Question: if there are 200 questions in a 3 hr examination . among these questions are 100 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?

<gadget id="calculator">3 * 60</gadget>
<output>180</output>

<gadget id="calculator">200 - 100</gadget>
<output>100</output>

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

<gadget id="calculator">100 + 200</gadget>
<output>300</output>

<gadget id="calculator">180 / 300</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">2 * (3/5)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 100</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 72 min
B. 62 min
C. 70 min
D. 74 min
E. 120 min

multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 100), multiply(const_2, 100)))), 100)

Explanation: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 100 x + 100 * 2 x = 180 x = 180 / 300 x = 0.6 time taken for type a problem = 100 * 2 * 0.6 = 120 min answer : e"


Question: a and b are 90 km apart they start to move each other simultaneously a at speed 10 and b at 5 km / hr if every hour they double their speed what is distance that a pass until he meet b ?

<gadget id="calculator">10 + 5</gadget>
<output>15</output>

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

<gadget id="calculator">15 + 30</gadget>
<output>45</output>

<gadget id="calculator">15 + 45</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 30 km
B. 40 km
C. 50 km
D. 60 km
E. 70 km

Explanation: in 2 hours a covers ( 10 + 20 ) = 30 km b covers ( 5 + 10 ) = 15 km , total covered = 45 in the next hour they have to cover ( 90 - 45 ) km with the speeds 40 km / hr and 20 km / hr respectively let them take another t hrs to meet so sum of the distance to be covered by both is 45 km ( 40 * t ) + ( 20 * t ) = 45 km gives t = ( 3 / 4 ) hrs we need to fid out the distance covered by a which equals to = 30 + ( 40 * ( 3 / 4 ) ) = 60 km answer : d


Question: a card board of size 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the card box . find the total number of pins used .

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

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

<gadget id="calculator">9 * 5</gadget>
<output>45</output>

<gadget id="calculator">45 - 10</gadget>
<output>35</output>

<gadget id="calculator">100 + 35</gadget>
<output>135</output>
<result>135</result>

Choices:
A. 135
B. 136
C. 137
D. 138
E. 139

add(const_100, subtract(multiply(subtract(const_10, const_1), add(const_4, const_1)), const_10))

Explanation: total 35 pins are there and 4 sides of card board . . . so 35 x 4 = 140 now in the rectangle 4 vertices have 4 pins which is common to the sides . . . . so 140 - 4 = 136 answer : b


Question: a cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 4 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?

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

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

<gadget id="calculator">(1/2) - (1/4)</gadget>
<output>1/4 = around 0.25</output>

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

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

divide(const_1, subtract(divide(const_1, 2), divide(const_1, 4)))

Explanation: "net part filled in 1 hour 1 / 2 - 1 / 4 = 1 / 4 the cistern will be filled in 4 hr answer is e"


Question: evaluate combination 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) !

<gadget id="calculator">98 - 1</gadget>
<output>97</output>

<gadget id="calculator">98 * 97</gadget>
<output>9_506</output>

<gadget id="calculator">9_506 / 2</gadget>
<output>4_753</output>
<result>4_753</result>

Choices:
A. 1617
B. 4753
C. 1417
D. 4353
E. none of these

divide(multiply(98, subtract(98, const_1)), 2)

Explanation: explanation : ncr = n ! / ( r ) ! ( n − r ) ! 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) ! = 98 ∗ 97 * 96 ! / ( 96 ) ! ( 2 ) ! = 98 * 97 / 2 ∗ 1 = 4753 option b


Question: a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?

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

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

<gadget id="calculator">lcm(10, 16)</gadget>
<output>80</output>

<gadget id="calculator">80 + 4</gadget>
<output>84</output>

<gadget id="calculator">84 + 80</gadget>
<output>164</output>
<result>164</result>

Choices:
A. 116
B. 132
C. 148
D. 164
E. 180

add(add(lcm(10, multiply(divide(10, 5), 8)), 4), lcm(10, multiply(divide(10, 5), 8)))

Explanation: 3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 4 = 84 . the minimum number of horses and ponies is 164 . the answer is d .


Question: there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 8 other amateurs , what is the total number of chess games possible to be played in the tournament ?

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

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 10
B. 20
C. 40
D. 60
E. 120

Explanation: "method 2 : each person is one participant of 4 games . so there are in all 8 * 5 = 40 instances of one participant games . but each game has 2 participants so total number of games = 40 / 2 = 20 b"


Question: the speed of a train is 90 kmph . what is the distance covered by it in 12 minutes ?

<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 90</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 15
B. 18
C. 77
D. 52
E. 42

Explanation: 90 * 12 / 60 = 18 kmph answer : b


Question: in a chess competition involving some men and women , every player needs to play exactly one game with every other player . it was found that in 45 games , both the players were women and in 190 games , both players were men . what is the number of games in which one person was a man and other person was a woman ?

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

<gadget id="calculator">90 * 4</gadget>
<output>360</output>

<gadget id="calculator">1 + 360</gadget>
<output>361</output>

<gadget id="calculator">361 ** (1/2)</gadget>
<output>19</output>

<gadget id="calculator">1 + 19</gadget>
<output>20</output>

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

<gadget id="calculator">190 * 2</gadget>
<output>380</output>

<gadget id="calculator">380 * 4</gadget>
<output>1_520</output>

<gadget id="calculator">1 + 1_520</gadget>
<output>1_521</output>

<gadget id="calculator">1_521 ** (1/2)</gadget>
<output>39</output>

<gadget id="calculator">1 + 39</gadget>
<output>40</output>

<gadget id="calculator">40 / 2</gadget>
<output>20</output>

<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 40
B. 120
C. 180
D. 200
E. 220

multiply(divide(add(const_1, sqrt(add(const_1, multiply(multiply(45, const_2), const_4)))), const_2), divide(add(const_1, sqrt(add(const_1, multiply(multiply(190, const_2), const_4)))), const_2))

Explanation: this is similar to handshake problem , if there are nn people , then number of handshakes = 1 + 2 + . . . n = n ∗ ( n − 1 ) / 2 no . of women be xx and given x ∗ ( x − 1 ) / 2 = 45 this gives x = 10 | | | y no . of men : solve y ∗ ( y − 1 ) / 2 = 190 . this gives y = 20 so total men vs . women = 10 * 20 = 200 . answer is d


Question: 11 is subtracted from 40 % of a number and results is 23 . what is the number ?

<gadget id="calculator">11 + 23</gadget>
<output>34</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">34 / (2/5)</gadget>
<output>85</output>
<result>85</result>

Choices:
A. 160
B. 92
C. 88
D. 85
E. 34

divide(add(11, 23), divide(40, const_100))

Explanation: "( 40 / 100 ) * x â € “ 11 = 23 4 x = 340 x = 85 answer : d"


Question: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required is :

<gadget id="calculator">12 * 8</gadget>
<output>96</output>

<gadget id="calculator">96 * 10</gadget>
<output>960</output>

<gadget id="calculator">960 / 15</gadget>
<output>64</output>

<gadget id="calculator">64 / 8</gadget>
<output>8</output>
<result>8</result>

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

divide(divide(multiply(multiply(12, 8), 10), 15), 8)

Explanation: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 8 : : 12 : x = > 8 x 15 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 15 ) = > x = 8 answer : d"


Question: what is the maximum number of pieces of birthday cake of size 4 ” by 4 ” that can be cut from a cake 20 ” by 20 ” ?

<gadget id="calculator">20 * 20</gadget>
<output>400</output>

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

<gadget id="calculator">400 / 16</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 5
B. 10
C. 16
D. 20
E. 25

divide(multiply(20, 20), multiply(4, 4))

Explanation: "each length = 20 ' ' each piece = 4 ' ' cake could be divided to maximum of 25 pieces answer : e"


Question: the present worth of rs . 845 due in 2 years at 4 % per annum compound interest is

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

<gadget id="calculator">(1/25) + 1</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>

<gadget id="calculator">845 / (676/625)</gadget>
<output>3_125/4 = around 781.25</output>
<result>3_125/4 = around 781.25</result>

Choices:
A. rs . 150.50
B. rs . 154.75
C. rs . 781.25
D. rs . 158
E. none

divide(845, power(add(divide(4, const_100), const_1), 2))

Explanation: "solution present worth = rs . [ 845 / ( 1 + 4 / 100 ) ² ] = rs . ( 845 x 25 / 26 x 25 / 26 ) = rs . 781.25 answer c"


Question: on the first of the year , james invested x dollars at proudstar bank in an account that yields 4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?

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

Choices:
A. 22.04 %
B. 26.12 %
C. 28 %
D. 16.25 %
E. 30 %

Explanation: per quarter , interest = 4 % so for a year , interest = 16 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 16.25 % answer = 16.25 % = answer : d


Question: if a store owner increases a product ’ s price by 20 percent and then increases this price by another 15 percent , what percent of the original price is the total price increase ?

