ 5.10
C. $ 5.30
D. $ 5.50
E. $ 6.50

add(3.20, multiply(divide(subtract(6.80, 3.20), add(5, subtract(sqrt(2), 1))), 5))

Explanation: "i tried using time / rate approach : - initial price difference = 6.80 - 3.20 = 3.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 3.6 = t ( 5.4 x ) - > t = ( 3.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 3.6 / 5.4 = 6.5 answer e ."


Question: a shopkeeper has 280 kg of apples . he sells 40 % of these at 30 % profit and remaining 60 % at 30 % profit . find his % profit on total .

<gadget id="calculator">280 * 40</gadget>
<output>11_200</output>

<gadget id="calculator">11_200 / 100</gadget>
<output>112</output>

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">112 * (13/10)</gadget>
<output>728/5 = around 145.6</output>

<gadget id="calculator">280 * 60</gadget>
<output>16_800</output>

<gadget id="calculator">16_800 / 100</gadget>
<output>168</output>

<gadget id="calculator">168 * (13/10)</gadget>
<output>1_092/5 = around 218.4</output>

<gadget id="calculator">(728/5) + (1_092/5)</gadget>
<output>364</output>

<gadget id="calculator">364 - 280</gadget>
<output>84</output>

<gadget id="calculator">84 * 100</gadget>
<output>8_400</output>

<gadget id="calculator">8_400 / 280</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 24 %
B. 25 %
C. 26 %
D. 28 %
E. 30 %

divide(multiply(subtract(add(multiply(divide(multiply(280, 40), const_100), divide(add(const_100, 30), const_100)), multiply(divide(multiply(280, 60), const_100), divide(add(const_100, 30), const_100))), 280), const_100), 280)

Explanation: "if the total quantity was 100 then 40 x 30 % + 60 x 30 % = 30 this profit will remain same for any total quantity unless the % of products remains the same . hence ' e ' is the answer"


Question: the speed of a boat in still water in 42 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 44 minutes is :

<gadget id="calculator">42 + 4</gadget>
<output>46</output>

<gadget id="calculator">44 / 60</gadget>
<output>11/15 = around 0.733333</output>

<gadget id="calculator">46 * (11/15)</gadget>
<output>506/15 = around 33.733333</output>
<result>506/15 = around 33.733333</result>

Choices:
A. 86.6 km
B. 46.6 km
C. 33.7 km
D. 35.6 km
E. 26.6 km

multiply(add(42, 4), divide(44, const_60))

Explanation: "speed downstream = ( 42 + 4 ) = 46 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 46 = 33.7 km answer : c"


Question: a rectangular field has a length 10 meters more than it is width . if the area of the field is 119 , what is the length ( in meters ) of the rectangular field ?

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">119 / 10</gadget>
<output>119/10 = around 11.9</output>

<gadget id="calculator">(119/10) / 2</gadget>
<output>119/20 = around 5.95</output>

<gadget id="calculator">(1/3) + (119/20)</gadget>
<output>377/60 = around 6.283333</output>

<gadget id="calculator">(1/4) + (377/60)</gadget>
<output>98/15 = around 6.533333</output>

<gadget id="calculator">10 + (98/15)</gadget>
<output>248/15 = around 16.533333</output>
<result>248/15 = around 16.533333</result>

Choices:
A. 13
B. 15
C. 17
D. 19
E. 21

add(10, add(const_0_25, add(const_0_33, divide(divide(119, 10), const_2))))

Explanation: "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 ( too high ) 18 * 8 = 144 ( too high ) 17 * 7 = 119 the length is 17 meters . the answer is c ."


Question: in country z , 12 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?

<gadget id="calculator">100 - 40</gadget>
<output>60</output>

<gadget id="calculator">25 * 60</gadget>
<output>1_500</output>

<gadget id="calculator">1_500 / 100</gadget>
<output>15</output>

<gadget id="calculator">40 - 12</gadget>
<output>28</output>

<gadget id="calculator">15 + 28</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 35 %
B. 43 %
C. 55 %
D. 65 %
E. 75 %

add(divide(multiply(25, subtract(const_100, 40)), const_100), subtract(40, 12))

Explanation: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 12 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 28 % of the people have their job of choice and a diploma ( 40 % - 12 % = 28 % ) . 28 % + 15 % = 43 % . therefore 43 % of the people in country z have a diploma . ans b"


Question: in a village of 2,500 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">25 / (1/4)</gadget>
<output>100</output>

<gadget id="calculator">26 * 100</gadget>
<output>2_600</output>

<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">850 * (3/5)</gadget>
<output>510</output>

<gadget id="calculator">2_600 - 510</gadget>
<output>2_090</output>

<gadget id="calculator">2_090 / 2_600</gadget>
<output>209/260 = around 0.803846</output>
<result>209/260 = around 0.803846</result>

Choices:
A. 221 / 250
B. 199 / 250
C. 33 / 50
D. 8 / 25
E. 51 / 250

divide(subtract(multiply(const_26, divide(multiply(const_5, const_5), const_0_25)), multiply(850, subtract(const_1, divide(40, divide(multiply(const_5, const_5), const_0_25))))), multiply(const_26, divide(multiply(const_5, const_5), const_0_25)))

Explanation: "to solve this we would need to know the number of people who are less than 70 years old , the number of males , and the number of males who are less than 70 years old . overlapping sets : quantity of a or b = a + b - ( a ∩ b ) = quantity of a + quantity of b - ( intersection of a and b ) number of males = 2500 - 850 = 1650 number of people below 70 years old = 2500 - 800 = 1700 number of males below 70 years old = 1700 - ( 850 * 0.4 ) = 1360 total number of people who are male or below 70 = 1650 + 1700 - 1360 = 1990 probability of male or below 70 = 1990 / 2500 = 199 / 250 answer : b"


Question: in 10 years , a will be twice as old as b was 10 years ago . if a is now 5 years older than b the present age of b is

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">20 + 10</gadget>
<output>30</output>

<gadget id="calculator">30 + 5</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 37
B. 38
C. 39
D. 35
E. 41

Explanation: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 5 = > 2 b - b - 5 = 30 b = 35 so the present age of b is 35 years answer : d"


Question: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many ways can the test be completed if every question is unanswered ?

