Question: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 6000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?

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

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

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/8) + (1/6)</gadget>
<output>7/24 = around 0.291667</output>

<gadget id="calculator">(1/3) - (7/24)</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">(1/24) * 6_000</gadget>
<output>250</output>

<gadget id="calculator">250 * 3</gadget>
<output>750</output>
<result>750</result>

Choices:
A. s . 375
B. s . 400
C. s . 600
D. s . 750
E. s . 850

multiply(multiply(subtract(inverse(3), add(inverse(8), inverse(6))), 6000), 3)

Explanation: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 6000 ) = rs . 750 answer = d"


Question: if an organization were to sell n tickets for a theater production , the total revenue from ticket sales would be 20 percent greater than the total costs of the production . if the organization actually sold all but 5 percent of the n tickets , the total revenue from ticket sales was what percent greater than the total costs of the production ?

<gadget id="calculator">12 + 4</gadget>
<output>16</output>

<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 4 %
B. 10 %
C. 14 %
D. 15 %
E. 18 %

Explanation: let cost of prod for 1 ticket = 1 so cop for n tickets = n so for selling n tickets , sp = 1.2 * n = 1.2 n so sp of 1 ticket = 1.2 sp of 95 % tickets = 1.2 * 0.95 n so profit % = ( 1.2 * 0.95 n - n ) / n * 100 = 0.14 * 100 = 14 % answer - c


Question: virginia , adrienne , and dennis have taught history for a combined total of 96 years . if virginia has taught for 9 more years than adrienne and for 12 fewer years than dennis , for how many years has dennis taught ?

<gadget id="calculator">9 + 12</gadget>
<output>21</output>

<gadget id="calculator">21 + 9</gadget>
<output>30</output>

<gadget id="calculator">96 - 30</gadget>
<output>66</output>

<gadget id="calculator">66 / 3</gadget>
<output>22</output>

<gadget id="calculator">22 + 21</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 23
B. 32
C. 35
D. 41
E. 42

add(divide(subtract(96, add(add(9, 12), 9)), const_3), add(9, 12))

Explanation: let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 12 = > a = ( d - 12 ) - 9 = d - 21 d - 9 + d - 21 + d = 96 = > 3 d = 96 + 30 = 126 = > d = 42 answer e


Question: an aeroplane covers a certain distance of 670 kmph in 6 hours . to cover the same distance in 6 1 / 4 hours , it must travel at a speed of

<gadget id="calculator">670 * 6</gadget>
<output>4_020</output>

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

<gadget id="calculator">24 + 1</gadget>
<output>25</output>

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

<gadget id="calculator">4_020 / (25/4)</gadget>
<output>3_216/5 = around 643.2</output>
<result>3_216/5 = around 643.2</result>

Choices:
A. 440
B. 540
C. 643
D. 740
E. 250

divide(multiply(670, 6), divide(add(multiply(4, 6), 1), 4))

Explanation: "speed of aeroplane = 670 kmph distance travelled in 6 hours = 670 * 6 = 4020 km speed of aeroplane to acver 4020 km in 25 / 4 = 4020 * 4 / 25 = 643 km answer c ."


Question: a cube is divided into 216 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?

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

<gadget id="calculator">8 * 3</gadget>
<output>24</output>

<gadget id="calculator">216 - 24</gadget>
<output>192</output>

<gadget id="calculator">192 / 2</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 72
B. 84
C. 96
D. 108
E. 120

divide(subtract(216, multiply(multiply(const_4, const_2), const_3)), const_2)

Explanation: each side of the cube has 6 x 6 = 36 cubelets . only the interior cubelets are painted one colour . on each side , 4 x 4 = 16 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 16 = 96 the answer is c .


Question: a sum fetched a total simple interest of $ 4061.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?

<gadget id="calculator">4_061.25 * 100</gadget>
<output>406_125</output>

<gadget id="calculator">406_125 / 9</gadget>
<output>45_125</output>

<gadget id="calculator">45_125 / 5</gadget>
<output>9_025</output>
<result>9_025</result>

Choices:
A. $ 8829
B. $ 2840
C. $ 6578
D. $ 7782
E. $ 8926

divide(divide(multiply(4061.25, const_100), 9), 5)

Explanation: "e 8926 principal = $ 100 x 4016.25 / 9 x 5 = $ 406125 / 45 = $ 8926 ."


Question: the average of 5 consecutive odd numbers is 55 . what is the difference between the highest and lowest numbers ?

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

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

Choices:
A. 2
B. 5
C. 8
D. 9
E. 10

Explanation: explanation : let the numbers be x , x + 2 , x + 4 , x + 6 and x + 8 . then , ( x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) ) / 5 = 55 5 x + 20 = 275 x = 255 / 5 = 51 . so , required difference = ( 51 + 8 ) 51 = 8 answer : c


Question: in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?

<gadget id="calculator">5 + 3</gadget>
<output>8</output>

<gadget id="calculator">25 - 8</gadget>
<output>17</output>

<gadget id="calculator">45 * 17</gadget>
<output>765</output>

<gadget id="calculator">95 * 3</gadget>
<output>285</output>

<gadget id="calculator">765 + 285</gadget>
<output>1_050</output>

<gadget id="calculator">1_050 / 25</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 47
B. 45.6
C. 42
D. 48
E. 49

divide(add(multiply(45, subtract(25, add(5, 3))), multiply(95, 3)), 25)

Explanation: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 5 * 0 + 17 * 45 = 1050 average marks of whole class = 1050 / 25 = 42 answer : option c"


Question: a school has 4 section of chemistry in class x having 40 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>

<gadget id="calculator">35 * 60</gadget>
<output>2_100</output>

<gadget id="calculator">2_000 + 2_100</gadget>
<output>4_100</output>

<gadget id="calculator">45 * 55</gadget>
<output>2_475</output>

<gadget id="calculator">4_100 + 2_475</gadget>
<output>6_575</output>

<gadget id="calculator">42 * 45</gadget>
<output>1_890</output>

<gadget id="calculator">6_575 + 1_890</gadget>
<output>8_465</output>

<gadget id="calculator">40 + 35</gadget>
<output>75</output>

<gadget id="calculator">75 + 45</gadget>
<output>120</output>

<gadget id="calculator">120 + 42</gadget>
<output>162</output>

<gadget id="calculator">8_465 / 162</gadget>
<output>8_465/162 = around 52.253086</output>
<result>8_465/162 = around 52.253086</result>

Choices:
A. 50.25
B. 52.25
C. 51.25
D. 53.25
E. none of the above

Explanation: "required average marks = 40 × 50 + 35 × 60 + 45 × 55 + 42 × 45 / 40 + 35 + 45 + 42 = 2000 + 2100 + 2475 + 1890 / 162 = 8465 ⁄ 162 = 52.25 answer b"


Question: ajay can walk 7 km in 1 hour . in how many hours he can walk 80 km ?

<gadget id="calculator">80 / 7</gadget>
<output>80/7 = around 11.428571</output>
<result>80/7 = around 11.428571</result>

Choices:
A. 5 hrs
B. 11.4 hrs
C. 15.5 hrs
D. 20.4 hrs
E. 30 hrs

Explanation: "1 hour he walk 8 km he walk 80 km in = 80 / 7 * 1 = 11.4 hours answer is b"


Question: the percentage profit earned by selling an article for rs . 1320 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?

<gadget id="calculator">100 + 25</gadget>
<output>125</output>

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">1_320 + 1_280</gadget>
<output>2_600</output>

<gadget id="calculator">2_600 / 2</gadget>
<output>1_300</output>

<gadget id="calculator">(5/4) * 1_300</gadget>
<output>1_625</output>
<result>1_625</result>

Choices:
A. 3000
B. 1230
C. 2000
D. 1625
E. 3400

multiply(divide(add(const_100, 25), const_100), divide(add(1320, 1280), const_2))

Explanation: "c . p . be rs . x . then , ( 1320 - x ) / x * 100 = ( x - 1280 ) / x * 100 1320 - x = x - 1280 2 x = 2600 = > x = 1300 required s . p . = 125 % of rs . 1300 = 125 / 100 * 1300 = rs . 1625 . anser d"


Question: 130 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?