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

<gadget id="calculator">100 * (1/5)</gadget>
<output>20</output>

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

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">120 * (3/20)</gadget>
<output>18</output>

<gadget id="calculator">18 + 20</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 20 %
B. 35 %
C. 38 %
D. 65 %
E. 135 %

add(multiply(add(multiply(const_100, divide(20, const_100)), const_100), divide(15, const_100)), multiply(const_100, divide(20, const_100)))

Explanation: let the initial price be 100 1 st increase = 20 % the price now is 120 2 nd increase of 15 % on 120 = 18 final price = 138 , total increase = 38 % answer : c


Question: if 5 students are made to sit in a row , then 6 do n ' t have seats . if 12 students are made to sit in a row , then 3 rows are empty . how many students have to sit a row such that each row has equal number of students and all students are seated ?

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

<gadget id="calculator">36 + 6</gadget>
<output>42</output>

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

<gadget id="calculator">42 / 7</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 0
B. 1
C. 4
D. 5
E. 6

divide(add(multiply(12, 3), 6), subtract(12, 5))

Explanation: let there be a rows . then 5 a + 6 = 12 ( a - 3 ) [ equating the number of students ] = > a = 6 and total number of students = 36 therefore 6 students much sit in each row such that each row has an equal number of students and all students are seated . option ( e )


Question: a pupil ' s marks were wrongly entered as 85 instead of 33 . due to that the average marks for the class got increased by half . the number of pupils in the class is :

<gadget id="calculator">85 - 33</gadget>
<output>52</output>

<gadget id="calculator">52 * 2</gadget>
<output>104</output>
<result>104</result>

Choices:
A. 30
B. 104
C. 20
D. 25
E. 26

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 33 ) = > x / 2 = 52 = > x = 104 . answer : b"


Question: if the ratio of two number is 6 : 7 and lcm of the number is 450 then what is the number .

<gadget id="calculator">6 * 7</gadget>
<output>42</output>

<gadget id="calculator">450 / 42</gadget>
<output>75/7 = around 10.714286</output>
<result>75/7 = around 10.714286</result>

Choices:
A. 11
B. 20
C. 25
D. 30
E. 35

Explanation: "product of two no = lcm * hcf 6 x * 7 x = 450 * x x = 11 answer : a"


Question: jim is able to sell a hand - carved statue for $ 620 which was a 25 % profit over his cost . how much did the statue originally cost him ?

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">620 / (5/4)</gadget>
<output>496</output>
<result>496</result>

Choices:
A. $ 496.00
B. $ 512.40
C. $ 555.40
D. $ 574.90
E. $ 588.20

divide(620, add(divide(25, const_100), const_1))

Explanation: "620 = 1.25 * x x = 620 / 1.25 = 496.00 which rounds to $ 496.00 , which is ( a ) ."


Question: praveen starts business with rs . 3780 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">1 - (5/12)</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">3_780 / (7/12)</gadget>
<output>6_480</output>

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">6_480 / (2/3)</gadget>
<output>9_720</output>
<result>9_720</result>

Choices:
A. s . 7500
B. s . 8000
C. s . 8500
D. s . 9720
E. s . 6000

divide(divide(3780, subtract(const_1, divide(5, const_12))), divide(2, 3))

Explanation: "let hari ’ s capital be rs . x . then , 3780 * 12 / 7 x = 2 / 3 = > 14 x = 136080 = > x = 9720 . answer : d"


Question: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are ?

<gadget id="calculator">125 + 40</gadget>
<output>165</output>

<gadget id="calculator">33 / 100</gadget>
<output>33/100 = around 0.33</output>

<gadget id="calculator">165 / (33/100)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 450
B. 300
C. 500
D. 610
E. 175

divide(add(125, 40), divide(33, const_100))

Explanation: "let the maximum marks be x then , 33 % of x = 125 + 40 33 x / 100 = 165 x = 500 answer is c"


Question: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 524 different signs . if the company used 522 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 524 signs ?

<gadget id="calculator">524 - 522</gadget>
<output>2</output>

<gadget id="calculator">522 * 2</gadget>
<output>1_044</output>

<gadget id="calculator">1_044 * 2</gadget>
<output>2_088</output>
<result>2_088</result>

Choices:
A. 46
B. 248
C. 2092
D. 15,128
E. 30,256

multiply(multiply(522, subtract(524, 522)), subtract(524, 522))

Explanation: # of 2 - letter codes possible from 524 different signs = 524 * 524 . # of 2 - letter codes possible from 522 different signs = 522 * 522 . the difference = 524 ^ 2 - 522 ^ 2 = ( 524 - 522 ) ( 524 + 522 ) = 2092 . answer : c .


Question: a case contains c cartons . each carton contains b boxes , and each box contains 200 paper clips . how many paper clips are contained in 2 cases ?

<gadget id="calculator">2 * 200</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 200 bc
B. 200 b / c
C. 400 bc
D. 400 b / c
E. 400 / bc

Explanation: "2 cases * c cartons / case * b boxes / carton * 200 clips / box = 400 bc paper clips the answer is c ."


Question: what is the value of x ^ 2 yz − xyz ^ 2 , if x = − 2 , y = 1 , and z = 1 ?

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

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

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

<gadget id="calculator">(-2) * (-3)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 24
C. 30
D. 32
E. 48

multiply(multiply(multiply(negate(2), 1), 1), subtract(negate(2), 1))

Explanation: 4 * 1 * 1 - ( - 2 * 1 * 1 ) = 4 + 2 = 6 ans : a


Question: 2.205 divided by 0.3 gives

<gadget id="calculator">2.205 / 0.3</gadget>
<output>7.35</output>
<result>7.35</result>

Choices:
A. 7.35
B. 6.25
C. 8.15
D. 6.95
E. none of these

Explanation: "explanation : 2.205 / 0.3 = 22.05 / 3 = 7.35 . answer : option a"


Question: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.88 at the candy store . what is john ’ s weekly allowance ?

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

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

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

<gadget id="calculator">(1/3) * (2/5)</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">(3/5) + (2/15)</gadget>
<output>11/15 = around 0.733333</output>

<gadget id="calculator">1 - (11/15)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">0.88 / (4/15)</gadget>
<output>3.3</output>
<result>3.3</result>

Choices:
A. $ 2.70
B. $ 3.00
C. $ 3.30
D. $ 3.60
E. $ 3.90

divide(0.88, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))

Explanation: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 88 4 x / 15 = 88 x = 330 = $ 3.30 the answer is c ."


Question: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 10 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?

<gadget id="calculator">7 * 10</gadget>
<output>70</output>

<gadget id="calculator">70 * 3</gadget>
<output>210</output>

<gadget id="calculator">210 / 7</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 21
B. 35
C. 39
D. 30
E. 65

Explanation: "the total number of the people in the room must be a multiple of both 7 and 10 ( in order 3 / 7 and 5 / 10 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 10 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 7 * 70 = 30 people in the room under the age of 21 . answer : d ."


Question: a 5 - digit number is formed by the digits 2 , 45 , 68 ( each digit used exactly once ) . what is the probability that the number formed is divisible by 4 ?

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

<gadget id="calculator">24 * 2</gadget>
<output>48</output>

<gadget id="calculator">factorial(5)</gadget>
<output>120</output>

<gadget id="calculator">48 / 120</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 2 / 5
B. 3 / 5
C. 4 / 5
D. 6 / 5
E. 7 / 5

Explanation: a no . is divisible by 4 if last two digit is divisible by 4 so numbers ending with 2428 , 4852 , 5664 , 6884 are divisible by 4 last two places are fixed by 2428 , 4852 , 5664 , 6884 so remaining 3 places can be filled in 3 ! ways for each total = 8 * 3 ! = 48 = n ( e ) n ( s ) = 5 c 4 = 120 p = 48 / 120 = 2 / 5 answer : a


Question: if x is 20 percent more than y and y is 60 percent less than z , then x is what percent of z ?

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

<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>

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

<gadget id="calculator">(6/5) * 40</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 500 %
B. 48 %
C. 500 / 3 %
D. 125 %
E. 60 %

multiply(add(const_1, divide(20, const_100)), subtract(const_100, 60))

Explanation: "z = 100 ; y = 40 so x = 48 x as % of z = 48 / 100 * 100 = > 48 % answer will be ( b )"


Question: from mumbai railway station , two trains a and b start simultaneously from stations 400 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 40 miles per hour and 40 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?

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

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

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

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

<gadget id="calculator">400 / 90</gadget>
<output>40/9 = around 4.444444</output>

<gadget id="calculator">(40/9) * 40</gadget>
<output>1_600/9 = around 177.777778</output>
<result>1_600/9 = around 177.777778</result>

Choices:
A. 112
B. 133
C. 150
D. 167
E. 180

multiply(divide(400, add(add(40, multiply(const_2, add(const_4, const_1))), 40)), 40)

Explanation: since we know the distance ( 400 ) and the combined rate ( 80 ) , we plug it into the formula : distance = rate * time 400 = 80 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 400 / 80 from dividing 80 on both sides to isolate time in the equation above . time will be 20 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 40 * 20 distance = 180 according to answer choice e .


Question: there is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall . there is one each bird sitting on top of both the towers . they fly at a constant speed and time to reach a grain in b / w the towers at the same time . at what distance from the church is the grain ?