<gadget id="calculator">5 ** 4</gadget>
<output>625</output>
<result>625</result>

Choices:
A. 24
B. 120
C. 625
D. 720
E. 1024

Explanation: "5 choices for each of the 4 questions , thus total of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways . answer : c ."


Question: the total number of digits used in numbering the pages of a book having 369 pages is

<gadget id="calculator">369 * 3</gadget>
<output>1_107</output>

<gadget id="calculator">100 - 1</gadget>
<output>99</output>

<gadget id="calculator">1_107 - 99</gadget>
<output>1_008</output>

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">1_008 - 9</gadget>
<output>999</output>
<result>999</result>

Choices:
A. 732
B. 990
C. 999
D. 1305
E. 1405

subtract(subtract(multiply(369, const_3), subtract(const_100, const_1)), subtract(const_10, const_1))

Explanation: total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 270 ) = ( 9 + 180 + 810 ) = 999 . answer : c


Question: when 732 is subtracted form the square of a number , the answer that is obtained is 5280 . what is the number ?

<gadget id="calculator">732 ** (1/2)</gadget>
<output>2*sqrt(183) = around 27.055499</output>

<gadget id="calculator">(2*sqrt(183)) * 4</gadget>
<output>8*sqrt(183) = around 108.221994</output>

<gadget id="calculator">(8*sqrt(183)) - 4</gadget>
<output>-4 + 8*sqrt(183) = around 104.221994</output>
<result>-4 + 8*sqrt(183) = around 104.221994</result>

Choices:
A. 228
B. 103
C. 286
D. 122
E. 102

Explanation: explanation : let the number be x x 2 - 732 = 5280 x 2 = 5280 + ( 70 + 3 ) 2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2 ( 100 ) ( 3 ) + 32 = ( 100 + 3 ) 2 x = 100 + 3 = 103 . answer : b


Question: the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?

<gadget id="calculator">35 * 182</gadget>
<output>6_370</output>

<gadget id="calculator">6_370 - 166</gadget>
<output>6_204</output>

<gadget id="calculator">6_204 + 106</gadget>
<output>6_310</output>

<gadget id="calculator">6_310 / 35</gadget>
<output>1_262/7 = around 180.285714</output>

<gadget id="calculator">floor(1_262/7)</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 187.89 cm
B. 180.29 cm
C. 123.98 cm
D. 149.98 cm
E. 146.89 cm

floor(divide(add(subtract(multiply(35, 182), 166), 106), 35))

Explanation: "calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b"


Question: the length of a train and that of a platform are equal . if with a speed of 108 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?

<gadget id="calculator">108 * 1_000</gadget>
<output>108_000</output>

<gadget id="calculator">60 / 1</gadget>
<output>60</output>

<gadget id="calculator">108_000 / 60</gadget>
<output>1_800</output>

<gadget id="calculator">1_800 / 2</gadget>
<output>900</output>
<result>900</result>

Choices:
A. 299
B. 266
C. 299
D. 900
E. 261

divide(divide(multiply(108, const_1000), divide(const_60, const_1)), const_2)

Explanation: "speed = [ 108 * 5 / 18 ] m / sec = 30 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 30 = > x = 30 * 60 / 2 = 900 answer : d"


Question: ravi and sunil are partners in a business . ravi invests rs . 12,000 for 4 months and sunil invested rs . 10000 for 5 months then after one year ratio of their profits will be

<gadget id="calculator">4 * 3</gadget>
<output>12</output>

<gadget id="calculator">5 * 2</gadget>
<output>10</output>

<gadget id="calculator">12 * 10</gadget>
<output>120</output>

<gadget id="calculator">120 * 100</gadget>
<output>12_000</output>

<gadget id="calculator">12_000 * 4</gadget>
<output>48_000</output>

<gadget id="calculator">10_000 * 5</gadget>
<output>50_000</output>

<gadget id="calculator">48_000 / 50_000</gadget>
<output>24/25 = around 0.96</output>
<result>24/25 = around 0.96</result>

Choices:
A. 1 : 3
B. 2 : 3
C. 24 : 25
D. 20 : 22
E. 3 : 4

divide(multiply(multiply(multiply(multiply(const_4, const_3), multiply(5, const_2)), const_100), 4), multiply(10000, 5))

Explanation: = ( 12000 * 4 ) : ( 10000 * 5 ) = 48000 : 50000 = 24 : 25 answer : c


Question: the value of “ a ” varies in inverse proportion as the square of “ b ” . if the value of “ a ” is equal to 40 when “ b ” is equal to 12 . what would be the value of “ a ” when “ b ” is equal to 24 ?

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>

<gadget id="calculator">144 * 40</gadget>
<output>5_760</output>

<gadget id="calculator">24 ** 2</gadget>
<output>576</output>

<gadget id="calculator">5_760 / 576</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 10
B. 88
C. 26
D. 27
E. 28

divide(multiply(power(12, const_2), 40), power(24, const_2))

Explanation: explanation : we have , a α 1 / b 2 a * b 2 = k ( constant ) when b = 12 , a = 40 … . . given k = 40 * ( 12 ) 2 = 5760 now , b = 24 . hence , a = 5760 / 576 = 10 answer : a


Question: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?

<gadget id="calculator">2 * 12</gadget>
<output>24</output>

<gadget id="calculator">15 + 25</gadget>
<output>40</output>

<gadget id="calculator">24 * 40</gadget>
<output>960</output>

<gadget id="calculator">6 * 3</gadget>
<output>18</output>

<gadget id="calculator">960 - 18</gadget>
<output>942</output>

<gadget id="calculator">4 * 3</gadget>
<output>12</output>

<gadget id="calculator">3 * 12</gadget>
<output>36</output>

<gadget id="calculator">942 - 36</gadget>
<output>906</output>

<gadget id="calculator">906 * 4</gadget>
<output>3_624</output>
<result>3_624</result>

Choices:
A. 4000
B. 3624
C. 5673
D. 4530
E. 4566

multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 4)

Explanation: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 4 = rs . 3624 answer : option b"


Question: of the 65 cars on a car lot , 45 have power steering , 25 have power windows , and 17 have both power steering and power windows . how many of the cars on the lot have neither power steering nor power windows ?