<gadget id="calculator">130 * 7</gadget>
<output>910</output>

<gadget id="calculator">5 / 910</gadget>
<output>1/182 = around 0.005495</output>

<gadget id="calculator">130 * 14</gadget>
<output>1_820</output>

<gadget id="calculator">130 / 1_820</gadget>
<output>1/14 = around 0.071429</output>

<gadget id="calculator">(1/182) + (1/14)</gadget>
<output>1/13 = around 0.076923</output>

<gadget id="calculator">1 / (1/13)</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 8 days
B. 6 days
C. 7 days
D. 9 days
E. 13 days

inverse(add(divide(5, multiply(130, 7)), divide(130, multiply(130, 14))))

Explanation: "1 women ' s 1 day work = 1 / 910 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 910 + 10 / 140 ) = 1 / 13 5 women and 10 children will complete the work in 13 days . answer : e"


Question: a grocer has a sale of rs . 3435 , rs . 3920 , rs . 3855 , rs . 4230 and rs . 3560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?

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

<gadget id="calculator">6 * 3_500</gadget>
<output>21_000</output>

<gadget id="calculator">3_435 + 3_920</gadget>
<output>7_355</output>

<gadget id="calculator">7_355 + 3_855</gadget>
<output>11_210</output>

<gadget id="calculator">11_210 + 4_230</gadget>
<output>15_440</output>

<gadget id="calculator">15_440 + 3_560</gadget>
<output>19_000</output>

<gadget id="calculator">21_000 - 19_000</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 500
B. 1000
C. 6000
D. 7000
E. 2000

Explanation: "total sale for 5 months = rs . ( 3435 + 3920 + 3855 + 4230 + 3560 ) = rs . 19000 . required sale = rs . [ ( 3500 x 6 ) - 19000 ] = rs . ( 21000 - 19000 ) = rs . 2000 answer : option e"


Question: a number of 55 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?

<gadget id="calculator">55 / 3</gadget>
<output>55/3 = around 18.333333</output>
<result>55/3 = around 18.333333</result>

Choices:
A. 10
B. 12
C. 15
D. 16
E. 19

Explanation: to maximize # of boxes we should minimize marbles per box : 17 * 3 + 1 * 4 + 1 * 5 = 50 - - > 17 + 1 + 1 = 19 . answer : e .


Question: the length of a side of a hexagon is 7 inches . what is the perimeter ?

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

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

Choices:
A. 48
B. 42
C. 44
D. 45
E. 40

Explanation: "hexagon . it means 6 equal sides . p = 6 ( 7 ) = 42 inches answer b"


Question: how many numbers from 45 to 110 are exactly divisible by 12 ?

<gadget id="calculator">110 / 12</gadget>
<output>55/6 = around 9.166667</output>

<gadget id="calculator">floor(55/6)</gadget>
<output>9</output>

<gadget id="calculator">9 * 12</gadget>
<output>108</output>

<gadget id="calculator">45 / 12</gadget>
<output>15/4 = around 3.75</output>

<gadget id="calculator">floor(15/4)</gadget>
<output>3</output>

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

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

<gadget id="calculator">108 - 48</gadget>
<output>60</output>

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

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

Choices:
A. 5
B. 7
C. 6
D. 11
E. 12

add(divide(subtract(multiply(floor(divide(110, 12)), 12), multiply(add(floor(divide(45, 12)), const_1), 12)), 12), const_1)

Explanation: "option ' c ' 45 / 12 = 3 and 110 / 12 = 9 = = > 9 - 3 = 6 numbers"


Question: 40 is subtracted from 60 % of a number , the result is 50 . find the number ?

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

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

<gadget id="calculator">90 / (3/5)</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 150
B. 330
C. 277
D. 279
E. 712

divide(add(40, 50), divide(60, const_100))

Explanation: "( 60 / 100 ) * x – 40 = 50 6 x = 900 x = 150 answer : a"


Question: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 108 . find the number of notes of rs . 50 denomination .

<gadget id="calculator">500 * 108</gadget>
<output>54_000</output>

<gadget id="calculator">54_000 - 10_350</gadget>
<output>43_650</output>

<gadget id="calculator">500 - 50</gadget>
<output>450</output>

<gadget id="calculator">43_650 / 450</gadget>
<output>97</output>
<result>97</result>

Choices:
A. 15
B. 21
C. 17
D. 19
E. 97

divide(subtract(multiply(500, 108), 10350), subtract(500, 50))

Explanation: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 108 - x now , 50 * x + 500 * ( 108 - x ) = 10350 50 x + 54000 - 500 x = 10350 - 450 x = - 43650 x = 97 . no . of 50 rupees note = 97 . answer : option e"


Question: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day 5 miles per hour for 6 hours . how many miles in total did she walk ?

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

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

<gadget id="calculator">5 * 6</gadget>
<output>30</output>

<gadget id="calculator">38 + 30</gadget>
<output>68</output>
<result>68</result>

Choices:
A. 68
B. 44
C. 58
D. 60
E. 62

add(add(18, multiply(5, const_4)), multiply(5, 6))

Explanation: first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 6 hours - 30 miles total 18 + 20 + 30 = 68 answer : option a .


Question: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 85 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?

<gadget id="calculator">120 + 220</gadget>
<output>340</output>

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">340 / (17/20)</gadget>
<output>400</output>

<gadget id="calculator">220 / 400</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">(11/20) * 100</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 45 %
B. 48 %
C. 55 %
D. 58 %
E. 65 %

multiply(divide(220, divide(add(120, 220), divide(85, const_100))), const_100)

Explanation: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 220 + 120 = 340 billion gallons if this is only 85 % of the capacity of the reservoir , the total capacity of the reservoir = 340 / 0.85 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 400 ) * 100 = 55 % option c"


Question: find the value of 72517 x 9999 = m ?

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>

<gadget id="calculator">9_995 * 72_517</gadget>
<output>724_807_415</output>
<result>724_807_415</result>

Choices:
A. 345434667
B. 246465757
C. 465767867
D. 725097483
E. 645354643

Explanation: "72518 x 9999 = 72517 x ( 10000 - 1 ) = 72517 x 10000 - 72517 x 1 = 725170000 - 72517 = 725097483 d"


Question: 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2907 , how much was it in the beginning ?

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

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

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">(9/10) * (17/20)</gadget>
<output>153/200 = around 0.765</output>

<gadget id="calculator">2_907 / (153/200)</gadget>
<output>3_800</output>

<gadget id="calculator">floor(3_800)</gadget>
<output>3_800</output>
<result>3_800</result>

Choices:
A. 3800
B. 4200
C. 4400
D. 4500
E. 4600

floor(divide(2907, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 15), const_100))))

Explanation: "x * ( 90 / 100 ) * ( 85 / 100 ) = 2907 x = 3800 answer : a"


Question: average of 5 numbers is 20 , and the sum of 3 of the numbers is 48 , what is the average of the other 2 numbers ?

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

<gadget id="calculator">100 - 48</gadget>
<output>52</output>

<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 24
B. 34
C. 29
D. 35
E. 26

divide(subtract(multiply(20, 5), 48), 2)

Explanation: let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e ) / 5 = 20 a + b + c = 48 ( 48 + d + e ) / 5 = 20 48 + d + e = 100 d + e = 52 average = 52 / 2 = 26 ans e


Question: the population of a city increases by 4 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?

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

<gadget id="calculator">100 + 3</gadget>
<output>103</output>

<gadget id="calculator">103 * 3</gadget>
<output>309</output>

<gadget id="calculator">309 / 100</gadget>
<output>309/100 = around 3.09</output>

<gadget id="calculator">(309/100) + 3</gadget>
<output>609/100 = around 6.09</output>

<gadget id="calculator">100 + (609/100)</gadget>
<output>10_609/100 = around 106.09</output>

<gadget id="calculator">(10_609/100) * 3</gadget>
<output>31_827/100 = around 318.27</output>

<gadget id="calculator">(31_827/100) / 100</gadget>
<output>31_827/10_000 = around 3.1827</output>

<gadget id="calculator">(31_827/10_000) + (609/100)</gadget>
<output>92_727/10_000 = around 9.2727</output>
<result>92_727/10_000 = around 9.2727</result>

Choices:
A. 9 %
B. 9.27 %
C. 27 %
D. 12 %
E. none of these

add(divide(multiply(add(const_100, add(divide(multiply(add(const_100, subtract(4, 1)), subtract(4, 1)), const_100), subtract(4, 1))), subtract(4, 1)), const_100), add(divide(multiply(add(const_100, subtract(4, 1)), subtract(4, 1)), const_100), subtract(4, 1)))

Explanation: "actual increase in population = 3 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 3 / 100 ) ^ 3 = 109.2727 ∴ required percentage = 9.27 % answer : b"


Question: a rectangle measures 8 cm on length and its diagonal measures 17 cm . what is the perimeter of the rectangle ?