<gadget id="calculator">150 ** 2</gadget>
<output>22_500</output>

<gadget id="calculator">350 ** 2</gadget>
<output>122_500</output>

<gadget id="calculator">22_500 + 122_500</gadget>
<output>145_000</output>

<gadget id="calculator">200 ** 2</gadget>
<output>40_000</output>

<gadget id="calculator">145_000 - 40_000</gadget>
<output>105_000</output>

<gadget id="calculator">2 * 350</gadget>
<output>700</output>

<gadget id="calculator">105_000 / 700</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 170 meters
B. 160 meters
C. 150 meters
D. 140 meters
E. 130 meters

divide(subtract(add(power(150, const_2), power(350, const_2)), power(200, const_2)), multiply(const_2, 350))

Explanation: if x ft is the distance of grain from 200 ft tall tower , then 150 ^ 2 + ( 350 - x ) ^ 2 = 200 ^ 2 + x ^ 2 then x = 150 meters answer : c


Question: for 1 rs 4 p interest wat will be for 5000 rs ?

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

<gadget id="calculator">5_000 * (1/25)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 350 rs
B. 450 rs
C. 200 rs
D. 30 rs
E. 448 rs

Explanation: for 1 rs , 4 p interest for 5000 rs , x x = 5000 / 1 * 4 p = = > 20000 paise to express in rs , 20000 / 100 = 200 rs answer : c


Question: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train .

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

<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) * 15</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 150 m
B. 145 m
C. 240 m
D. 135 m
E. 250 m

multiply(divide(multiply(60, const_1000), const_3600), 15)

Explanation: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : e"


Question: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 600 more . what was the sum ?

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

<gadget id="calculator">(1/20) * 10</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. rs . 1200
B. rs . 1300
C. rs . 1400
D. rs . 1500
E. none of these

divide(600, multiply(divide(5, const_100), 10))

Explanation: "explanation : at 5 % more rate , the increase in s . i for 10 years = rs . 600 ( given ) so , at 5 % more rate , the increase in si for 1 year = 600 / 10 = rs . 60 / - i . e . rs . 60 is 5 % of the invested sum so , 1 % of the invested sum = 60 / 5 therefore , the invested sum = 60 × 100 / 5 = rs . 1200 answer : a"


Question: a shop owner sells 60 mtr of cloth and gains sp of 10 mtrs . find the gain % ?

<gadget id="calculator">60 - 10</gadget>
<output>50</output>

<gadget id="calculator">10 / 50</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20 %
B. 40 %
C. 50 %
D. 60 %
E. 70 %

multiply(divide(10, subtract(60, 10)), const_100)

Explanation: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 60 m cloth ) – ( c . p . of 60 m cloth ) selling price of 50 m cloth = selling price of 60 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 50 m cloth = rs . 5000 and s . p . of 50 m cloth = rs . rs . 6000 profit % = 10 / 50 × 100 = 20 % 20 profit of 20 % was made by the merchant . a"


Question: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9 . if the shop carries 364 dogs and bunnies total in stock , how many dogs are there ?

<gadget id="calculator">4 + 9</gadget>
<output>13</output>

<gadget id="calculator">364 / 13</gadget>
<output>28</output>

<gadget id="calculator">28 * 4</gadget>
<output>112</output>
<result>112</result>

Choices:
A. 42
B. 66
C. 98
D. 112
E. 154

Explanation: "let us assume the number of dogs , cats and bunnies to be 4 x , 7 x and 9 x total dogs and bunnies = 13 x . and we are given that 13 x = 364 . hence x = 28 . dogs = 4 x = 4 * 28 = 112 ( option d )"


Question: albert invested rs . 6500 in a scheme for 2 years at compound interest rate 6.5 % p . a . how much amount will albert get on maturity of the fixed deposit ?

<gadget id="calculator">6.5 / 100</gadget>
<output>0.065</output>

<gadget id="calculator">1 + 0.065</gadget>
<output>1.065</output>

<gadget id="calculator">1.065 ** 2</gadget>
<output>1.134225</output>

<gadget id="calculator">6_500 * 1.134225</gadget>
<output>7_372.4625</output>
<result>7_372.4625</result>

Choices:
A. s . 8829
B. s . 7200
C. s . 7200.5
D. s . 4000
E. s . 7372.46

multiply(6500, power(add(const_1, divide(6.5, const_100)), 2))

Explanation: amount = [ 6500 * ( 1 + 6.5 / 100 ) 2 ] = 6500 * 106.5 / 100 * 106.5 / 100 = rs . 7372.46 answer : e


Question: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 30 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?

<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>

<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>

<gadget id="calculator">3_000 - 2_000</gadget>
<output>1_000</output>

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

<gadget id="calculator">1_000 / 70</gadget>
<output>100/7 = around 14.285714</output>

<gadget id="calculator">(100/7) / 20</gadget>
<output>5/7 = around 0.714286</output>

<gadget id="calculator">(5/7) * 100</gadget>
<output>500/7 = around 71.428571</output>
<result>500/7 = around 71.428571</result>

Choices:
A. 47 %
B. 59 %
C. 71 %
D. 83 %
E. 95 %

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

Explanation: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.3 ( 5 b + x ) = b + x 0.5 b = 0.7 x x = 0.71 b the answer is c ."


Question: if the average ( arithmetic mean ) of the 4 numbers 3 , 16 , 33 , and ( n + 1 ) is 20 , then n =

<gadget id="calculator">20 * 4</gadget>
<output>80</output>

<gadget id="calculator">3 + 16</gadget>
<output>19</output>

<gadget id="calculator">19 + 33</gadget>
<output>52</output>

<gadget id="calculator">52 + 1</gadget>
<output>53</output>

<gadget id="calculator">80 - 53</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 19
B. 20
C. 21
D. 27
E. 29

subtract(multiply(20, 4), add(add(add(3, 16), 33), 1))

Explanation: 3 + 16 + 33 + n + 1 = 20 x 4 = 80 = > n + 53 = 80 = > n = 27 answer d


Question: the mean of 50 observations is 200 . but later he found that there is decrements of 6 from each observations . what is the the updated mean is ?

<gadget id="calculator">200 - 6</gadget>
<output>194</output>
<result>194</result>

Choices:
A. 165
B. 185
C. 190
D. 198
E. 194

Explanation: 194 answer is e


Question: the ` ` racing magic ' ' takes 120 seconds to circle the racing track once . the ` ` charging bull ' ' makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?

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

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

Choices:
A. 3
B. 6
C. 9
D. 12
E. 15

add(add(const_2, const_4), add(const_2, const_4))

Explanation: time taken by racing magic to make one circle = 120 seconds = 2 mins time taken by ` ` charging bull ' ' to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 120 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d


Question: find the constant k so that : - x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 )

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

<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 11
B. 12
C. 16
D. 14
E. 15

Explanation: "- x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 10 ) x - 8 = - x 2 + 6 x - 8 - ( k + 10 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 16 : solve the above for k correct answer c"


Question: 102 ã — 102 + 98 ã — 98 = ?

<gadget id="calculator">102 ** 2</gadget>
<output>10_404</output>

<gadget id="calculator">10_404 - 102</gadget>
<output>10_302</output>

<gadget id="calculator">98 ** 2</gadget>
<output>9_604</output>

<gadget id="calculator">9_604 - 98</gadget>
<output>9_506</output>

<gadget id="calculator">10_302 + 9_506</gadget>
<output>19_808</output>
<result>19_808</result>

Choices:
A. 20018
B. 20028
C. 20108
D. 10008
E. 20008

add(subtract(power(102, const_2), 102), subtract(power(98, const_2), 98))

Explanation: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1022 + 982 = ( 100 + 2 ) 2 + ( 100 â ˆ ’ 2 ) 2 = 2 ( 1002 + 22 ) = 2 ( 10000 + 4 ) = 20008 . answer : option e"


Question: two trains 140 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

<gadget id="calculator">140 + 190</gadget>
<output>330</output>

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

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

<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>

<gadget id="calculator">330 / (250/9)</gadget>
<output>297/25 = around 11.88</output>
<result>297/25 = around 11.88</result>

Choices:
A. 11.88 sec
B. 13.8 sec
C. 53.8 sec
D. 10.8 sec
E. 10.4 sec

Explanation: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 190 = 330 m . required time = 330 * 9 / 250 = 11.88 sec . answer : a :"


Question: mary works in a restaurant a maximum of 70 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?

<gadget id="calculator">70 * 8</gadget>
<output>560</output>

<gadget id="calculator">70 - 20</gadget>
<output>50</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">8 * (1/4)</gadget>
<output>2</output>

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

<gadget id="calculator">560 + 100</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 600
B. 620
C. 660
D. 320
E. 400

add(multiply(70, 8), multiply(subtract(70, 20), multiply(8, divide(25, const_100))))

Explanation: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 50 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 50 ( 20 ) = $ 500 . the total amount is $ 160 + $ 500 = $ 660 answer c 660 ."


Question: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 4 per metre approximately

Choices:
A. 4457
B. 4567
C. 5943
D. 4547
E. 4675

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 4)

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 4 ) = rs . 5943 . answer : option c"


Question: 30 pens and 75 pencils were purchased for 750 . if the average price of a pencil was 2.00 , find the average price of a pen .