<gadget id="calculator">45 + 25</gadget>
<output>70</output>

<gadget id="calculator">70 - 17</gadget>
<output>53</output>

<gadget id="calculator">65 - 53</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 2
B. 8
C. 12
D. 15
E. 18

Explanation: total - neither = all power steering + all power windows - both or 65 - neither = 45 + 25 - 17 = 53 . = > neither = 12 , hence c . answer : c


Question: convert 0.32 in to a vulgar fraction ?

<gadget id="calculator">3 + 2</gadget>
<output>5</output>

<gadget id="calculator">5 * 2</gadget>
<output>10</output>

<gadget id="calculator">10 * 10</gadget>
<output>100</output>

<gadget id="calculator">100 * 0.32</gadget>
<output>32</output>

<gadget id="calculator">32 / 100</gadget>
<output>8/25 = around 0.32</output>
<result>8/25 = around 0.32</result>

Choices:
A. 8 / 25
B. 16 / 50
C. 17 / 50
D. 19 / 50
E. none

divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.32), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))

Explanation: "answer 0.32 = 32 / 100 = 8 / 25 correct option : a"


Question: the l . c . m . of two numbers is 60 . the numbers are in the ratio 2 : 3 . then sum of the number is :

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">60 / 6</gadget>
<output>10</output>

<gadget id="calculator">10 * 3</gadget>
<output>30</output>

<gadget id="calculator">10 * 2</gadget>
<output>20</output>

<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 28
B. 32
C. 40
D. 53
E. 50

add(multiply(divide(60, multiply(2, 3)), 3), multiply(divide(60, multiply(2, 3)), 2))

Explanation: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 60 or x = 10 . the numbers are 20 and 30 . hence , required sum = ( 20 + 30 ) = 50 . answer : option e"


Question: a cycle is bought for rs . 900 and sold for rs . 1170 , find the gain percent ?

<gadget id="calculator">1_170 - 900</gadget>
<output>270</output>

<gadget id="calculator">270 / 900</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 27 %
B. 20 %
C. 80 %
D. 30 %
E. 24 %

multiply(divide(subtract(1170, 900), 900), const_100)

Explanation: "900 - - - - 270 100 - - - - ? = > 30 % answer : d"


Question: rs 378 is divided among the 3 children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of esha . how much the rupee anusha get ?

<gadget id="calculator">12 / 8</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">1 + (3/2)</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">12 / 6</gadget>
<output>2</output>

<gadget id="calculator">(5/2) + 2</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">378 / (9/2)</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 74
B. 84
C. 94
D. 104
E. 114

divide(378, add(add(const_1, divide(12, 8)), divide(12, 6)))

Explanation: if money with anusha = a , babu = b & esha = e , then a + b + e = 378 - - - ( i ) & 12 a = 8 b = 6 e , so b = 3 a / 2 & e = 2 a substituting these values of b & e in ( i ) , a + ( 3 a / 2 ) + 2 a = 378 , on solving , a = 84 so , b = 126 , e = 168 answer : b


Question: the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is ?

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">15 * (2/5)</gadget>
<output>6</output>

<gadget id="calculator">6 + 2</gadget>
<output>8</output>

<gadget id="calculator">4_000 / 8</gadget>
<output>500</output>

<gadget id="calculator">500 * 3</gadget>
<output>1_500</output>

<gadget id="calculator">(2/5) * 500</gadget>
<output>200</output>

<gadget id="calculator">200 * 12</gadget>
<output>2_400</output>

<gadget id="calculator">1_500 + 2_400</gadget>
<output>3_900</output>
<result>3_900</result>

Choices:
A. rs . 3900
B. rs . 4900
C. rs . 4980
D. rs . 5000
E. rs . 5900

add(multiply(divide(4000, add(multiply(15, divide(4, 10)), 2)), 3), multiply(multiply(divide(4, 10), divide(4000, add(multiply(15, divide(4, 10)), 2))), 12))

Explanation: let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a )


Question: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 12 multiples of 14 , how many multiples of 7 are there in q ?

<gadget id="calculator">12 * 2</gadget>
<output>24</output>

<gadget id="calculator">24 - 1</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 20
B. 21
C. 22
D. 23
E. 24

Explanation: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 12 + 11 = 23 . the answer is d ."


Question: the average age of 15 students of a class is 15 years . out of these , the average age of 6 students is 14 years and that of the other 8 students is 16 years . the age of the 15 th student is

<gadget id="calculator">15 * 15</gadget>
<output>225</output>

<gadget id="calculator">6 * 14</gadget>
<output>84</output>

<gadget id="calculator">8 * 16</gadget>
<output>128</output>

<gadget id="calculator">84 + 128</gadget>
<output>212</output>

<gadget id="calculator">225 - 212</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 9 years
B. 13 years
C. 14 years
D. 21 years
E. 25 years

subtract(multiply(15, 15), add(multiply(6, 14), multiply(8, 16)))

Explanation: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 6 + 16 x 8 ) ] = ( 225 - 212 ) = 13 years . answer b"


Question: a can do a work in 6 days . b can do the same work in 12 days . if both a & b are working together in how many days they will finish the work ?

<gadget id="calculator">6 * 12</gadget>
<output>72</output>

<gadget id="calculator">6 + 12</gadget>
<output>18</output>

<gadget id="calculator">72 / 18</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3
B. 5
C. 4
D. 2
E. 6

Explanation: "a rate = 1 / 6 b rate = 1 / 12 ( a + b ) rate = ( 1 / 6 ) + ( 1 / 12 ) = 1 / 4 a & b finish the work in 4 days correct option is c"


Question: in an organisation there are 1000 employees out of which 250 earn below 10 k $ and 500 earn between 10 k $ and 50 k $ . what is the total percentage of employees who earn less than 50 k $ ?