<gadget id="calculator">17 ** 2</gadget>
<output>289</output>

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

<gadget id="calculator">289 - 64</gadget>
<output>225</output>

<gadget id="calculator">225 ** (1/2)</gadget>
<output>15</output>

<gadget id="calculator">2 * (15 + 8)</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 44 cm
B. 42 cm
C. 46 cm
D. 49 cm
E. 41 cm

rectangle_perimeter(sqrt(subtract(power(17, const_2), power(8, const_2))), 8)

Explanation: second side = √ 17 power 2 - 8 power 2 = √ 289 - 64 = 15 cm perimeter = 2 ( l + b ) = 2 ( 8 + 5 ) cm = 2 ( 23 ) = 46 cm answer is c .


Question: a train running at the speed of 48 km / hr crosses a pole in 9 seconds . what is the length of the train ?

<gadget id="calculator">48 * 1_000</gadget>
<output>48_000</output>

<gadget id="calculator">48_000 / 3_600</gadget>
<output>40/3 = around 13.333333</output>

<gadget id="calculator">(40/3) * 9</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 140
B. 130
C. 120
D. 170
E. 160

multiply(divide(multiply(48, const_1000), const_3600), 9)

Explanation: "speed = ( 48 x 5 / 18 ) m / sec = ( 40 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( 40 / 3 x 9 ) m = 120 m . answer is c ."


Question: the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?

<gadget id="calculator">35 * 185</gadget>
<output>6_475</output>

<gadget id="calculator">6_475 - 166</gadget>
<output>6_309</output>

<gadget id="calculator">6_309 + 106</gadget>
<output>6_415</output>

<gadget id="calculator">6_415 / 35</gadget>
<output>1_283/7 = around 183.285714</output>

<gadget id="calculator">floor(1_283/7)</gadget>
<output>183</output>
<result>183</result>

Choices:
A. 178.27 cm
B. 183.29 cm
C. 978.29 cm
D. 178.89 cm
E. 176.29 cm

floor(divide(add(subtract(multiply(35, 185), 166), 106), 35))

Explanation: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 185 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"


Question: the cost to park a car in a certain parking garage is $ 10.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?

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

<gadget id="calculator">1.75 * 7</gadget>
<output>12.25</output>

<gadget id="calculator">10 + 12.25</gadget>
<output>22.25</output>

<gadget id="calculator">22.25 / 9</gadget>
<output>2.472222</output>
<result>2.472222</result>

Choices:
A. $ 1.09
B. $ 1.67
C. $ 2.225
D. $ 2.47
E. $ 2.50

divide(add(10.00, multiply(1.75, subtract(9, 2))), 9)

Explanation: "total cost of parking for 10 hours = 10 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 10 + 7 * 1.75 = 22.25 thus the average parking price = 22.25 / 9 = 2.47 $ d is the correct answer ."


Question: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 205 ?

<gadget id="calculator">205 / 22.95</gadget>
<output>8.932462</output>

<gadget id="calculator">8.932462 * 250</gadget>
<output>2_233.1155</output>
<result>2_233.1155</result>

Choices:
A. 1,108
B. 2,100
C. 2,140
D. 2,124
E. 2,256

Explanation: "i think it should be c . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 7 20 - pack for 3.05 * 7 = $ 21.35 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 7 = 2140"


Question: a man can row upstream at 25 kmph and downstream at 45 kmph , and then find the speed of the man in still water ?

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

<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 11
B. 77
C. 30
D. 88
E. 35

Explanation: "us = 25 ds = 45 m = ( 45 + 25 ) / 2 = 35 answer : e"


Question: the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :

<gadget id="calculator">lcm(5, 6)</gadget>
<output>30</output>

<gadget id="calculator">lcm(30, 7)</gadget>
<output>210</output>

<gadget id="calculator">lcm(210, 8)</gadget>
<output>840</output>

<gadget id="calculator">840 * 2</gadget>
<output>1_680</output>
<result>1_680</result>

Choices:
A. 2377
B. 1683
C. 2677
D. 9972
E. 1611

multiply(lcm(lcm(lcm(5, 6), 7), 8), const_2)

Explanation: "explanation : l . c . m . of 5 , 6 , 7 , 8 = 840 . { \ color { blue } \ therefore } required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . { \ color { blue } \ therefore } required number = ( 840 x 2 + 3 ) = 1683 . answer : b ) 1683"


Question: 1 men takes 37 $ to eat a pizza in restaurant such that it have discount multiple of 4 if u eat more pizza . discount increase by multiple of 4 every pizza u eat . for 1 pizza 0 % off . for 2 pizza % off for 3 pizza 8 % off . pizza without discount is 10 $ . how much that man eats the pizza .

<gadget id="calculator">10 * 4</gadget>
<output>40</output>

<gadget id="calculator">40 - 37</gadget>
<output>3</output>
<result>3</result>

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

Explanation: solution : b . for 1 pizza 10 $ . for 2 pizza 10 $ + 9.6 $ ( 4 % off ) = 19.6 , for 3 pizza 19.6 + 9.2 ( 8 % off ) = 28.8 , for 4 pizza 28.8 + 8.8 ( 12 % off ) = 37.6 . so he have 37 so he cant eat 4 th pizza .


Question: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 46 ?

<gadget id="calculator">46 - 2</gadget>
<output>44</output>

<gadget id="calculator">44 / 4</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 11
B. 12
C. 13
D. 14
E. 15

Explanation: "four wheeler = 11 * 4 = 44 ( max ) 2 wheel = 1 so no of 4 wheeler = 11 answer : a"


Question: a train 250 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?

<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">25 * 20</gadget>
<output>500</output>

<gadget id="calculator">500 - 250</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 150 m
B. 200 m
C. 250 m
D. 270 m
E. 300 m

subtract(multiply(25, multiply(72, const_0_2778)), 250)

Explanation: "d = 72 * 5 / 18 = 25 = 500 – 250 = 250 m answer : c"


Question: a 9 % stock yields 8 % . the market value of the stock is :

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

<gadget id="calculator">(25/2) * 9</gadget>
<output>225/2 = around 112.5</output>
<result>225/2 = around 112.5</result>

Choices:
A. rs . 72
B. rs . 92
C. rs . 112.50
D. rs . 116.50
E. none of these

Explanation: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 9 , investment = rs . ( 100 / 8 x 9 ) = rs . 112.50 ∴ market value of rs . 100 stock = rs . 112.50 answer c"


Question: one side of a rectangular field is 15 m and one of its diagonal is 18 m . find the area of the field .

<gadget id="calculator">18 ** 2</gadget>
<output>324</output>

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

<gadget id="calculator">324 - 225</gadget>
<output>99</output>

<gadget id="calculator">99 ** (1/2)</gadget>
<output>3*sqrt(11) = around 9.949874</output>

<gadget id="calculator">15 * (3*sqrt(11))</gadget>
<output>45*sqrt(11) = around 149.248116</output>
<result>45*sqrt(11) = around 149.248116</result>

Choices:
A. 100
B. 120
C. 150
D. 148.5
E. none

rectangle_area(15, sqrt(subtract(power(18, const_2), power(15, const_2))))

Explanation: "solution other side = √ ( 18 ) 2 - ( 15 ) 2 = √ 324 - 225 = √ 99 = 9.9 m . ∴ area = ( 15 x 9.9 ) m 2 = 148.5 m 2 . answer d"


Question: the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?

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

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

<gadget id="calculator">40 * 4</gadget>
<output>160</output>

<gadget id="calculator">300 - 160</gadget>
<output>140</output>

<gadget id="calculator">140 - 40</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 100
B. 25
C. 40
D. 45
E. 75

subtract(subtract(multiply(60, add(const_2, const_3)), multiply(40, const_4)), 40)

Explanation: "average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 40 , max would be 300 - 4 * 40 = 140 - - > the range = 140 ( max ) - 40 ( min ) = 100 answer : a"


Question: find out the square of a number which when doubled exceeds its one sixth by 11 ?