<gadget id="calculator">75 * 2</gadget>
<output>150</output>

<gadget id="calculator">750 - 150</gadget>
<output>600</output>

<gadget id="calculator">600 / 30</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 11
C. 12
D. 13
E. 14

divide(subtract(750, multiply(75, 2.00)), 30)

Explanation: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 750 – 150 ) = 600 ∴ average price of a pen = 600 ⁄ 60 = 20 answer a"


Question: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 16 and 17 . the larger of the two numbers is :

<gadget id="calculator">23 * 17</gadget>
<output>391</output>
<result>391</result>

Choices:
A. 338
B. 278
C. 322
D. 231
E. 391

Explanation: "clearly , the numbers are ( 23 * 16 ) and ( 23 * 17 ) . larger number = ( 23 * 17 ) = 391 . answer : e"


Question: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two - fifth of its present ?

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

<gadget id="calculator">25 * 5</gadget>
<output>125</output>

<gadget id="calculator">125 / 2</gadget>
<output>125/2 = around 62.5</output>
<result>125/2 = around 62.5</result>

Choices:
A. 52.5
B. 62.5
C. 72.5
D. 82.5
E. 81.5

divide(multiply(25, add(const_4, const_1)), const_2)

Explanation: explanation : let the capacity of 1 bucket = x . then , capacity of tank = 25 x . new capacity of bucket = 2 / 5 x . required no of buckets = 25 x / ( 2 x / 5 ) = 62.5 answer is b


Question: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 110 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?

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

<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">110 / (1/4)</gadget>
<output>440</output>
<result>440</result>

Choices:
A. 90
B. 120
C. 160
D. 360
E. 440

divide(110, subtract(const_1, divide(3, 4)))

Explanation: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 110 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 110 n = 440 answer = ( e )"


Question: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area r covered by the two roads ?

<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>

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

<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>
<result>1_600</result>

Choices:
A. 400
B. 1550
C. 1575
D. 1600
E. 1625

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

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


Question: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 21 days , a finished the remaining work . in how many days a alone can finish the job ?

<gadget id="calculator">21 * 40</gadget>
<output>840</output>

<gadget id="calculator">40 - 10</gadget>
<output>30</output>

<gadget id="calculator">840 / 30</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 10
B. 25
C. 60
D. 30
E. 28

divide(multiply(21, 40), subtract(40, 10))

Explanation: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 21 days whole work will be done by a in 21 * 4 / 3 = 28 days answer is e"


Question: what will be the cost of building to paint which area equal to 196 sq ft , if the price per foot of building is rs . 15 ?

<gadget id="calculator">196 ** (1/2)</gadget>
<output>14</output>

<gadget id="calculator">4 * 14</gadget>
<output>56</output>

<gadget id="calculator">56 * 15</gadget>
<output>840</output>
<result>840</result>

Choices:
A. 120
B. 240
C. 360
D. 380
E. 840

Explanation: let the side of the square plot be a ft . a 2 = 196 = > a = 14 length of the fence = perimeter of the plot = 4 a = 56 ft . cost of building the fence = 56 * 15 = rs . 840 . answer : e


Question: exactly 3 sides of a certain 10 - sided die are red . what is the probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll ?

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

<gadget id="calculator">7 / 10</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(7/10) ** 2</gadget>
<output>49/100 = around 0.49</output>

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

<gadget id="calculator">(49/100) * (3/10)</gadget>
<output>147/1_000 = around 0.147</output>
<result>147/1_000 = around 0.147</result>

Choices:
A. 0.184
B. 0.16
C. 0.18
D. 0.147
E. 0.148

multiply(power(divide(subtract(10, 3), 10), const_2), divide(3, 10))

Explanation: total no . of sides = 10 sides that are red = 3 probability that the die lands with red side up = 3 / 10 therefore , probability that the die does not land with red side up = 1 - 3 / 10 = 7 / 10 probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = ( 1 st roll - non red face ) x ( 2 nd roll - non red face ) x ( 3 rd roll - red face ) = ( 7 / 10 ) x ( 7 / 10 ) x ( 3 / 10 ) = 128 / 1000 = 0.147 d


Question: the average runs scored by a batsman in 25 matches is 45 . in the next 7 matches the batsman scored an average of 15 runs . find his average in all the 32 matches ?

<gadget id="calculator">45 * 25</gadget>
<output>1_125</output>

<gadget id="calculator">15 * 7</gadget>
<output>105</output>

<gadget id="calculator">1_125 + 105</gadget>
<output>1_230</output>

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

<gadget id="calculator">1_230 / 32</gadget>
<output>615/16 = around 38.4375</output>
<result>615/16 = around 38.4375</result>

Choices:
A. 31355
B. 38.44
C. 29.55
D. 97.66
E. 45.66

divide(add(multiply(45, 25), multiply(15, 7)), add(25, 7))

Explanation: total score of the batsman in 25 matches = 1125 . total score of the batsman in the next 7 matches = 105 . total score of the batsman in the 32 matches = 1230 . average score of the batsman = 1230 / 32 = 38.44 . answer : b


Question: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 4 % . what is the approximate interest he pays annually ?

Choices:
A. $ 1750
B. $ 2000
C. $ 2150
D. $ 2500
E. $ 12000

subtract(multiply(multiply(const_100, const_100), power(add(const_1, divide(4, const_100)), const_4)), multiply(const_100, const_100))

Explanation: "an easy way too attempt this is by approximation : for the first quarter , he pays 4 % of 10,000 which is $ 400 . so for the four quarters in the year , he will approximately play 400 * 4 = 1600 over the entire year . because of compound interest it will be more than 1600 . approx . option a is correct . answer : a"


Question: jack and jill work at a hospital with 7 other workers . for an internal review , 2 of the 9 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?

<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>

<gadget id="calculator">factorial(2)</gadget>
<output>2</output>

<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>

<gadget id="calculator">2 * 5_040</gadget>
<output>10_080</output>

<gadget id="calculator">362_880 / 10_080</gadget>
<output>36</output>

<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<result>1/36 = around 0.027778</result>

Choices:
A. 1 / 3
B. 1 / 4
C. 1 / 15
D. 3 / 8
E. 1 / 36

Explanation: "1 / 9 c 2 = 1 / 36 . answer : e ."


Question: a student has to obtain 50 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are ?

<gadget id="calculator">200 + 20</gadget>
<output>220</output>

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">220 / (1/2)</gadget>
<output>440</output>
<result>440</result>

Choices:
A. 510
B. 520
C. 530
D. 540
E. 440

divide(add(200, 20), divide(50, const_100))

Explanation: "let the maximum marks be x then , 50 % of x = 200 + 20 50 x / 100 = 220 50 x = 220 * 100 = 22000 x = 440 answer is e"


Question: the cost of 3 pens and 5 pencils is rs . 150 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?

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

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

<gadget id="calculator">150 / 4</gadget>
<output>75/2 = around 37.5</output>

<gadget id="calculator">12 * (75/2)</gadget>
<output>450</output>
<result>450</result>

Choices:
A. rs . 200
B. rs . 250
C. rs . 300
D. rs . 450
E. none of these

multiply(multiply(3, const_4), divide(150, add(3, 1)))

Explanation: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 150 15 x + 5 x = rs . 150 x = 150 / 20 = 7.50 : . cost of 1 pen = 5 x = 5 x 7.50 = 37.50 : . cost of 12 pens , i . e . ( one dozen ) = 37.50 x 12 = rs . 450 answer : option d"


Question: the tax on a commodity is diminished by 20 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?

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

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

<gadget id="calculator">110 * 80</gadget>
<output>8_800</output>

<gadget id="calculator">8_800 / 100</gadget>
<output>88</output>

<gadget id="calculator">100 - 88</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 20 %
B. 19 %
C. 15 %
D. 12 %
E. 24 %

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

Explanation: "answer : option d 100 * 100 = 10000 80 * 110 = 8800 10000 - - - - - - - 1200 100 - - - - - - - ? = 12 %"


Question: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 72 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )

<gadget id="calculator">72 * 2</gadget>
<output>144</output>

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">72 * (3/5)</gadget>
<output>216/5 = around 43.2</output>

<gadget id="calculator">144 - (216/5)</gadget>
<output>504/5 = around 100.8</output>

<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(504/5) / (8/5)</gadget>
<output>63</output>
<result>63</result>

Choices:
A. 55
B. 84
C. 63
D. 75
E. 70

divide(subtract(multiply(72, 2), multiply(72, divide(60, const_100))), add(divide(60, const_100), 1))

Explanation: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 72 or 1 / 7 t + 1 t = 60 therefore t = 72 * 7 / 8 = 63 c"


Question: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25 % , what is the total capacity of the pool in gallons ?