<gadget id="calculator">1_000 - 250</gadget>
<output>750</output>

<gadget id="calculator">750 / 1_000</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 66 %
B. 75 %
C. 70 %
D. 50 %
E. 82 %

multiply(divide(subtract(1000, 250), 1000), const_100)

Explanation: total percentage = ( 250 + 500 ) / 1000 = 0.75 b


Question: how many quarters are equal to 6 dollars ?

<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 1
B. 8
C. 12
D. 9
E. 24

Explanation: 6 * 4 = 24 quarters answer : e


Question: the price of 2 sarees and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?

<gadget id="calculator">6 - 4</gadget>
<output>2</output>

<gadget id="calculator">2 - 1</gadget>
<output>1</output>

<gadget id="calculator">2 / 1</gadget>
<output>2</output>

<gadget id="calculator">2 * 2</gadget>
<output>4</output>

<gadget id="calculator">4 + 4</gadget>
<output>8</output>

<gadget id="calculator">1_600 / 8</gadget>
<output>200</output>

<gadget id="calculator">200 * 12</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 2500
B. 2700
C. 2200
D. 2900
E. 2400

multiply(divide(1600, add(multiply(2, divide(subtract(6, 4), subtract(2, 1))), 4)), 12)

Explanation: let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . answer is e .


Question: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number y of employees who take the subway to work ?

<gadget id="calculator">48 * 3</gadget>
<output>144</output>

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">144 / 12</gadget>
<output>12</output>

<gadget id="calculator">48 - 12</gadget>
<output>36</output>

<gadget id="calculator">36 / 12</gadget>
<output>3</output>

<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 12
B. 13
C. 14
D. 15
E. 16

add(divide(multiply(48, 3), multiply(3, 4)), divide(subtract(48, multiply(3, 4)), divide(multiply(48, 3), multiply(3, 4))))

Explanation: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible y : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"


Question: a garden center sells a certain grass seed in 5 - pound bags at $ 13.80 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?

<gadget id="calculator">2 * 32.25</gadget>
<output>64.5</output>

<gadget id="calculator">1 * 20.43</gadget>
<output>20.43</output>

<gadget id="calculator">64.5 + 20.43</gadget>
<output>84.93</output>

<gadget id="calculator">1 * 13.8</gadget>
<output>13.8</output>

<gadget id="calculator">84.93 + 13.8</gadget>
<output>98.73</output>
<result>98.73</result>

Choices:
A. $ 98.73
B. $ 96.75
C. $ 98.78
D. $ 102.07
E. $ 105.3

add(add(multiply(const_2, 32.25), multiply(const_1, 20.43)), multiply(const_1, 13.8))

Explanation: there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.73 or 2 ) 25 + 25 + 25 = $ 96.75 a


Question: in the manufacture of a certain product , 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">5 * (1/25)</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 0.125 %
B. 0.2 %
C. 0.8 %
D. 1.25 %
E. 2.0 %

Explanation: "percent of defective produced = 5 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 5 / 100 ) * 100 % = ( 20 / 10000 ) * 100 % = ( 20 / 100 ) % = . 2 % answer b"


Question: a student appeared in the mock cat . the test paper contained 3 sections namely qa , di and va . the percentage marks in all va was equal to the average of percentage marks in all the 3 sections . coincidentally , if we reverse the digit of the percentage marks of qa we get the percentage marks of di . the percentage marks in va scored by student could be :

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

<gadget id="calculator">9 + 2</gadget>
<output>11</output>

<gadget id="calculator">11 + 11</gadget>
<output>22</output>

<gadget id="calculator">22 + 11</gadget>
<output>33</output>

<gadget id="calculator">33 + 11</gadget>
<output>44</output>

<gadget id="calculator">44 + 11</gadget>
<output>55</output>

<gadget id="calculator">55 + 11</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 81
B. 48
C. 66
D. 69
E. none of these

add(add(add(add(add(add(multiply(3, 3), const_2), add(multiply(3, 3), const_2)), add(multiply(3, 3), const_2)), add(multiply(3, 3), const_2)), add(multiply(3, 3), const_2)), add(multiply(3, 3), const_2))

Explanation: solution : let the percentage marks in qa = ( 10 a + b ) % let the percentage marks in di = ( 10 b + a ) % let the percentage marks in va = x % . now , according to the question , we have , [ ( 10 a + b ) + x + ( 10 b + a ) ] / 3 = x → 11 a + 11 b + x = 3 x . or , x = 11 ( a + b ) / 2 . clearly , we can see that the percentage of the va section will be a multiple of 11 . so , required answer will be 66 . answer : option c


Question: two trains of equal are running on parallel lines in the same direction at 45 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?

<gadget id="calculator">45 - 36</gadget>
<output>9</output>

<gadget id="calculator">9 * 1_000</gadget>
<output>9_000</output>

<gadget id="calculator">9_000 / 3_600</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">36 * (5/2)</gadget>
<output>90</output>

<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 45
B. 88
C. 66
D. 55
E. 22

divide(multiply(36, divide(multiply(subtract(45, 36), const_1000), const_3600)), const_2)

Explanation: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 45 - 36 = 9 km / hr . = 9 * 5 / 18 = 5 / 2 m / sec . 2 x / 36 = 5 / 2 = > x = 45 . answer : a"


Question: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 2 cm when a man gets on it . the mass of man is

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">6 * (1/50)</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) * 1_000</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 12 kg
B. 60 kg
C. 72 kg
D. 120 kg
E. none

multiply(multiply(multiply(3, 2), divide(2, const_100)), const_1000)

Explanation: "solution volume of water displaced = ( 3 x 2 x 0.02 ) m 3 = 0.12 m 3 . mass of man = volume of water displaced × density of water = ( 0.12 × 1000 ) kg = 120 kg . answer d"


Question: in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 kg ?