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

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

<gadget id="calculator">2 - (1/5)</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">11 / (9/5)</gadget>
<output>55/9 = around 6.111111</output>

<gadget id="calculator">(55/9) ** 2</gadget>
<output>3_025/81 = around 37.345679</output>
<result>3_025/81 = around 37.345679</result>

Choices:
A. 36
B. 25
C. 19
D. 26
E. 17

power(divide(11, subtract(const_2, divide(const_1, add(const_4, const_1)))), const_2)

Explanation: "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 6 ) + 11 = > 12 p = p + 66 = > p = 6 p ^ 2 = 6 ^ 2 = 36 . answer : a"


Question: a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . find the length of train ?

<gadget id="calculator">9 / 3_600</gadget>
<output>1/400 = around 0.0025</output>

<gadget id="calculator">2 * (1/400)</gadget>
<output>1/200 = around 0.005</output>

<gadget id="calculator">10 / 3_600</gadget>
<output>1/360 = around 0.002778</output>

<gadget id="calculator">4 * (1/360)</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">(1/200) - (1/90)</gadget>
<output>-11/1_800 = around -0.006111</output>

<gadget id="calculator">(1/400) - (1/360)</gadget>
<output>-1/3_600 = around -0.000278</output>

<gadget id="calculator">(-11/1_800) / (-1/3_600)</gadget>
<output>22</output>

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

<gadget id="calculator">20 * (1/400)</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) * 1_000</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 45 m
B. 50 m
C. 55 m
D. 60 m
E. 65 m

multiply(multiply(subtract(divide(subtract(multiply(2, divide(9, const_3600)), multiply(4, divide(10, const_3600))), subtract(divide(9, const_3600), divide(10, const_3600))), 2), divide(9, const_3600)), const_1000)

Explanation: "explanation : first person speed = 2 * ( 5 / 18 ) = 5 / 9 m / sec second person speed = 4 * ( 5 / 18 ) = 10 / 9 m / sec let the length of train is x metre and speed is y m / sec then , x / y − 5 / 9 = 9 = > 9 y − 5 = x = > 9 y − x = 5 . . . . . ( i ) also , x / y − 10 / 9 = 10 90 y − 9 x = 100 . . . . . ( ii ) from ( i ) and ( ii ) , we get , x = 50 so length of train is 50 metre option b"


Question: a number is doubled and 9 is added . if resultant is trebled , it becomes 63 . what is that number

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

<gadget id="calculator">63 - 27</gadget>
<output>36</output>

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

<gadget id="calculator">36 / 6</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 10
C. 12
D. 14
E. 15

divide(subtract(63, multiply(const_3, 9)), multiply(const_3, const_2))

Explanation: "explanation : = > 3 ( 2 x + 9 ) = 63 = > 2 x + 9 = 21 = > x = 6 answer : option a"


Question: a 80 cm long wire is to be cut into two pieces so that one piece will be 3 / 5 th of the other , how many centimeters will the shorter piece be ?

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

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

<gadget id="calculator">80 / (8/5)</gadget>
<output>50</output>

<gadget id="calculator">80 - 50</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30
B. 20
C. 83
D. 21
E. 52

subtract(80, divide(80, add(divide(3, 5), const_1)))

Explanation: "explanation : 1 : 3 / 5 = 5 : 3 3 / 8 * 80 = 30 answer : option a"


Question: a waiter ' s salary consists of his salary and tips . during one week his tips were 7 / 4 of his salary . what fraction of his income came from tips ?

<gadget id="calculator">7 / 4</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">(7/4) + 1</gadget>
<output>11/4 = around 2.75</output>

<gadget id="calculator">(7/4) / (11/4)</gadget>
<output>7/11 = around 0.636364</output>
<result>7/11 = around 0.636364</result>

Choices:
A. 4 / 9
B. 5 / 4
C. 5 / 8
D. 5 / 9
E. 7 / 11

divide(divide(7, 4), add(divide(7, 4), const_1))

Explanation: "income = salary ( s ) + tips = s + s * 7 / 4 = s * 11 / 4 tips = s * 7 / 4 fraction of his income came from tips = ( s * 7 / 4 ) / ( s * 11 / 4 ) = 7 / 11 answer : e"


Question: the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than

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

Choices:
A. 14 years
B. 12 years
C. 56 years
D. 66 years
E. 15 years

Explanation: "given that a + b = 15 + b + c = > a â € “ c = 15 + b â € “ b = 15 = > c is younger than a by 15 years answer : e"


Question: a bag has 9 green balls and 23 pink balls . how many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1 : 1 ?

<gadget id="calculator">23 - 9</gadget>
<output>14</output>
<result>14</result>

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

Explanation: suppose x green balls need to be added . then , the number of green balls becomes 9 + x , and the number of pink balls remains the same , 23 . but now the ratio of green and pink balls is 1 : 1 this means , ( 9 + x ) / 23 = 1 / 1 solving this we get x = 14 . ans e


Question: what is remainder of the division ( 1625 * 1627 * 1629 ) / 12 ?

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

subtract(multiply(multiply(1625, 1627), 1629), subtract(multiply(multiply(1625, 1627), 1629), const_3))

Explanation: remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : a


Question: if henry were to add 8 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>

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

<gadget id="calculator">(7/8) - (3/4)</gadget>
<output>1/8 = around 0.125</output>

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

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

Choices:
A. 25
B. 40
C. 64
D. 80
E. 96

multiply(8, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

Explanation: "7 / 8 x - 3 / 4 x = 8 galls 1 / 8 * x = 8 gallons x = 64 gallons answer c"


Question: find compound interest on $ 4000 at 15 % per annum for 2 years 4 months , compounded annually .

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

<gadget id="calculator">4_000 * (3/20)</gadget>
<output>600</output>

<gadget id="calculator">4_000 + 600</gadget>
<output>4_600</output>

<gadget id="calculator">4_600 * (3/20)</gadget>
<output>690</output>

<gadget id="calculator">600 + 690</gadget>
<output>1_290</output>

<gadget id="calculator">4_600 + 690</gadget>
<output>5_290</output>

<gadget id="calculator">(3/20) / 3</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">5_290 * (1/20)</gadget>
<output>529/2 = around 264.5</output>

<gadget id="calculator">1_290 + (529/2)</gadget>
<output>3_109/2 = around 1_554.5</output>
<result>3_109/2 = around 1_554.5</result>

Choices:
A. 1554.5
B. 1509.5
C. 1108.5
D. 1107.5
E. 1100.5

add(add(multiply(4000, divide(15, const_100)), multiply(add(4000, multiply(4000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(4000, multiply(4000, divide(15, const_100))), multiply(add(4000, multiply(4000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3)))

Explanation: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 4000 x ( 1 +  ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 4000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 5554.50 . : . c . i . = rs . ( 5554.50 - 4000 ) = $ 1554.50 answer a ."


Question: a train is 485 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length

<gadget id="calculator">485 + 140</gadget>
<output>625</output>

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

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

<gadget id="calculator">625 / (25/2)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 20 seconds
B. 30 seconds
C. 40 seconds
D. 50 seconds
E. none of these

divide(add(485, 140), divide(multiply(45, const_1000), const_3600))

Explanation: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 485 + 140 = 625 meter time = distance / speed = 625 ∗ 2 / 25 = 50 seconds option d"


Question: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1110 will be :

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

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

<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">(5/4) * (6/5)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) + (6/5)</gadget>
<output>27/10 = around 2.7</output>

<gadget id="calculator">(27/10) + 1</gadget>
<output>37/10 = around 3.7</output>

<gadget id="calculator">1_110 / (37/10)</gadget>
<output>300</output>
<result>300</result>

Choices:
A. rs . 300
B. rs . 200
C. rs . 240
D. rs . 350
E. none of these

divide(1110, add(add(multiply(add(const_1, divide(25, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_1))

Explanation: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 111 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1110 3.7 z = 1110 , z = 300 answer : . a"


Question: a train moves with a speed of 135 kmph . its speed in metres per second is

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

<gadget id="calculator">135 * (5/18)</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>

Choices:
A. 10.8
B. 37.5
C. 30
D. 38.8
E. none

Explanation: "solution speed = 135 kmph = ( 135 x 5 / 18 ) m / sec = 37.5 m / sec . answer b"


Question: a 50 ml after - shave lotion at 30 % alcohol is mixed with 30 ml of pure water . what is the percentage of alcohol in the new solution ?