<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>

<gadget id="calculator">30_000 / 25</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 + 300</gadget>
<output>1_500</output>

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

<gadget id="calculator">1_500 / (4/5)</gadget>
<output>1_875</output>
<result>1_875</result>

Choices:
A. 1875
B. 1250
C. 1300
D. 1600
E. 1625

divide(add(divide(multiply(300, const_100), 25), 300), divide(80, const_100))

Explanation: "300 gallons of water increases capacity by 25 % that means 25 % is 300 gallons , so 100 % would be = 300 * 100 / 25 = 1200 gallons now 1200 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1500 * 100 / 80 = 1875 a is the answer"


Question: at 3 : 40 , the hour hand and the minute hand of a clock form an angle of

<gadget id="calculator">60 * 3</gadget>
<output>180</output>

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

<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">360 * (2/3)</gadget>
<output>240</output>

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

<gadget id="calculator">120 / 4</gadget>
<output>30</output>

<gadget id="calculator">(2/3) + 3</gadget>
<output>11/3 = around 3.666667</output>

<gadget id="calculator">30 * (11/3)</gadget>
<output>110</output>

<gadget id="calculator">240 - 110</gadget>
<output>130</output>
<result>130</result>

Choices:
A. 160 °
B. 180 °
C. 130 °
D. 110 °
E. 150 °

subtract(multiply(multiply(multiply(const_60, 3), const_2), divide(40, const_60)), multiply(divide(divide(multiply(multiply(const_60, 3), const_2), 3), const_4), add(divide(40, const_60), 3)))

Explanation: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 3 , m = 40 and minute hand is ahead of the hour hand . hence the angle = 30 ( m / 5 − h ) − m / 2 = 30 ( 40 / 5 − 3 ) − 40 / 2 = 30 ( 8 − 3 ) − 20 = 30 × 5 − 20 = 130 ° answer is c ."


Question: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 20 litres of tomato juice ?

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

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

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

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

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

<gadget id="calculator">2 / (4/5)</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>

Choices:
A. 2.8 liters .
B. 2.5 liters .
C. 8.5 liters .
D. 2.6 liters .
E. 2.1 liters .

divide(multiply(divide(subtract(const_100, 90), const_100), 20), divide(subtract(const_100, 20), const_100))

Explanation: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . ⇒ ⇒ 10 % ( 20 ) = 80 % ( x ) ⇒ ⇒ x = 2.5 liters . answer : b"


Question: if 2 ^ 5 , 3 ^ 3 , and 14 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

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

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

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

<gadget id="calculator">12 * 7</gadget>
<output>84</output>

<gadget id="calculator">84 * 2</gadget>
<output>168</output>
<result>168</result>

Choices:
A. 26
B. 39
C. 42
D. 65
E. 168

multiply(multiply(multiply(power(2, 2), 3), divide(14, 2)), 2)

Explanation: here 156 has three two ' s two three ' s and one 14 rest of them must be in w so w = 14 * 3 * 4 = 168 smash e


Question: a and b can finish a work in 10 days while b and c can do it in 18 days . a started the work , worked for 5 days , then b worked for 10 days and the remaining work was finished by c in 15 days . in how many days could c alone have finished the whole work ?

<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>

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

<gadget id="calculator">(1/2) + (5/18)</gadget>
<output>7/9 = around 0.777778</output>

<gadget id="calculator">1 - (7/9)</gadget>
<output>2/9 = around 0.222222</output>

<gadget id="calculator">10 / (2/9)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 30 days
B. 15 days
C. 45 days
D. 24 days
E. none of these

divide(10, subtract(const_1, add(divide(5, 10), divide(5, 18))))

Explanation: let c completes the work in x days . work done by ( a + b ) in 1 day = 1 ⁄ 10 work done by ( b + c ) in 1 day = 1 ⁄ 18 a ’ s 5 days ’ work + b ’ s 10 days ’ work + c ’ s 15 days ’ work = 1 or ( a + b ) ’ s 5 days ’ work + ( b + c ) ’ s 5 days ’ work + c ’ s 10 days ’ work = 1 or 5 ⁄ 10 + 5 ⁄ 18 + 10 ⁄ x = 1 or x = 45 days answer c


Question: a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it take 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?

<gadget id="calculator">48 / 60</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) + 8</gadget>
<output>44/5 = around 8.8</output>

<gadget id="calculator">(44/5) / 4</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">(11/5) + 1</gadget>
<output>16/5 = around 3.2</output>

<gadget id="calculator">(16/5) / 2</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(11/5) - 1</gadget>
<output>6/5 = around 1.2</output>

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

<gadget id="calculator">(8/5) / (3/5)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>

Choices:
A. 1 : 3
B. 3 : 8
C. 6 : 3
D. 8 : 3
E. none

divide(divide(add(divide(add(divide(48, const_60), 8), 4), const_1), const_2), divide(subtract(divide(add(divide(48, const_60), 8), 4), const_1), const_2))

Explanation: "sol . let the man rate upstream be x kmph and that downstream be y kmph . then , distance coverd upstream in 8 hrs 48 min . = distance coverd downstream in 4 hrs . ⇒ [ x 8 4 / 5 ] = ( y * 4 ) ⇒ 44 / 5 x = 4 y ⇒ y = 11 / 5 x . ∴ required ratio = [ y + x / 2 ] : [ 6 x / 5 * 1 / 2 ] : [ 6 x / 5 * 1 / 2 ] = 8 / 5 : 3 / 5 = 8 : 3 . answer d"


Question: if 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 , where x and y are non negative integers , what is the greatest possible value of | x â € “ y | ?

<gadget id="calculator">2 - 2</gadget>
<output>0</output>
<result>0</result>

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

Explanation: | x â € “ y | for x and y 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 a . x = y x = y = 0 1 + 1 = 1 + 1 right b . 1 x = 2 , y = 1 4 + 2 = 1 + 1 wrong c . 2 x = 3 , y = 1 8 + 2 = 1 + 1 wrong d . 3 x = 4 , y = 1 16 + 2 = 1 + 1 wrong e . 4 x = 5 , y = 1 32 + 2 = 1 + 1 wrong my answer is a .


Question: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1032 in total compensation , how many total hours did he work that week ?

<gadget id="calculator">16 * 40</gadget>
<output>640</output>

<gadget id="calculator">1_032 - 640</gadget>
<output>392</output>

<gadget id="calculator">100 + 75</gadget>
<output>175</output>

<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>

<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>

<gadget id="calculator">392 / 28</gadget>
<output>14</output>

<gadget id="calculator">40 + 14</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 36
B. 40
C. 44
D. 48
E. 54

add(40, divide(subtract(1032, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))

Explanation: for 40 hrs = 40 * 16 = 640 excess = 1032 - 640 = 392 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 392 / 28 = 98 / 7 = 14 total hrs = 40 + 14 = 54 answer e 52


Question: find the length of the wire required to go 15 times round a square field containing 69696 m 2 ?

<gadget id="calculator">69_696 ** (1/2)</gadget>
<output>264</output>

<gadget id="calculator">4 * 264</gadget>
<output>1_056</output>

<gadget id="calculator">1_056 * 15</gadget>
<output>15_840</output>
<result>15_840</result>

Choices:
A. 15840
B. 19879
C. 27997
D. 15842
E. 15823

Explanation: "a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a"


Question: p , q and r have rs . 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">1 + (2/3)</gadget>
<output>5/3 = around 1.666667</output>

<gadget id="calculator">7_000 / (5/3)</gadget>
<output>4_200</output>

<gadget id="calculator">4_200 * (2/3)</gadget>
<output>2_800</output>
<result>2_800</result>

Choices:
A. rs . 3000
B. rs . 3600
C. rs . 2400
D. rs . 2800
E. none of these

multiply(divide(7000, add(const_1, divide(const_2, const_3))), divide(const_2, const_3))

Explanation: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . answer : d"


Question: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach a target of 282 runs ?

<gadget id="calculator">10 * 3.2</gadget>
<output>32</output>

<gadget id="calculator">282 - 32</gadget>
<output>250</output>

<gadget id="calculator">250 / 40</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>

Choices:
A. 6.25
B. 6.5
C. 6.75
D. 7.0
E. none of the above

divide(subtract(282, multiply(10, 3.2)), 40)

Explanation: "total runs in the first 10 overs = 10 × 3.2 = 32 run rate required in the remaining 40 overs = 282 − 32 / 40 = 250 / 40 = 6.25 runs per over . answer a"


Question: a and b together can complete a piece of work in 10 days . if a alone can complete the same work in 15 days , in how many days , in how many days can b alone complete that work ?

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

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/10) - (1/15)</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 10
B. 30
C. 25
D. 15
E. 45

divide(const_1, subtract(divide(const_1, 10), divide(const_1, 15)))

Explanation: ( a + b ) ' s 1 day ' s work = 1 / 10 a ' s 1 day ' s work = 1 / 15 b ' s 1 days ' s work = ( 1 / 10 ) - ( 1 / 15 ) = 1 / 30 hence , b alone can complete the work in 30 days . answer is b


Question: a garrison of 2000 men has provisions for 54 days . at the end of 18 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?

<gadget id="calculator">2_000 * 54</gadget>
<output>108_000</output>

<gadget id="calculator">2_000 * 18</gadget>
<output>36_000</output>

<gadget id="calculator">108_000 - 36_000</gadget>
<output>72_000</output>

<gadget id="calculator">72_000 / 20</gadget>
<output>3_600</output>

<gadget id="calculator">3_600 - 2_000</gadget>
<output>1_600</output>
<result>1_600</result>

Choices:
A. 1977
B. 1600
C. 1979
D. 1900
E. 1278

subtract(divide(subtract(multiply(2000, 54), multiply(2000, 18)), 20), 2000)

Explanation: "2000 - - - - 54 2000 - - - - 36 x - - - - - 20 x * 20 = 2000 * 36 x = 3600 2000 - - - - - - - 1600 answer : b"


Question: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?