<gadget id="calculator">20 - 16.5</gadget>
<output>3.5</output>

<gadget id="calculator">16.5 - 15</gadget>
<output>1.5</output>

<gadget id="calculator">3.5 / 1.5</gadget>
<output>2.333333</output>
<result>2.333333</result>

Choices:
A. 7 : 3
B. 3 : 7
C. 4 : 6
D. 5 : 7
E. 8 : 9

Explanation: "required rate = 3.50 : 1.50 = 7 : 3 . answer a"


Question: if the personal income tax rate is lowered from 46 % to 32 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36000 ?

<gadget id="calculator">36_000 / 100</gadget>
<output>360</output>

<gadget id="calculator">46 - 32</gadget>
<output>14</output>

<gadget id="calculator">360 * 14</gadget>
<output>5_040</output>
<result>5_040</result>

Choices:
A. $ 3500
B. $ 5040
C. $ 3150
D. $ 7000
E. $ 10000

multiply(divide(36000, const_100), subtract(46, 32))

Explanation: "saving = ( 46 - 32 ) % of 36000 = 5040 . answer : b"


Question: how many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number ?

<gadget id="calculator">100 / 5</gadget>
<output>20</output>

<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 4
B. 10
C. 11
D. 12
E. 15

Explanation: the question basically asks how many positive odd integers less than 100 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 , 85,95 = 10 ans b


Question: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 625 meters in length ?

<gadget id="calculator">165 + 625</gadget>
<output>790</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">790 / 15</gadget>
<output>158/3 = around 52.666667</output>
<result>158/3 = around 52.666667</result>

Choices:
A. 62
B. 72
C. 55
D. 82
E. 52.7

Explanation: "explanation : t = ( 625 + 165 ) / 54 * 18 / 5 t = 52.7 answer : option e"


Question: the length of a rectangle is one fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 784 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 5 units ?

<gadget id="calculator">784 ** (1/2)</gadget>
<output>28</output>

<gadget id="calculator">28 / 4</gadget>
<output>7</output>

<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 35 sq . units
B. 45 sq . units
C. 55 sq . units
D. 50 sq . units
E. 40 sq . units

Explanation: given that the area of the square = 784 sq . units = > side of square = â ˆ š 784 = 28 units the radius of the circle = side of the square = 28 units length of the rectangle = 1 / 4 * 28 = 7 units given that breadth = 5 units area of the rectangle = lb = 7 * 5 = 35 sq . units answer : a


Question: 33 1 / 3 % of 36 ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">33 + (1/3)</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">(100/3) * 36</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 16
B. 21
C. 18
D. 12 number
E. 18

divide(multiply(add(33, divide(1, 3)), 36), const_100)

Explanation: explanation : 33 1 / 3 % = 1 / 3 1 / 3 * 36 = 12 answer : option d


Question: an engine moves at the speed of 30 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 18 kmph . what will be the speed of train when 16 coaches are attached .

<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>

<gadget id="calculator">30 - 18</gadget>
<output>12</output>

<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>

<gadget id="calculator">12 / 3</gadget>
<output>4</output>

<gadget id="calculator">4 * 4</gadget>
<output>16</output>

<gadget id="calculator">30 - 16</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 14
B. 16
C. 18
D. 20
E. 22

subtract(30, multiply(sqrt(16), divide(subtract(30, 18), sqrt(9))))

Explanation: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 16 swr root = 4 decrease = 4 * 4 = 16 new speed = 30 - 16 = 14 a"


Question: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 10.50 per hour , how much less than a manager does a chef earn each hour ?

<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">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(6/5) * (1/2)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 10.5</gadget>
<output>4.2</output>
<result>4.2</result>

Choices:
A. $ 1.40
B. $ 2.40
C. $ 3.40
D. $ 4.40
E. $ 4.30

multiply(subtract(const_1, multiply(divide(add(const_100, 20), const_100), divide(const_1, const_2))), 10.50)

Explanation: "manager wages per hour = $ 10.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 10.50 ) = = > $ 5.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 5.25 = ( 20 * ( $ 5.25 ) ) / 100 - - > ( $ 95 ) / 100 - - > $ 0.95 therefore , chef wages per hour = $ 5.25 + $ 0.95 = = > $ 6.20 difference of wages between manager and chef = $ 10.50 - $ 6.20 = = > $ 4.30 answer : e"


Question: if the height of a cone is increased by 140 % then its volume is increased by ?

<gadget id="calculator">140 * 1</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 100
B. 140
C. 998
D. 729
E. 2879

Explanation: 140 % answer : b


Question: 1345 - ( 1002 / 20.04 ) = ?

<gadget id="calculator">1_002 / 20.04</gadget>
<output>50</output>

<gadget id="calculator">1_345 - 50</gadget>
<output>1_295</output>
<result>1_295</result>

Choices:
A. 2984
B. 2983
C. 2982
D. 1295
E. none of these

Explanation: "1345 - 50 = 1295 answer : d"


Question: the guests at a football banquet consumed a total of 325 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?

<gadget id="calculator">325 / 2</gadget>
<output>325/2 = around 162.5</output>

<gadget id="calculator">floor(325/2)</gadget>
<output>162</output>

<gadget id="calculator">162 + 1</gadget>
<output>163</output>
<result>163</result>

Choices:
A. 160
B. 161
C. 162
D. 163
E. 164

Explanation: "to minimize one quantity maximize other . 162 * 2 ( max possible amount of food a guest could consume ) = 324 pounds , so there must be more than 162 guests , next integer is 163 . answer : d ."


Question: how many 3 - digit numbers abc , in which a , b , and c are each digits , satisfy the equation 2 b = a + c ?