<gadget id="calculator">30 * 50</gadget>
<output>1_500</output>

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

<gadget id="calculator">50 + 30</gadget>
<output>80</output>

<gadget id="calculator">15 / 80</gadget>
<output>3/16 = around 0.1875</output>

<gadget id="calculator">(3/16) * 100</gadget>
<output>75/4 = around 18.75</output>
<result>75/4 = around 18.75</result>

Choices:
A. 16.75 %
B. 17.75 %
C. 18.75 %
D. 19.75 %
E. none of these

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

Explanation: the amount of the final mixture is given by 50 ml + 30 ml = 80 ml the amount of alcohol is equal to the amount of alcohol in pure water ( which is 0 ) plus the amount of alcohol in the 30 % solution . let x be the percentage of alcohol in the final solution . hence 0 + 30 % 50 ml = x ( 80 ) solve for x x = 0.1817 = 18.75 % answer c


Question: what is the value of 11 ^ x - 11 ^ ( x + 2 ) , where x is the largest integer such that 11 ^ x is a factor of 30030 ?

<gadget id="calculator">11 ** 3</gadget>
<output>1_331</output>

<gadget id="calculator">11 - 1_331</gadget>
<output>-1_320</output>
<result>-1_320</result>

Choices:
A. - 1331
B. - 1320
C. - 121
D. - 120
E. - 1

Explanation: the given expression is 11 x - 11 ( x ^ + 2 ) = 11 x ( 1 - x ) 1 x needs to be factor of 30030 and x needs to be the largest integer possible . this means 11 x needs to be the largest factor possible . the largest factor of a number is the number itself . the largest factor of 30030 is 30030 = ( 11 * 2730 ) x must be 2730 the value of 11 x ( 1 - x ) = – 1320 . answer : b


Question: a ’ s speed is 17 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?

<gadget id="calculator">17 - 14</gadget>
<output>3</output>

<gadget id="calculator">3 / 17</gadget>
<output>3/17 = around 0.176471</output>
<result>3/17 = around 0.176471</result>

Choices:
A. 1 / 14
B. 1 / 17
C. 3 / 14
D. 3 / 17
E. 1 / 31

Explanation: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 14 ) = xd / v ( 14 / 17 ) * d / v = x * d / v x = 14 / 17 b should have a head start of 3 / 17 of the full distance . the answer is d ."


Question: a invested $ 100 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?

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

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

<gadget id="calculator">100 / 200</gadget>
<output>1/2 = around 0.5</output>

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

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

Choices:
A. $ 100
B. $ 75
C. $ 20
D. $ 120
E. $ 50

multiply(100, subtract(const_1, divide(divide(200, const_2), add(100, divide(200, const_2)))))

Explanation: "a : b = 100 * 12 : 200 * 6 a : b = 1 : 1 a ' s share = 100 / 2 = $ 50 answer is e"


Question: in a family 13 people eat only vegetarian , 8 people eat only non veg . , 6 people eat both veg and non veg . . how many people eat veg in the family ?

<gadget id="calculator">13 + 6</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 20
B. 11
C. 19
D. 31
E. 21

Explanation: "total people eat veg = only veg + both veg and non veg total = 13 + 6 = 19 answer = c"


Question: a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

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

<gadget id="calculator">140 * (1/20)</gadget>
<output>7</output>

<gadget id="calculator">140 - 7</gadget>
<output>133</output>

<gadget id="calculator">133 - 100</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 18 %
B. 20 %
C. 17 %
D. 33 %
E. none of these

subtract(subtract(add(const_100, 40), multiply(add(const_100, 40), divide(5, const_100))), const_100)

Explanation: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 5 % of 140 = rs . 140 - 7 = rs . 133 . gain = rs . 133 â € “ rs . 100 = rs . 33 therefore , gain / profit percent = 33 % . answer : option d"


Question: the total of 336 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is

<gadget id="calculator">336 * 25</gadget>
<output>8_400</output>

<gadget id="calculator">71 * 100</gadget>
<output>7_100</output>

<gadget id="calculator">8_400 - 7_100</gadget>
<output>1_300</output>

<gadget id="calculator">25 - 20</gadget>
<output>5</output>

<gadget id="calculator">1_300 / 5</gadget>
<output>260</output>
<result>260</result>

Choices:
A. 238
B. 277
C. 278
D. 260
E. 288

divide(subtract(multiply(336, 25), multiply(71, const_100)), subtract(25, 20))

Explanation: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 336 - x ) . 0.20 * ( x ) + 0.25 ( 336 - x ) = 71 = > x = 260 . . answer : d ) 260"


Question: a factory produces 6400 toys per week . if the workers at this factory work 3 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?

Choices:
A. 1375 toys
B. 2133 toys
C. 3375 toys
D. 4375 toys
E. 5375 toys

Explanation: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 3 days ) by 3 . 6400 / 3 = 2133 toys correct answer b"


Question: walking at 5 / 6 th of its usual speed a cab is 15 mnts late . find its usual time to cover the journey ?

<gadget id="calculator">5 * 15</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 25 m
B. 45 m
C. 32 m
D. 75 m
E. 62 m

Explanation: new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 15 m ut / 5 = 15 m ut = 75 m answer is d


Question: a person purchased a tv set for rs . 16000 and a dvd player for rs . 6250 . he sold both the items together for rs . 35600 . what percentage of profit did he make ?

<gadget id="calculator">16_000 + 6_250</gadget>
<output>22_250</output>

<gadget id="calculator">35_600 / 22_250</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(8/5) - 1</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 80 %
B. 49 %
C. 40 %
D. 60 %
E. 90 %

multiply(subtract(divide(35600, add(16000, 6250)), const_1), const_100)

Explanation: the total cp = rs . 16000 + rs . 6250 = rs . 22250 and sp = rs . 35600 profit ( % ) = ( 35600 - 22250 ) / 22250 * 100 = 60 % answer : d


Question: two trains each 180 m in length are running on the same parallel lines in opposite directions with the speed of each 80 kmph . in what time will they cross each other completely ?

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

<gadget id="calculator">80 * (5/18)</gadget>
<output>200/9 = around 22.222222</output>

<gadget id="calculator">180 / (200/9)</gadget>
<output>81/10 = around 8.1</output>
<result>81/10 = around 8.1</result>

Choices:
A. 7.8 sec
B. 8.1 sec
C. 8.3 sec
D. 8.2 sec
E. 8.4 sec

Explanation: d = 180 m + 180 m = 360 m * 1 / 1000 = 0.36 kms rs = 80 + 80 = 160 kmph t = ( 0.36 / 160 ) * 3600 = 8.1 sec answer : b


Question: 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?

<gadget id="calculator">13.5 * 20</gadget>
<output>270</output>

<gadget id="calculator">270 / 9</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30
B. 32
C. 60
D. data inadequate
E. none of these

Explanation: "capacity of the tank = 20 × 13.5 = 270 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 270 ⁄ 9 = 30 answer a"


Question: the number of the members of a club is more than 50 and less than 80 . when 4 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?

<gadget id="calculator">lcm(8, 7)</gadget>
<output>56</output>

<gadget id="calculator">56 + 4</gadget>
<output>60</output>

<gadget id="calculator">60 % 9</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 0
B. 2
C. 4
D. 6
E. 8

Explanation: "the number of members is 7 k + 4 = 8 j + 4 the only number in this range which satisfies this is 60 . 60 / 9 = 6 ( 9 ) + 6 the answer is d ."


Question: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train .

<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 * 9</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 150 meter
B. 286 meter
C. 180 meter
D. 288 meter
E. 265 meter

multiply(divide(multiply(72, const_1000), const_3600), 9)

Explanation: "speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : c"


Question: two clocks are set correctly at 1 0 ' clock in the afternoon . one keeps correct time . the other gains 5 seconds per minute . that evening , when the fast clock shows 6 : 20 , what does the correct clock show ?