<gadget id="calculator">8 * 2.5</gadget>
<output>20</output>

<gadget id="calculator">20 + 75</gadget>
<output>95</output>
<result>95</result>

Choices:
A. 95 kg
B. 90 kg
C. 85 kg
D. data inadequate
E. none of these

Explanation: "a 95 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg ."


Question: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.20 , what was the total value of the item ?

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">109.2 / (7/100)</gadget>
<output>1_560</output>

<gadget id="calculator">1_000 + 1_560</gadget>
<output>2_560</output>
<result>2_560</result>

Choices:
A. $ 1,600
B. $ 1,850
C. $ 2,250
D. $ 2,440
E. $ 2,560

Explanation: "let x be the value of the item . 0.07 * ( x - 1000 ) = 109.20 x = 2560 the answer is e ."


Question: a can finish a piece of work in 4 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?

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

<gadget id="calculator">(1/4) * 2</gadget>
<output>1/2 = around 0.5</output>

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

<gadget id="calculator">(1/10) * 2</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/2) + (1/5)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>

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

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

divide(subtract(const_1, add(multiply(divide(const_1, 4), const_2), multiply(divide(const_1, 10), const_2))), divide(const_1, 10))

Explanation: 2 / 4 + ( 2 + x ) / 10 = 1 = > x = 3 days answer : a


Question: if the sides of a triangle are 26 cm , 24 cm and 15 cm , what is its area ?

<gadget id="calculator">24 * 15</gadget>
<output>360</output>

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

Choices:
A. 120
B. 772
C. 180
D. 266
E. 2848

Explanation: "the triangle with sides 26 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : c"


Question: two trains , a and b , started simultaneously from opposite ends of a 125 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 125 - mile trip in 12 hours ; train b , traveling at a constant rate , completed the 125 - mile trip in 8 hours . how many miles had train a traveled when it met train b ?

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

<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 125</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 25
B. 37.5
C. 40
D. 45.5
E. 50

Explanation: as the ratio of the rates of a and b is 8 to 12 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 8 / ( 8 + 12 ) = 8 / 20 of 125 miles : 125 * 8 / 20 = 50 miles . answer : e .


Question: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2400 less than the principal . what was the principal ?

<gadget id="calculator">4 * 5</gadget>
<output>20</output>

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

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

<gadget id="calculator">2_400 / (4/5)</gadget>
<output>3_000</output>
<result>3_000</result>

Choices:
A. 1500
B. 2500
C. 2507
D. 3000
E. 11500

divide(2400, subtract(const_1, divide(multiply(4, 5), const_100)))

Explanation: "p - 2400 = ( p * 5 * 4 ) / 100 p = 3000 answer : d"


Question: out of 250 students of a college , 160 play football , 90 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?

<gadget id="calculator">160 + 90</gadget>
<output>250</output>

<gadget id="calculator">50 + 250</gadget>
<output>300</output>

<gadget id="calculator">300 - 250</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 30
B. 40
C. 50
D. 60
E. 70

Explanation: explanation : solution : n ( a ) = 160 , n ( b ) = 90 , n ( a u b ) = 250 - 50 = 200 . required number = > n ( a ^ b ) = n ( a ) + n ( b ) - n ( a u b ) = 160 + 90 - 200 = 250 - 200 = 50 . answer : c


Question: what is the area a of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 5 ) , ( x , 5 ) ?

<gadget id="calculator">20 - 5</gadget>
<output>15</output>

<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<result>225</result>

Choices:
A. 60 .
B. 85 .
C. 125 .
D. 225 .
E. it can not be determined from the information given

Explanation: length of one side = 15 ( 20 - 5 ) since , its a square , the area will be a = 15 ^ 2 = 225 d is the answer


Question: a van takes 5 hours to cover a distance of 495 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?

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

<gadget id="calculator">(3/2) * 5</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">495 / (15/2)</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 60
B. 63
C. 66
D. 69
E. 72

Explanation: "( 3 / 2 ) * 5 = 7.5 hours 495 / 7.5 = 66 kph the answer is c ."


Question: find the compound interest on $ 1000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?

Choices:
A. $ 645.56
B. $ 82.43
C. $ 954.26
D. $ 745.69
E. $ 1020.45

subtract(multiply(power(add(divide(divide(4, const_100), 2), const_1), 4), 1000), 1000)

Explanation: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 1000 * ( 1 + 2 / 100 ) ^ 4 = 1000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 1082.43 c . i . = 1082.43 - 1000 = $ 82.43 answer is b"


Question: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds . what is the length of the platform in meters ?

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>

<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>

<gadget id="calculator">20 * 30</gadget>
<output>600</output>

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

<gadget id="calculator">600 - 300</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 240 meters
B. 360 meters
C. 300 meters
D. 600 meters
E. can not be determined

subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 15))

Explanation: speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 15 * 20 = 300 = length of train length of platform = 600 - 300 = 300 answer : c


Question: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 50 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?

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

<gadget id="calculator">100 + 150</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 250
B. 300
C. 350
D. 400
E. 500

Explanation: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 50 meters , thus second time she runs 2 * 50 = 100 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 150 meters , thus the circumference is 100 + 150 = 250 meters . answer : a ."


Question: a man buys a cycle for rs . 1900 and sells it at a loss of 18 % . what is the selling price of the cycle ?

<gadget id="calculator">100 - 18</gadget>
<output>82</output>

<gadget id="calculator">82 * 1_900</gadget>
<output>155_800</output>

<gadget id="calculator">155_800 / 100</gadget>
<output>1_558</output>
<result>1_558</result>

Choices:
A. s . 1590
B. s . 1560
C. s . 1558
D. s . 1252
E. s . 1062

divide(multiply(subtract(const_100, 18), 1900), const_100)

Explanation: "s . p . = 82 % of rs . 1900 = rs . 82 x 1900 / 100 = rs . 1558 answer : option c"


Question: at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?

<gadget id="calculator">120 / 3</gadget>
<output>40</output>

<gadget id="calculator">120 - 40</gadget>
<output>80</output>

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

<gadget id="calculator">20 - 10</gadget>
<output>10</output>

<gadget id="calculator">80 * 10</gadget>
<output>800</output>

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

<gadget id="calculator">800 / 20</gadget>
<output>40</output>

<gadget id="calculator">40 / 80</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 20 %
B. 50 %
C. 55 %
D. 75 %
E. 80 %

multiply(divide(divide(multiply(subtract(120, divide(120, const_3)), subtract(subtract(divide(120, const_3), 20), 10)), add(10, subtract(subtract(divide(120, const_3), 20), 10))), subtract(120, divide(120, const_3))), const_100)

Explanation: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 20 short - stemmed pink = 10 = > short - stemmed red = 10 10 / p = 10 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 120 = > 2 r = 100 and r = 50 long stemmed r = 50 - 10 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - b"


Question: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 27 . what is the difference between the two digits of that number ?

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

<gadget id="calculator">27 / 9</gadget>
<output>3</output>
<result>3</result>

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

Explanation: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 27 ⇔ 9 ( x - y ) = 27 ⇔ x - y = 3 answer a"


Question: a fair price shopkeeper takes 10 % profit on his goods . he lost 60 % goods during theft . his loss percent is :

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

<gadget id="calculator">110 * 60</gadget>
<output>6_600</output>

<gadget id="calculator">6_600 / 100</gadget>
<output>66</output>

<gadget id="calculator">110 - 66</gadget>
<output>44</output>

<gadget id="calculator">100 - 44</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 72 %
B. 42 %
C. 56 %
D. 12 %
E. 22 %

subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 60), const_100)))

Explanation: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 40 . s . p . of each item = rs . 1.10 total sale = 1.10 * 40 = rs . 44 hence , loss % = 56 / 100 * 100 = 56 % answer : c"


Question: a corporation that had $ 115.19 billion in profits for the year paid out $ 230.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )

Choices:
A. 50 %
B. 20 %
C. 5 %
D. 2 %
E. 0.2 %

multiply(divide(multiply(230.1, power(10, add(const_3, const_3))), multiply(115.19, power(10, 9))), const_100)

Explanation: required answer = [ employee benefit / profit ] * 100 = [ ( 230.10 million ) / ( 115.19 billion ) ] * 100 = [ ( 230.10 * 10 ^ 6 ) / ( 115.19 * 10 ^ 9 ) ] * 100 = ( 2 / 1000 ) * 100 = 0.2 % so answer is ( e )


Question: 39 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?

<gadget id="calculator">18 * 39</gadget>
<output>702</output>

<gadget id="calculator">702 / 27</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 24
B. 77
C. 26
D. 25
E. 13

Explanation: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 39 : : 18 : x [ please pay attention , we have written 27 : 39 rather than 39 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 39 \ times 18 } { 27 } } x = 26 so 26 days will be required to get work done by 27 men . answer : c"


Question: a metallic sphere of radius 24 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ?