<gadget id="calculator">3 * 12</gadget>
<output>36</output>

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

<gadget id="calculator">36 + 8</gadget>
<output>44</output>

<gadget id="calculator">44 + 1</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 33
B. 36
C. 41
D. 45
E. 50

add(add(multiply(3, const_12), multiply(2, const_4)), const_1)

Explanation: possible solutions are diff of 0 - - 111222 , . . . . . . . . , 999 = 9 diff of 1 - - 123 , 234 , . . . . . , 789 = 7 x 2 = 14 diff of 2 - - 135 , 246 . . . . . . . 579 = 5 x 2 = 10 diff of 3 - - 147 , 258369 = 3 x 2 = 6 diff of 4 - - 159 = 1 x 2 = 2 last 210 , 420 , 630840 = 4 so total is 9 + 14 + 10 + 6 + 2 + 4 = 45 . answer : d


Question: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 2 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 40</gadget>
<output>240</output>

<gadget id="calculator">240 / 2</gadget>
<output>120</output>

<gadget id="calculator">120 * 3</gadget>
<output>360</output>

<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 180
B. 45
C. 60
D. 90
E. 135

divide(multiply(divide(multiply(multiply(2, 3), 40), 2), 3), 2)

Explanation: we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 2 / 3 ) of total igneous rocks . ( 2 / 3 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 3 / 2 ) = 60 total sedimentary rocks = 2 * total igneous rocks = 2 * 60 = 120 total number of rocks = 60 + 120 = 180 answer ( a )


Question: 3 sets of 40 , 50 and 60 students appeared for an examination and the pass percentage was 100 , 90 and 80 respectively . the pass percentage of the whole set is

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">50 * (9/10)</gadget>
<output>45</output>

<gadget id="calculator">40 + 45</gadget>
<output>85</output>

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">60 * (4/5)</gadget>
<output>48</output>

<gadget id="calculator">85 + 48</gadget>
<output>133</output>

<gadget id="calculator">40 + 50</gadget>
<output>90</output>

<gadget id="calculator">90 + 60</gadget>
<output>150</output>

<gadget id="calculator">133 / 150</gadget>
<output>133/150 = around 0.886667</output>

<gadget id="calculator">(133/150) * 100</gadget>
<output>266/3 = around 88.666667</output>
<result>266/3 = around 88.666667</result>

Choices:
A. 88.33
B. 84.33
C. 88.66
D. 84.66
E. none of these

multiply(divide(add(add(40, multiply(50, divide(90, const_100))), multiply(60, divide(80, const_100))), add(add(40, 50), 60)), const_100)

Explanation: total passed student = 40 + 45 + 48 = 133 133 is 88.66 % of 150 answer : c


Question: ake can dig a well in 16 days . paul can dig the same well in 24 days . jake , paul and hari together dig the well in 8 days . hari alone can dig the well in

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">(1/16) + (1/24)</gadget>
<output>5/48 = around 0.104167</output>

<gadget id="calculator">(1/8) - (5/48)</gadget>
<output>1/48 = around 0.020833</output>

<gadget id="calculator">1 / (1/48)</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 48
B. 39
C. 37
D. 27
E. 29

divide(const_1, subtract(divide(const_1, 8), add(divide(const_1, 16), divide(const_1, 24))))

Explanation: simple one . let the total work to be done is 48 meters . now jake can dig 3 mts , paul can dig 2 mts a day . now all of them combined dug in 8 days so per day they dug 48 / 8 = 6 mts . so of these 8 mts , hari capacity is 1 mt . so he takes 48 / 1 = 48 days to complete the digging job . answer : a


Question: a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is

<gadget id="calculator">1 + 2</gadget>
<output>3</output>

<gadget id="calculator">2 - 1</gadget>
<output>1</output>

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

Choices:
A. 1 : 2
B. 1 : 3
C. 2 : 1
D. 3 : 1
E. none

divide(add(const_1, const_2), subtract(const_2, const_1))

Explanation: "sol . let man ’ s rate upstream be x kmph . then , his rate downstream = 2 x kmph . ∴ ( speed in still water ) : ( speed of stream ) = [ 2 x + x / 2 ] : [ 2 x - x / 2 ] 3 x / 2 : x / 2 = 3 : 1 . answer d"


Question: a can complete the job in 6 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete

<gadget id="calculator">6 - 1</gadget>
<output>5</output>

<gadget id="calculator">5 - 3</gadget>
<output>2</output>

<gadget id="calculator">6 * 3</gadget>
<output>18</output>

<gadget id="calculator">2 / 18</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 1 / 9
B. 3 / 10
C. 1 / 2
D. 5 / 6
E. 8 / 9

divide(subtract(subtract(6, 1), 3), multiply(6, 3))

Explanation: a = 1 / 9


Question: list r contains 5 numbers that have an average value of 60 . if the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number , what is the smallest possible value in the list ?

<gadget id="calculator">60 * 5</gadget>
<output>300</output>

<gadget id="calculator">300 - 60</gadget>
<output>240</output>

<gadget id="calculator">240 - 60</gadget>
<output>180</output>

<gadget id="calculator">180 - 20</gadget>
<output>160</output>

<gadget id="calculator">160 - 20</gadget>
<output>140</output>

<gadget id="calculator">140 / 5</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 25
B. 28
C. 31
D. 34
E. 37

divide(subtract(subtract(subtract(subtract(multiply(60, 5), 60), 60), 20), 20), 5)

Explanation: the middle number is 60 . let the smallest number be x . then the largest number is 2 x + 20 . to make x as small as possible , let ' s make the remaining numbers as large as possible . so the second largest = the largest = 2 x + 20 . the second smallest should be equal to the median . the numbers are x , 60 , 60 , 2 x + 20 , 2 x + 20 . x + 60 + 60 + 2 x + 20 + 2 x + 20 = 5 * 60 = 300 5 x = 140 x = 28 the answer is b .


Question: if a - b = 6 and a 2 + b 2 = 50 , find the value of ab .

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>

<gadget id="calculator">50 - 36</gadget>
<output>14</output>

<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 12
C. 15
D. 18
E. 20

Explanation: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 50 - 36 = 14 ab = 7 . answer : a"


Question: in 5 football games thus far this season , barry has run for 98 , 107 , 85 , 89 , and 91 yards . at a minimum , how many yards m will he need to gain this sunday if he wants to keep his season average above 100 yards ?