<gadget id="calculator">5 * 3_600</gadget>
<output>18_000</output>

<gadget id="calculator">20 * 60</gadget>
<output>1_200</output>

<gadget id="calculator">18_000 + 1_200</gadget>
<output>19_200</output>

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

<gadget id="calculator">3_600 + 300</gadget>
<output>3_900</output>

<gadget id="calculator">19_200 / 3_900</gadget>
<output>64/13 = around 4.923077</output>

<gadget id="calculator">1 + (64/13)</gadget>
<output>77/13 = around 5.923077</output>
<result>77/13 = around 5.923077</result>

Choices:
A. 4.0
B. 5.0
C. 6.0
D. 7.2
E. 3.5

add(1, divide(add(multiply(5, const_3600), multiply(20, const_60)), add(const_3600, multiply(5, const_60))))

Explanation: faster clock gains 5 seconds per minute or 5 * 60 = 300 seconds or 5 minutes per hour . both clocks are set at 1 : 00 at 2 : 00 correct clock is at 2 : 00 faster clock is at 2 : 05 : 00 ( 1 hour + gained 5 minutes ) at 3 : 00 - correct clock is at 3 : 00 faster clock is at 3 : 10 : 00 ( 2 hours + gained 10 minutes ) . in 5 hours , faster clock would gain 20 minutes . it will show 6 : 20 . at that point , the correct clock would show 6 : 00 . answer is c


Question: the triplicate ratio of 1 : 3 is ?

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

<gadget id="calculator">3 ** 3</gadget>
<output>27</output>

<gadget id="calculator">1 / 27</gadget>
<output>1/27 = around 0.037037</output>
<result>1/27 = around 0.037037</result>

Choices:
A. 1 : 27
B. 1 : 8
C. 1 : 3
D. 1 : 1
E. 1 : 2

Explanation: "1 ^ 3 : 3 ^ 3 = 1 : 27 answer : a"


Question: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 22.55 % . what would have been the percentage of profit earned if no discount was offered ?

<gadget id="calculator">100 + 22.55</gadget>
<output>122.55</output>

<gadget id="calculator">122.55 * 100</gadget>
<output>12_255</output>

<gadget id="calculator">100 - 5</gadget>
<output>95</output>

<gadget id="calculator">12_255 / 95</gadget>
<output>129</output>

<gadget id="calculator">129 - 100</gadget>
<output>29</output>
<result>29</result>

Choices:
A. 60 %
B. 29 %
C. 39 %
D. 56 %
E. 73 %

subtract(divide(multiply(add(const_100, 22.55), const_100), subtract(const_100, 5)), const_100)

Explanation: "let c . p . be rs . 100 . then , s . p . = rs . 122.55 let marked price be rs . x . then , 95 / 100 x = 122.55 x = 12255 / 95 = rs . 129 now , s . p . = rs . 129 , c . p . = rs . 100 profit % = 29 % . answer : b"


Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn $ 90 only . men ’ s wages are ?

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

<gadget id="calculator">90 / 15</gadget>
<output>6</output>
<result>6</result>

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

Explanation: "b $ 6 5 m = xw = 8 b 5 m + xw + 8 b - - - - - $ 90 rs . 5 m + 5 m + 5 m - - - - - $ 90 rs . 15 m - - - - - - $ 90 = > 1 m = $ 6 ."


Question: two trains of equal are running on parallel lines in the same direction at 48 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?

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

<gadget id="calculator">12 * 1_000</gadget>
<output>12_000</output>

<gadget id="calculator">12_000 / 3_600</gadget>
<output>10/3 = around 3.333333</output>

<gadget id="calculator">36 * (10/3)</gadget>
<output>120</output>

<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 60 m
B. 72 m
C. 80 m
D. 82 m
E. 84 m

divide(multiply(36, divide(multiply(subtract(48, 36), const_1000), const_3600)), const_2)

Explanation: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 48 - 36 = 12 km / hr . = 12 * 5 / 18 = 10 / 3 m / sec . 2 x / 36 = 10 / 3 = > x = 60 . answer : a"


Question: a number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t . what is the greatest two digit prime saturated integer ?

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

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

<gadget id="calculator">6 + 90</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 99
B. 98
C. 97
D. 96
E. 95

add(multiply(const_2, const_3), subtract(const_100, const_10))

Explanation: "t = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."


Question: a cycle is bought for rs . 1500 and sold for rs . 1620 , find the gain percent ?

<gadget id="calculator">1_620 - 1_500</gadget>
<output>120</output>

<gadget id="calculator">120 / 1_500</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) * 100</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 11
B. 8
C. 10
D. 20
E. 12

multiply(divide(subtract(1620, 1500), 1500), const_100)

Explanation: "1500 - - - - 120 100 - - - - ? = > 8 % answer : b"


Question: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 76 , how many questions did student a answer correctly ?

<gadget id="calculator">100 - 76</gadget>
<output>24</output>

<gadget id="calculator">24 / 3</gadget>
<output>8</output>

<gadget id="calculator">100 - 8</gadget>
<output>92</output>
<result>92</result>

Choices:
A. 92
B. 60
C. 73
D. 82
E. 91

subtract(100, divide(subtract(100, 76), const_3))

Explanation: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 76 ( subtracting twice of incorrect from correct ) 3 x = 276 x = 92 answer : a"


Question: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent . overall he make a .

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

<gadget id="calculator">1 - (1/25)</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">15_000 * (24/25)</gadget>
<output>14_400</output>

<gadget id="calculator">11 / 100</gadget>
<output>11/100 = around 0.11</output>

<gadget id="calculator">1 + (11/100)</gadget>
<output>111/100 = around 1.11</output>

<gadget id="calculator">8_000 * (111/100)</gadget>
<output>8_880</output>

<gadget id="calculator">14_400 + 8_880</gadget>
<output>23_280</output>

<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>

<gadget id="calculator">23_280 - 23_000</gadget>
<output>280</output>
<result>280</result>

Choices:
A. 228
B. 288
C. 27
D. 200
E. 280

subtract(add(multiply(15000, subtract(const_1, divide(4, const_100))), multiply(8000, add(const_1, divide(11, const_100)))), add(15000, 8000))

Explanation: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 11 / 100 ) = 8000 + 880 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 880 = rs . 280 as this is positive , an overall profit of rs . 280 was made . answer : e"


Question: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 5 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?

<gadget id="calculator">100 - 5</gadget>
<output>95</output>

<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>

<gadget id="calculator">22 / (19/20)</gadget>
<output>440/19 = around 23.157895</output>
<result>440/19 = around 23.157895</result>

Choices:
A. 22 %
B. 23 %
C. 24 %
D. 25 %
E. 34 %

divide(22, divide(subtract(const_100, 5), const_100))

Explanation: "since 5 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.95 = 0.22 ; { % of customers who sample candy } = 0.231 . answer : b ."


Question: p , q and r have $ 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

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

<gadget id="calculator">4_000 * 4</gadget>
<output>16_000</output>

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>

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

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

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

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

<gadget id="calculator">16_000 / 10</gadget>
<output>1_600</output>
<result>1_600</result>

Choices:
A. 2400
B. 2403
C. 3998
D. 2539
E. 1600

divide(multiply(4000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))

Explanation: "e 1600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 ."


Question: rahul and sham together can complete a task in 35 days , but rahul alone can complete same work in 60 days . calculate in how many days sham can complete this work ?

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

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">(1/35) - (1/60)</gadget>
<output>1/84 = around 0.011905</output>

<gadget id="calculator">1 / (1/84)</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 84 days
B. 82 days
C. 76 days
D. 68 days
E. 60 days

Explanation: explanation : as rahul and sham together can finish work in 35 days . 1 days work of rahul and sham is 1 / 35 rahul can alone complete this work in 60 days , so , rahul one day work is 1 / 60 clearly , sham one day work will be = ( rahul and sham one day work ) - ( rahul one day work ) = 1 / 35 - 1 / 60 = 1 / 84 hence sham will complete the given work in 84 days . answer is a


Question: a train running at the speed of 60 km / hr crosses a pole in 6 sec . what is 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) * 6</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 356
B. 278
C. 127
D. 100
E. 150

multiply(divide(multiply(60, const_1000), const_3600), 6)

Explanation: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 6 = 100 m answer : d"


Question: lucy bought a 1 - year , 10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually . what was the total amount of interest paid on this certificate at maturity ?