<gadget id="calculator">24 ** 3</gadget>
<output>13_824</output>

<gadget id="calculator">16 ** 2</gadget>
<output>256</output>

<gadget id="calculator">13_824 / 256</gadget>
<output>54</output>

<gadget id="calculator">4 * 54</gadget>
<output>216</output>

<gadget id="calculator">216 / 3</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 26 cm
B. 45 cm
C. 58 cm
D. 63 cm
E. 72 cm

divide(multiply(const_4, divide(power(24, const_3), power(16, const_2))), const_3)

Explanation: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 16 ) ^ 2 * h = ( 4 / 3 ) π ( 24 ) ^ 3 = > h = 72 cm answer : e"


Question: how many multiples of 4 are there between 32 and 252 ?

<gadget id="calculator">252 - 32</gadget>
<output>220</output>

<gadget id="calculator">220 / 4</gadget>
<output>55</output>

<gadget id="calculator">55 + 1</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 67
B. 64
C. 54
D. 56
E. 60

add(divide(subtract(252, 32), 4), const_1)

Explanation: "it should be mentioned whether 32 and 252 are inclusive . if 32 and 252 are inclusive , then the answer is ( 252 - 32 ) / 4 + 1 = 56 . if 32 and 252 are not inclusive , then the answer is ( 248 - 36 ) / 4 + 1 = 54 . since oa is c , then we have not inclusive case ."


Question: set # 1 = { a , b , c , d , e , f } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?

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

<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(2/3) * (5/6)</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">1 - (5/9)</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>

Choices:
A. 1 / 6
B. 1 / 3
C. 1 / 2
D. 2 / 3
E. 4 / 9

subtract(1, multiply(divide(const_4, add(const_4, const_2)), divide(add(const_3, const_2), add(const_4, const_2))))

Explanation: so not a vowel in set - 1 : 4 / 6 and not a vowel in ser - 2 : 5 / 6 now , 4 / 6 ∗ 5 / 6 = 5 / 9 this is for not a vowel . then for at least one vowel will be = 1 − 5 / 9 = 4 / 9 answer will be e .


Question: if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing thesame no . by 31

<gadget id="calculator">432 * 44</gadget>
<output>19_008</output>

<gadget id="calculator">19_008 % 31</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 2
B. 4
C. 5
D. 7
E. 8

Explanation: p ÷ 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 c


Question: the age of somu is one - third his father ' s . 7 years back he was one - fifth of his father ' s age . what is his persent age ?

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

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

<gadget id="calculator">35 - 7</gadget>
<output>28</output>

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

<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 11
B. 13
C. 14
D. 12
E. 10

divide(subtract(multiply(add(const_4, const_1), 7), 7), subtract(add(const_4, const_1), const_3))

Explanation: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 7 = 3 x - 7 / 5 = x = 14 answer : option c"


Question: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 6 more than 1 / 4 of the fine and peter paid $ 6 less than 1 / 3 of the fine , leaving pay $ 10 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?

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

<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">(1/4) + (1/3)</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">(1/2) + (7/12)</gadget>
<output>13/12 = around 1.083333</output>

<gadget id="calculator">(13/12) * 10</gadget>
<output>65/6 = around 10.833333</output>

<gadget id="calculator">(65/6) + 10</gadget>
<output>125/6 = around 20.833333</output>

<gadget id="calculator">(125/6) * 2</gadget>
<output>125/3 = around 41.666667</output>

<gadget id="calculator">(125/3) + 10</gadget>
<output>155/3 = around 51.666667</output>
<result>155/3 = around 51.666667</result>

Choices:
A. $ 50
B. $ 40
C. $ 35
D. $ 44
E. $ 45

add(multiply(add(multiply(add(divide(1, 2), add(divide(1, 4), divide(1, 3))), 10), 10), 2), const_10)

Explanation: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 6 ] + [ ( 1 / 3 ) f – 6 ] + [ ( 1 / 2 ) f – 10 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 10 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 120 12 f = 13 f – 120 – f = – 120 f = 120 well , if the fine cost $ 120 , then sam paid the part not covered by joe or peter . half the fine is $ 60 , and sam paid $ 10 less than this : $ 50 . answer = a"


Question: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 91 per day . what was his wage on the 8 th day ?

<gadget id="calculator">90 * 15</gadget>
<output>1_350</output>

<gadget id="calculator">87 * 7</gadget>
<output>609</output>

<gadget id="calculator">91 * 7</gadget>
<output>637</output>

<gadget id="calculator">609 + 637</gadget>
<output>1_246</output>

<gadget id="calculator">1_350 - 1_246</gadget>
<output>104</output>
<result>104</result>

Choices:
A. $ 83
B. $ 90
C. $ 92
D. $ 97
E. $ 104

subtract(multiply(90, 15), add(multiply(87, 7), multiply(91, 7)))

Explanation: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 91 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 91 * 7 ) = 1350 - ( 609 + 637 ) = 1350 - 1246 = 104 answer e"


Question: in a class , there are 18 boys who are over 160 cm tall . if these constitute 3 - fourths of the boys and the total number of boys is two - thirds of the total number of students in the class , what is the number of girls in the class ?

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

<gadget id="calculator">18 / (3/4)</gadget>
<output>24</output>

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">24 / (2/3)</gadget>
<output>36</output>

<gadget id="calculator">36 - 24</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 11
B. 12
C. 28
D. 27
E. 19

subtract(divide(divide(18, divide(3, const_4)), divide(const_2, 3)), divide(18, divide(3, const_4)))

Explanation: let the number of boys be x . then , ( 3 / 4 ) x = 18 or x = 18 x ( 4 / 3 ) = 24 . if total number of students is y , then ( 2 / 3 ) y = 24 or y = 24 x ( 3 / 2 ) = 36 . therefore number of girls in the class = ( 36 - 24 ) = 12 . answer : b


Question: the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?

<gadget id="calculator">(2.5 * 40) / 2</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 87 cm 2
B. 28 cm 2
C. 98 cm 2
D. 26 cm 2
E. 50 cm 2

Explanation: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e"


Question: if 75 percent of a class answered the first question on a certain test correctly , 70 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

<gadget id="calculator">75 + 70</gadget>
<output>145</output>

<gadget id="calculator">145 + 20</gadget>
<output>165</output>

<gadget id="calculator">165 - 100</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 10 %
B. ( 8 ) 20 %
C. 30 %
D. 50 %
E. 65 %

subtract(add(add(75, 70), 20), const_100)

Explanation: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 70 % - { both } + 20 % - - > { both } = 65 % . answer : e .


Question: if a man lost 4 % by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44 % ?

<gadget id="calculator">100 - 4</gadget>
<output>96</output>

<gadget id="calculator">96 * 72</gadget>
<output>6_912</output>

<gadget id="calculator">100 + 44</gadget>
<output>144</output>

<gadget id="calculator">6_912 / 144</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 41
B. 48
C. 49
D. 44
E. 43

divide(multiply(subtract(const_100, 4), 72), add(const_100, 44))

Explanation: "96 % - - - - 72 144 % - - - - ? 96 / 144 * 72 = 48 answer : b"


Question: | 5 - 2 | - | 6 - 9 | = ?

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

<gadget id="calculator">9 - 6</gadget>
<output>3</output>

<gadget id="calculator">3 - 3</gadget>
<output>0</output>
<result>0</result>

Choices:
A. 3
B. 2
C. 1
D. 0
E. 4

subtract(subtract(5, 2), subtract(9, 6))

Explanation: "| 5 - 2 | - | 6 - 9 | = | 3 | - | - 3 | = 3 - 3 = 0 correct answer d"


Question: find value of x : 121 × 54 = x

<gadget id="calculator">121 + 121</gadget>
<output>242</output>

<gadget id="calculator">121 * 121</gadget>
<output>14_641</output>

<gadget id="calculator">14_641 / 2</gadget>
<output>14_641/2 = around 7_320.5</output>

<gadget id="calculator">242 + (14_641/2)</gadget>
<output>15_125/2 = around 7_562.5</output>

<gadget id="calculator">(15_125/2) * 10</gadget>
<output>75_625</output>
<result>75_625</result>

Choices:
A. 34545
B. 46576
C. 67887
D. 57687
E. 75625

multiply(add(add(121, 121), divide(multiply(121, 121), const_2)), const_10)

Explanation: 121 × 54 = 121 × ( 102 ) 4 = 121 × 1000016 = 7.5625 × 10000 = 75625 e


Question: aishwarya rai walks into a bank to cash out her check . by mistake the bank teller gives her dollar amount in change , and her cent amount in dollars . on the way home she spends 5 cent , and then suddenly she notices that she has twice the amount of her check . how much was her check amount ?