<gadget id="calculator">5 + 1</gadget>
<output>6</output>

<gadget id="calculator">100 * 6</gadget>
<output>600</output>

<gadget id="calculator">98 + 107</gadget>
<output>205</output>

<gadget id="calculator">85 + 205</gadget>
<output>290</output>

<gadget id="calculator">89 + 290</gadget>
<output>379</output>

<gadget id="calculator">91 + 379</gadget>
<output>470</output>

<gadget id="calculator">600 - 470</gadget>
<output>130</output>

<gadget id="calculator">130 + 1</gadget>
<output>131</output>
<result>131</result>

Choices:
A. 101
B. 116
C. m = 130
D. m = 131
E. m = 141

add(subtract(multiply(100, add(5, const_1)), add(91, add(89, add(85, add(98, 107))))), const_1)

Explanation: sorry the answer m = 141 is d .


Question: the price of 3 pants and 6 t - shirts is rs . 750 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?

<gadget id="calculator">12 - 6</gadget>
<output>6</output>

<gadget id="calculator">3 - 1</gadget>
<output>2</output>

<gadget id="calculator">6 / 2</gadget>
<output>3</output>

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

<gadget id="calculator">9 + 6</gadget>
<output>15</output>

<gadget id="calculator">750 / 15</gadget>
<output>50</output>

<gadget id="calculator">50 * 8</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 150
B. 250
C. 400
D. 450
E. 550

multiply(divide(750, add(multiply(divide(subtract(12, 6), subtract(3, 1)), 3), 6)), 8)

Explanation: "let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 750 . . . . ( i ) and x + 12 y = 750 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 250 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 750 ( - ) x + 2 y = 250 - - - - - - - - - - - - - - - - 10 y = 500 - - - - - - - - - - - - - - - - y = 50 cost of 8 t - shirts = 8 * 50 = 400 answer : c"


Question: a certain debt will be paid in 65 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?

<gadget id="calculator">20 * 410</gadget>
<output>8_200</output>

<gadget id="calculator">410 + 65</gadget>
<output>475</output>

<gadget id="calculator">65 - 20</gadget>
<output>45</output>

<gadget id="calculator">475 * 45</gadget>
<output>21_375</output>

<gadget id="calculator">8_200 + 21_375</gadget>
<output>29_575</output>

<gadget id="calculator">29_575 / 65</gadget>
<output>455</output>
<result>455</result>

Choices:
A. 443
B. 455
C. 465
D. 468
E. 475

divide(add(multiply(20, 410), multiply(add(410, 65), subtract(65, 20))), 65)

Explanation: "total number of installments = 65 payment per installment for the first 20 installments = 410 payment per installment for the remaining 45 installments = 410 + 65 = 475 average = ( 20 * 410 + 45 * 475 ) / 65 = 455 answer b"


Question: in 7 given numbers , the average of first 4 numbers is 4 and that of last 4 numbers is also 4 . if the average of these 7 numbers is 3 , the fourth number is ?

<gadget id="calculator">4 * 4</gadget>
<output>16</output>

<gadget id="calculator">16 + 16</gadget>
<output>32</output>

<gadget id="calculator">7 * 3</gadget>
<output>21</output>

<gadget id="calculator">32 - 21</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 3
B. 4
C. 7
D. 11
E. 12

subtract(add(multiply(4, 4), multiply(4, 4)), multiply(7, 3))

Explanation: let 7 numbers are a , b , c , d , e , f , g . given avg of first 4 nums are 4 . . . i . e ( a + b + c + d ) / 4 = 4 a + b + c + d = 16 given avg of last 4 nums are also 4 . . i . e . ( d + e + f + g ) / 4 = 4 d + e + f + g = 16 e + f + g = 16 - d given avg of 7 nums are 3 . . . . i . e ( a + b + c + d + e + f + g ) / 7 = 3 a + b + c + d + e + f + g = 21 16 + 16 - d = 21 d = 32 - 21 d = 11 answer : d


Question: at the beginning of a year , the owner of a jewel shop raised the price of all the jewels in his shop by x % and lowered them by x % . the price of one jewel after this up and down cycle reduced by rs . 100 . the owner carried out the same procedure after a month . after this second up - down cycle , the price of that jewel was rs . 2304 . find the original price of that jewel ( in rs . )

<gadget id="calculator">2 * 100</gadget>
<output>200</output>

<gadget id="calculator">200 + 2_304</gadget>
<output>2_504</output>
<result>2_504</result>

Choices:
A. 2500
B. 550
C. 2600
D. 2650
E. none of these

Explanation: solution : let the original price = y , after first change , it becomes , y * ( 1 + ( x / 100 ) ) after second change , it becomes y * ( 1 + ( x / 100 ) ) ( 1 - ( x / 100 ) ) = y ( 1 - ( x / 100 ) ^ 2 ) thus , x 2 * y = 106 - - - - - - - ( 1 ) x 2 = 106 / y now , y ( 1 - ( 106 / 10000 y ) ) 2 = 2304 ( similar to above ) y ( 1 - 100 / y ) 2 = 2304 y = 2500 . answer : option a


Question: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?

<gadget id="calculator">25 + 25</gadget>
<output>50</output>

<gadget id="calculator">50 / 2</gadget>
<output>25</output>

<gadget id="calculator">10 + 25</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 25 %
B. 35 %
C. 45 %
D. 70 %
E. 80 %

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

Explanation: "since the problem does n ' t depend on the number of birds in reserve you can suppose that there are 100 birds . from them 100 * 0.3 = 30 are hawks . so , there are 70 non - hawks . there are 0.4 * 70 = 28 paddyfield - warblers . therefore , there are 0.25 * 28 = 7 kingfishers . the total number of birds in the nature reserve that are not hawks , paddyfield - warblers , or kingfishers is 100 - 30 - 28 - 7 = 35 . the answer is b"


Question: alfred buys an old scooter for $ 4700 and spends $ 600 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?