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) / 2</gadget>
<output>1/25 = around 0.04</output>

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

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

<gadget id="calculator">10_000 * (676/625)</gadget>
<output>10_816</output>

<gadget id="calculator">10_816 - 10_000</gadget>
<output>816</output>
<result>816</result>

Choices:
A. 10464
B. 864
C. 816
D. 800
E. 480

subtract(multiply(10000, power(add(const_1, divide(divide(8, const_100), const_2)), const_2)), 10000)

Explanation: solution : it says , 8 percent per annum per compounded semi annually . therefore r = 8 / 2 = 4 % . so , p = 10000 r = 4 n = 2 net amount a = 10816 , i = 800 . answer : d


Question: a bag marked at $ 125 is sold for $ 120 . the rate of discount is ?

<gadget id="calculator">125 - 120</gadget>
<output>5</output>

<gadget id="calculator">5 / 125</gadget>
<output>1/25 = around 0.04</output>

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

Choices:
A. 10 %
B. 25 %
C. 20 %
D. 50 %
E. 4 %

multiply(divide(subtract(125, 120), 125), const_100)

Explanation: rate of discount = 5 / 125 * 100 = 4 % answer is e


Question: the radius of a cylindrical vessel is 8 cm and height is 3 cm . find the whole surface of the cylinder ?

<gadget id="calculator">2 * pi * 8 * (8 + 3)</gadget>
<output>176*pi = around 552.920307</output>
<result>176*pi = around 552.920307</result>

Choices:
A. 308 sq cm
B. 220 sq cm
C. 440 sq cm
D. 553.1 sq cm
E. 138 sq cm

Explanation: "r = 8 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 8 ( 11 ) = 553.1 answer : d"


Question: the marks obtained by vijay and amith are in the ratio 6 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?

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

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

<gadget id="calculator">18 / 10</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>

Choices:
A. 1 : 5
B. 4 : 5
C. 9 : 5
D. 9 : 8
E. 9 : 7

Explanation: "6 : 5 3 : 2 - - - - - - - 18 : 15 : 10 18 : 10 9 : 5 answer : c"


Question: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 66 years . what is molly ' s age right now ?

<gadget id="calculator">66 - 6</gadget>
<output>60</output>

<gadget id="calculator">60 / 4</gadget>
<output>15</output>

<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 15 years
B. 35 years
C. 25 years
D. 45 years
E. 55 years

Explanation: "now , sandy is 66 - 6 = 60 molly ' s age is ( 3 / 4 ) * 60 = 45 the answer is d ."


Question: ( 935421 x 625 ) = ?

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

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

<gadget id="calculator">935_421 * 625</gadget>
<output>584_638_125</output>
<result>584_638_125</result>

Choices:
A. 542622125
B. 584632125
C. 544638125
D. 584638125
E. none of these

multiply(935421, power(add(const_4, const_1), const_4))

Explanation: "explanation : 935421 × 625 = 935421 × 54 = 935421 × ( 10 / 2 ) 4 = ( 935421 × 10000 ) / 16 = 584638125 . answer : option d"


Question: bert and rebecca were looking at the price of a condominium . the price of the condominium was 100 % more than bert had in savings , and separately , the same price was also 60 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .

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

<gadget id="calculator">100 / 200</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">100 + 60</gadget>
<output>160</output>

<gadget id="calculator">100 / 160</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">(1/2) / (5/8)</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>

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

divide(divide(const_100, add(const_100, 100)), divide(const_100, add(const_100, 60)))

Explanation: "suppose bert had 100 so price becomes 200 , this 200 = 1.6 times r ' s saving . . so r ' s saving becomes 125 so required ratio is 100 : 125 = 4 : 5 answer : d"


Question: a man swims downstream 30 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?

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

<gadget id="calculator">30 / 5</gadget>
<output>6</output>

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

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

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

divide(add(divide(20, 5), divide(30, 5)), const_2)

Explanation: "30 - - - 5 ds = 6 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : d"


Question: andrew purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?

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

<gadget id="calculator">9 * 55</gadget>
<output>495</output>

<gadget id="calculator">560 + 495</gadget>
<output>1_055</output>
<result>1_055</result>

Choices:
A. 1000
B. 1055
C. 1060
D. 1075
E. 1080

Explanation: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 b"


Question: how many integers v are prime numbers in the range 200 < v < 220 ?

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

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

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

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

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

subtract(divide(subtract(subtract(220, 200), const_12), const_4), const_1)

Explanation: my friend , every single odd number greater than can be written either as 4 v + 1 or as 4 v + 3 . if you divide any odd number by 4 , you will get a remainder of either 1 or 3 . that ' s not a rule unique to prime numbers at all . the 6 v + 1 or 6 v - 1 rule is basically every odd number that is not divisible by three , so it narrows the search a little . here ' s how i thought about the problem . first , eliminate all the even numbers and the odd multiples of 5 in that range . that leaves us with : { 201 , 203 , 207 , 209 , 211 , 213 , 217 , 219 } eliminate the four multiples of 3 . notice that 21 is a multiple of 3 , so 210 is also a multiple of 3 . if we add or subtract 3 or 9 , we get more multiples of three . when we eliminate those , we are left with . { 203 , 209 , 211 , 217 } now , notice that a cool thing about this range is that 210 is also a multiple 7 ( again , because 21 is a multiple of 7 ) . this means that 210 - 7 = 203 210 + 7 = 217 those two numbers are also multiples of 7 , so eliminate them from the list . now , we are left with { 209 , 211 } . we ' ve already checked all the prime numbers less than 10 , so we know that neither of these numbers is divisible by anything less than 10 . we have to check 11 now . we know that 22 is a multiple of 11 , so 220 is also a multiple of 11 . this means that 220 - 11 = 209 is also a multiple of 11 . we can eliminate this from the list also . that leaves us with just 211 . there ' s no zero option in the question , so this must be a prime number . answer = ( a )


Question: if the average of 20 digits is 500 and the average of 14 of them is 390 , calculate the average of the remaining 6 numbers ?

<gadget id="calculator">20 * 500</gadget>
<output>10_000</output>

<gadget id="calculator">14 * 390</gadget>
<output>5_460</output>

<gadget id="calculator">10_000 - 5_460</gadget>
<output>4_540</output>

<gadget id="calculator">4_540 / 6</gadget>
<output>2_270/3 = around 756.666667</output>
<result>2_270/3 = around 756.666667</result>

Choices:
A. 756.7
B. 751.7
C. 753.7
D. 752.7
E. 722.7

divide(subtract(multiply(20, 500), multiply(14, 390)), 6)

Explanation: "explanation : total of the 20 digits - 20 * 500 = 10000 total of the 14 digits - 14 * 390 = 5460 total of the remaining 6 digits - 10000 - 5460 = 4540 average of the remaining 6 numbers = 4540 / 6 = 756.7 answer : a"


Question: two bullet train s 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :

<gadget id="calculator">140 + 180</gadget>
<output>320</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">320 / (250/9)</gadget>
<output>288/25 = around 11.52</output>
<result>288/25 = around 11.52</result>

Choices:
A. 15.8 sec .
B. 11.52 sec .
C. 11.8 sec .
D. 10.8 sec .
E. 08.8 sec .

Explanation: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 180 ) m = 320 m . required time = 320 x 9 / 250 = 11.52 sec . answer b"


Question: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 25 per kg , then his gain percent is

<gadget id="calculator">5 + 3</gadget>
<output>8</output>

<gadget id="calculator">25 * 8</gadget>
<output>200</output>

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

<gadget id="calculator">3 * 20</gadget>
<output>60</output>

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

<gadget id="calculator">200 - 150</gadget>
<output>50</output>

<gadget id="calculator">50 * 100</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 / 150</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>

Choices:
A. 12 %
B. 33 %
C. 14 %
D. 15 %
E. 16 %

divide(multiply(subtract(multiply(25, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

Explanation: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 25 ) = rs . 200 . profit = 200 - 150 = 50 so , profit % = ( 50 / 150 ) * 100 = 33 % option b"


Question: if p / q = 4 / 5 , then the value of 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?