<gadget id="calculator">100 - 2</gadget>
<output>98</output>

<gadget id="calculator">5 / 98</gadget>
<output>5/98 = around 0.05102</output>

<gadget id="calculator">1 - (5/98)</gadget>
<output>93/98 = around 0.94898</output>

<gadget id="calculator">(93/98) * 98</gadget>
<output>93</output>

<gadget id="calculator">93 / 3</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 21.55
B. 25.89
C. 30.56
D. 31.55
E. 31.63

divide(multiply(subtract(const_1, divide(5, subtract(const_100, const_2))), subtract(const_100, const_2)), const_3)

Explanation: e the check was for dollars 31.63 . the bank teller gave her dollars 63.31 she spent . 05 , and then she had dollars 63.26 , which is twice the check . let x be the dollars of the check , and y be the cent . the check was for 100 x + y cent he was given 100 y + x cent also 100 y + x - 5 = 2 ( 100 x + y ) expanding this out and rearranging , we find : 98 y = 199 x + 5 or 199 x ≡ - 5 ( mod 98 ) or 98 * 2 * x + 3 x ≡ - 5 ( mod 98 ) 3 x ≡ - 5 ≡ 93 ( mod 98 ) this quickly leads to x = 31


Question: the length of a room is 9 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .

<gadget id="calculator">9 * 4.75</gadget>
<output>42.75</output>

<gadget id="calculator">900 * 42.75</gadget>
<output>38_475</output>
<result>38_475</result>

Choices:
A. 25650
B. 25750
C. 26550
D. 30750
E. 38475

Explanation: "area = 9 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 9 × 4.75 × 900 = 9 × 4275 = rs . 38475 answer is e ."


Question: if 2 ^ 5 , 3 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

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

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

<gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>

<gadget id="calculator">12 * (13/2)</gadget>
<output>78</output>

<gadget id="calculator">78 * 2</gadget>
<output>156</output>
<result>156</result>

Choices:
A. 26
B. 39
C. 42
D. 65
E. 156

multiply(multiply(multiply(power(2, 2), 3), divide(13, 2)), 2)

Explanation: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 3 * 4 = 156 answer : e"


Question: i chose a number and divide it by 12 . then i subtracted 240 from the result and got 8 . what was the number i chose ?

<gadget id="calculator">240 + 8</gadget>
<output>248</output>

<gadget id="calculator">248 * 12</gadget>
<output>2_976</output>
<result>2_976</result>

Choices:
A. 2976
B. 2989
C. 2789
D. 2888
E. 2098

Explanation: "let x be the number i chose , then x / 12 − 240 = 8 x / 12 = 248 x = 2976 answer is a ."


Question: in what time will a train 100 meters long cross an electric pole , if its speed is 72 km / hr

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

<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>

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

Choices:
A. 5 seconds
B. 2.8 seconds
C. 3.5 seconds
D. 2.5 seconds
E. 2.6 seconds

Explanation: "first convert speed into m / sec speed = 72 * ( 5 / 18 ) = 20 m / sec time = distance / speed = 100 / 20 = 5 seconds answer : a"


Question: at joel ’ s bookstore , the current inventory is 30 % historical fiction . of the historical fiction books , 40 % are new releases , while 50 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?

<gadget id="calculator">30 * 40</gadget>
<output>1_200</output>

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

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

<gadget id="calculator">50 * 70</gadget>
<output>3_500</output>

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

<gadget id="calculator">12 + 35</gadget>
<output>47</output>

<gadget id="calculator">12 / 47</gadget>
<output>12/47 = around 0.255319</output>
<result>12/47 = around 0.255319</result>

Choices:
A. 4 / 25
B. 12 / 47
C. 2 / 5
D. 8 / 15
E. 2 / 3

divide(divide(multiply(30, 40), const_100), add(divide(multiply(30, 40), const_100), divide(multiply(50, subtract(const_100, 30)), const_100)))

Explanation: let there be 100 books in all historic fiction books = 30 % of total = 30 other books = 70 new historic fiction = 40 % of 30 = 12 other new books = 50 % of 70 = 35 total new books = 35 + 12 = 47 fraction = 12 / 47 ans : b


Question: if 45 % of a class averages 95 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .

<gadget id="calculator">45 * 95</gadget>
<output>4_275</output>

<gadget id="calculator">50 * 78</gadget>
<output>3_900</output>

<gadget id="calculator">4_275 + 3_900</gadget>
<output>8_175</output>

<gadget id="calculator">45 + 50</gadget>
<output>95</output>

<gadget id="calculator">100 - 95</gadget>
<output>5</output>

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

<gadget id="calculator">8_175 + 300</gadget>
<output>8_475</output>

<gadget id="calculator">8_475 / 100</gadget>
<output>339/4 = around 84.75</output>
<result>339/4 = around 84.75</result>

Choices:
A. 83 %
B. 84 %
C. 85 %
D. 86 %
E. 87 %

divide(add(add(multiply(45, 95), multiply(50, 78)), multiply(subtract(const_100, add(45, 50)), 60)), const_100)

Explanation: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 95 + 0.50 x 78 + 0.05 x 60 = 84.75 the class average ( rounded ) is 85 % final answer c ) 85 %"


Question: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.30 per glass on the first day , what was the price per glass on the second day ?

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

<gadget id="calculator">2 * 0.3</gadget>
<output>0.6</output>

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

<gadget id="calculator">0.6 / 3</gadget>
<output>0.2</output>
<result>0.2</result>

Choices:
A. $ 0.15
B. $ 0.20
C. $ 0.30
D. $ 0.40
E. $ 0.45

divide(multiply(add(const_1, const_1), 0.30), add(const_1, const_2))

Explanation: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.3 = 3 * x - - > x = $ 0.2 . answer : b ."


Question: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 40 % and its breadth is decreased by 25 % ?

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">140 * 75</gadget>
<output>10_500</output>

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

<gadget id="calculator">10_500 - 10_000</gadget>
<output>500</output>

<gadget id="calculator">500 / 10_000</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>5</result>

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

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

Explanation: "let l and b be 100 each 100 * 100 = 10000 l increase by 40 % = 140 b decrease by 25 % = 75 140 * 75 = 10500 5 % increase answer : a"


Question: if 3 / w + 3 / x = 3 / y and wx = y , then the average ( arithmetic mean ) of w and x is

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

<gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 1 / 2
B. 1
C. 2
D. 4
E. 8

Explanation: "given : 3 / w + 3 / x = 3 / ywx = y find : ( w + x ) / 2 = ? 3 ( 1 / w + 1 / x ) = 3 ( 1 / y ) - divide both sides by 3 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"


Question: - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 140 students answered yes only for subject m , how many of the students did not answer yes for either subject ?

<gadget id="calculator">500 - 140</gadget>
<output>360</output>

<gadget id="calculator">140 + 360</gadget>
<output>500</output>

<gadget id="calculator">400 - 360</gadget>
<output>40</output>

<gadget id="calculator">500 + 40</gadget>
<output>540</output>

<gadget id="calculator">800 - 540</gadget>
<output>260</output>
<result>260</result>

Choices:
A. 100
B. 260
C. 360
D. 400
E. 500

Explanation: "since 140 students answered yes only for subject m , then the remaining 360 students who answered yes for subject m , also answered yes for subject r . so , 360 students answered yes for both subjects . if 360 students answered yes for both subjects , then 400 - 360 = 40 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 40 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 40 + 300 ) = 260 students did not answer yes for either subject . answer : b ."


Question: the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 2.4 km / hr ?

<gadget id="calculator">2.4 * 1_000</gadget>
<output>2_400</output>

<gadget id="calculator">7_201 / 2_400</gadget>
<output>7_201/2_400 = around 3.000417</output>
<result>7_201/2_400 = around 3.000417</result>

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

Explanation: area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 2.4 km / hour = 2400 m / hour = 40 m / min time taken by lady to cross the field diagonally = 120 / 40 = 3 min answer b


Question: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 8 such machines produce in 4 minutes ?

<gadget id="calculator">270 / 6</gadget>
<output>45</output>

<gadget id="calculator">45 * 4</gadget>
<output>180</output>

<gadget id="calculator">180 * 8</gadget>
<output>1_440</output>
<result>1_440</result>

Choices:
A. 648
B. 1800
C. 2700
D. 1440
E. none of these

multiply(multiply(divide(270, 6), 4), 8)

Explanation: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 8 ã — 4 ã — 270 â ‡ ” x = 8 x 4 x 270 / 6 = 1440 . answer d"


Question: a number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder . the number is :

<gadget id="calculator">555 - 445</gadget>
<output>110</output>

<gadget id="calculator">110 * 2</gadget>
<output>220</output>

<gadget id="calculator">220 * 100</gadget>
<output>22_000</output>

<gadget id="calculator">22_000 + 30</gadget>
<output>22_030</output>
<result>22_030</result>

Choices:
A. 1220
B. 1250
C. 2030
D. 22030
E. 1350

add(multiply(multiply(subtract(555, 445), const_2), const_100), 30)

Explanation: required number = ( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 . answer : d


Question: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 108 grams of compound x ?

<gadget id="calculator">108 * 10</gadget>
<output>1_080</output>

<gadget id="calculator">2 + 10</gadget>
<output>12</output>

<gadget id="calculator">1_080 / 12</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 90
B. 162
C. 250
D. 270
E. 322

Explanation: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 108 gms of x have 108 * 10 / 12 = 90 gms of b and 108 - 90 = 18 gms of a . cross check : - a / b = 18 / 90 = 2 / 10 ( as given ) ans a"