<gadget id="calculator">4_700 + 600</gadget>
<output>5_300</output>

<gadget id="calculator">5_800 - 5_300</gadget>
<output>500</output>

<gadget id="calculator">500 / 5_300</gadget>
<output>5/53 = around 0.09434</output>

<gadget id="calculator">(5/53) * 100</gadget>
<output>500/53 = around 9.433962</output>
<result>500/53 = around 9.433962</result>

Choices:
A. 5.45 %
B. 6.23 %
C. 7 %
D. 9.43 %
E. 10 %

Explanation: c . p . = 4700 + 600 = $ 5300 s . p . = $ 5800 gain = 5800 - 5300 = $ 500 gain % = 500 / 5300 * 100 = 9.43 % answer is d


Question: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord , in feet ?

<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 30
B. 25
C. 15
D. 10
E. 5

Explanation: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long answer : d"


Question: the sum of two numbers is 66 . how much should be added to the sum for it to be exactly divisible by 9 leaving 0 as the reminder ?

<gadget id="calculator">100 - 9</gadget>
<output>91</output>

<gadget id="calculator">91 - 9</gadget>
<output>82</output>

<gadget id="calculator">82 - 10</gadget>
<output>72</output>

<gadget id="calculator">72 - 66</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 1

subtract(subtract(subtract(subtract(const_100, 9), 9), const_10), 66)

Explanation: the sum is 66 . adding 6 to 66 = 66 + 6 = 72 . 72 is exactly divisible by 9 leaving 0 as the reminder = 8 . so the answer is a = 6


Question: what is next no . 11 23 47 83 131 191 263 347 443 551 ? ? ?

<gadget id="calculator">60 * 2</gadget>
<output>120</output>

<gadget id="calculator">551 + 120</gadget>
<output>671</output>
<result>671</result>

Choices:
A. 171
B. 181
C. 191
D. 201
E. 671

Explanation: 11 + 12 * 1 = 23 23 + 12 * 2 = 47 47 + 12 * 3 = 83 83 + 12 * 4 = 131 131 + 12 * 5 = 191 191 + 12 * 6 = 263 263 + 12 * 7 = 347 347 + 12 * 8 = 443 443 + 12 * 9 = 551 551 + 12 * 10 = 671 answer : e


Question: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 31.5 kg of zinc has been consumed in it ?

<gadget id="calculator">11 / 9</gadget>
<output>11/9 = around 1.222222</output>

<gadget id="calculator">(11/9) * 31.5</gadget>
<output>38.5</output>

<gadget id="calculator">38.5 + 31.5</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 58 kg
B. 60 kg
C. 64 kg
D. 70 kg
E. none

Explanation: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 31.5 kg zinc , mixture , melted = [ 20 / 9 x 31.5 ] kg = 70 kg . answer d"


Question: a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is

<gadget id="calculator">2 * 2</gadget>
<output>4</output>

<gadget id="calculator">4 - 2</gadget>
<output>2</output>

<gadget id="calculator">20 - 2</gadget>
<output>18</output>

<gadget id="calculator">2 - 1</gadget>
<output>1</output>

<gadget id="calculator">18 / 1</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 16
B. 14
C. 15
D. 18
E. 20

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

Explanation: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years = > ( x + 20 ) + 2 = 2 ( x + 2 ) = > x + 22 = 2 x + 4 so , x = 18 . answer : d"


Question: a person buys an article at rs . 400 . at what price should he sell the article so as to make a profit of 40 % ?

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">400 * (2/5)</gadget>
<output>160</output>

<gadget id="calculator">400 + 160</gadget>
<output>560</output>
<result>560</result>

Choices:
A. 600
B. 277
C. 560
D. 261
E. 281

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

Explanation: "cost price = rs . 400 profit = 40 % of 400 = rs . 160 selling price = cost price + profit = 400 + 160 = 560 answer : c"


Question: an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq m ?

<gadget id="calculator">6 * 1.44</gadget>
<output>8.64</output>

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">8.64 * (7/5)</gadget>
<output>12.096</output>

<gadget id="calculator">100 + 25</gadget>
<output>125</output>

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">6 * (5/4)</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">12.096 * (15/2)</gadget>
<output>90.72</output>

<gadget id="calculator">90.72 * 45</gadget>
<output>4_082.4</output>
<result>4_082.4</result>

Choices:
A. rs . 3642.40
B. rs . 3868.80
C. rs . 4216.20
D. rs . 4082.40
E. none of these

multiply(multiply(multiply(multiply(6, 1.44), divide(add(const_100, 40), const_100)), multiply(6, divide(add(const_100, 25), const_100))), 45)

Explanation: "length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 * 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer : d"


Question: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jill and sandy will make a basket but jack will miss ?

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/7) * (1/8)</gadget>
<output>1/56 = around 0.017857</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 - (1/6)</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(1/56) * (5/6)</gadget>
<output>5/336 = around 0.014881</output>
<result>5/336 = around 0.014881</result>

Choices:
A. 3 / 168
B. 5 / 168
C. 7 / 168
D. 5 / 336
E. 7 / 336

multiply(multiply(divide(1, 7), divide(1, 8)), subtract(const_1, divide(1, 6)))

Explanation: the probability that jill and sandy will make a basket but jack will miss is 5 / 6 * 1 / 7 * 1 / 8 = 5 / 336 . the answer is d .


Question: a 11 % stock yields 8 % . the market value of the stock is :

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

<gadget id="calculator">(25/2) * 11</gadget>
<output>275/2 = around 137.5</output>
<result>275/2 = around 137.5</result>

Choices:
A. rs . 72
B. rs . 137.50
C. rs . 112.50
D. rs . 116.50
E. none of these

Explanation: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 11 , investment = rs . ( 100 / 8 x 11 ) = rs . 137.50 ∴ market value of rs . 100 stock = rs . 137.50 answer b"