<gadget id="calculator">25 / 7</gadget>
<output>25/7 = around 3.571429</output>

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

<gadget id="calculator">2 - (4/5)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">2 + (4/5)</gadget>
<output>14/5 = around 2.8</output>

<gadget id="calculator">(6/5) / (14/5)</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(25/7) + (3/7)</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 4
B. 34
C. 1
D. 2
E. 3

add(divide(25, 7), divide(subtract(2, divide(4, 5)), add(2, divide(4, 5))))

Explanation: "answer given exp . = 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 25 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 25 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 25 / 7 + 6 / 14 = 25 / 7 + 3 / 7 = 28 / 7 = 4 correct option : a"


Question: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price r of the machine ?

<gadget id="calculator">90 * 20</gadget>
<output>1_800</output>

<gadget id="calculator">1_800 / 100</gadget>
<output>18</output>

<gadget id="calculator">90 + 18</gadget>
<output>108</output>

<gadget id="calculator">108 * 100</gadget>
<output>10_800</output>

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

<gadget id="calculator">9 * 10</gadget>
<output>90</output>

<gadget id="calculator">10_800 / 90</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 81
B. 100
C. 120
D. 135
E. 160

divide(multiply(add(90, divide(multiply(90, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10))

Explanation: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price r = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"


Question: bottle r contains 350 capsules and costs $ 6.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?

<gadget id="calculator">2.99 / 130</gadget>
<output>0.023</output>

<gadget id="calculator">6.25 / 350</gadget>
<output>0.017857</output>

<gadget id="calculator">0.023 - 0.017857</gadget>
<output>0.005143</output>
<result>0.005143</result>

Choices:
A. $ 0.25
B. $ 0.12
C. $ 0.0052
D. $ 0.003
E. $ 0.002

Explanation: "cost per capsule in r is 6.25 / 350 = 0.0178 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.0052 the answer is c"


Question: the milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )

<gadget id="calculator">58 * 25</gadget>
<output>1_450</output>

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

<gadget id="calculator">1_450 * (1/2)</gadget>
<output>725</output>

<gadget id="calculator">725 * 7.5</gadget>
<output>5_437.5</output>
<result>5_437.5</result>

Choices:
A. 100
B. 250
C. 750
D. 5437.5
E. 5635.5

multiply(multiply(multiply(58, 25), divide(1, const_2)), 7.5)

Explanation: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 58 * 25 * 1 / 2 = 725 feet ^ 3 of milk must be removed , which equals to 725 * 7.5 = 5437.5 gallons . answer : d ."


Question: a rectangular block 15 cm by 30 cm by 75 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?

<gadget id="calculator">360 * 1_000</gadget>
<output>360_000</output>

<gadget id="calculator">360_000 / 10</gadget>
<output>36_000</output>

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

<gadget id="calculator">1_000 * 6</gadget>
<output>6_000</output>

<gadget id="calculator">36_000 - 6_000</gadget>
<output>30_000</output>

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

<gadget id="calculator">75 * 10</gadget>
<output>750</output>

<gadget id="calculator">3_000 + 750</gadget>
<output>3_750</output>

<gadget id="calculator">30_000 + 3_750</gadget>
<output>33_750</output>

<gadget id="calculator">33_750 / 10</gadget>
<output>3_375</output>

<gadget id="calculator">33_750 / 3_375</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 6
B. 40
C. 15
D. 10
E. 22

divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(75, const_10))), divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(75, const_10))), const_10))

Explanation: volume of the block = 15 * 30 * 75 = 33750 cm ^ 3 side of the largest cube = h . c . f of 15 , 30,75 = 15 cm volume of the cube = 15 * 15 * 15 = 3375 cm ^ 3 number of cubes = 33750 / 3375 = 10 answer is d


Question: after replacing an old member by a new member , it was found that the average age of 5 members of a club is the same as it was 3 years ago . what is the difference between the ages of the replaced and the new member ?

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

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

Explanation: explanation : i ) let the ages of the five members at present be a , b , c , d & e years . and the age of the new member be f years . ii ) so the new average of five members ' age = ( a + b + c + d + f ) / 5 - - - - - - - ( 1 ) iii ) their corresponding ages 3 years ago = ( a - 3 ) , ( b - 3 ) , ( c - 3 ) , ( d - 3 ) & ( e - 3 ) years so their average age 3 years ago = ( a + b + c + d + e - 15 ) / 5 = x - - - - - ( 2 ) = = > a + b + c + d + e = 5 x + 15 = = > a + b + c + d = 5 x + 15 - e - - - - - - ( 3 ) iv ) substituting this value of a + b + c + d = 5 x + 15 - e in ( 1 ) above , the new average is : ( 5 x + 15 - e + f ) / 5 equating this to the average age of x years , 3 yrs , ago as in ( 2 ) above , ( 5 x + 15 - e + f ) / 5 = x = = > ( 5 x + 15 - e + f ) = 5 x solving e - f = 15 years . thus the difference of ages between replaced and new member = 15 years . answer : d


Question: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 26.1 kg of zinc has been consumed in it ?

<gadget id="calculator">11 / 9</gadget>
<output>11/9 = around 1.222222</output>

<gadget id="calculator">(11/9) * 26.1</gadget>
<output>31.9</output>

<gadget id="calculator">31.9 + 26.1</gadget>
<output>58</output>
<result>58</result>

Choices:
A. 58 kg
B. 60 kg
C. 64 kg
D. 70 kg
E. none

Explanation: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 26.1 kg zinc , mixture , melted = [ 20 / 9 x 26.1 ] kg = 58 kg . answer a"


Question: the ratio of boys to girls is 6 : 4.60 % of the boys and 40 % of girls take lunch in the canteen . what % of class takes lunch ?

<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>

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

<gadget id="calculator">(3/5) * 60</gadget>
<output>36</output>

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

<gadget id="calculator">(2/5) * 40</gadget>
<output>16</output>

<gadget id="calculator">36 + 16</gadget>
<output>52</output>
<result>52</result>

Choices:
A. 51 %
B. 52 %
C. 53 %
D. 54 %
E. 55 %

add(multiply(divide(6, const_10), subtract(const_100, 40)), multiply(divide(const_4, const_10), 40))

Explanation: let total no of students 100 , boy 60 and girl 40 , so lunch taken by boy and girl respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 students takes lunch out of 100 students . . so required % is 52 % answer : b


Question: a person x started at 3 hours earlier at 40 km / h from a place p , then another person y followed him at 60 km / h . started his journey at 3 o ' clock , afternoon . what is the diference in time when x was 30 km ahead of y and when y was 30 km ahead of x ?

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

<gadget id="calculator">120 + 30</gadget>
<output>150</output>

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

<gadget id="calculator">150 / 20</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">120 - 30</gadget>
<output>90</output>

<gadget id="calculator">90 / 20</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">(15/2) - (9/2)</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 8 h
B. 3 h
C. 6 h
D. 3 h
E. 1 h

subtract(divide(add(multiply(40, 3), 30), divide(40, const_2)), divide(subtract(multiply(40, 3), 30), divide(40, const_2)))

Explanation: explanation : time ( when x was 30 km ahead of y ) = ( 120 - 30 ) / 20 = 4.5 h time ( when y was 30 km ahead of x ) = ( 120 + 30 ) / 20 = 7.5 h thus , required difference in time = 3 h answer : b


Question: a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor ?

<gadget id="calculator">5 * 100</gadget>
<output>500</output>

<gadget id="calculator">500 + 44</gadget>
<output>544</output>

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

<gadget id="calculator">300 + 74</gadget>
<output>374</output>

<gadget id="calculator">544 * 374</gadget>
<output>203_456</output>

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

<gadget id="calculator">544 / 16</gadget>
<output>34</output>

<gadget id="calculator">34 ** 2</gadget>
<output>1_156</output>

<gadget id="calculator">203_456 / 1_156</gadget>
<output>176</output>
<result>176</result>

Choices:
A. 178
B. 128
C. 127
D. 176
E. 171

divide(multiply(add(multiply(5, const_100), 44), add(multiply(3, const_100), 74)), power(divide(add(multiply(5, const_100), 44), power(const_2, const_4)), const_2))

Explanation: "area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d"


Question: if 35 % of a number is 24 less than 50 % of that number , then the number is ?

<gadget id="calculator">50 - 35</gadget>
<output>15</output>

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

<gadget id="calculator">24 / (3/20)</gadget>
<output>160</output>
<result>160</result>

Choices:
A. 180
B. 450
C. 160
D. 170
E. 185

divide(24, divide(subtract(50, 35), const_100))

Explanation: explanation : let the number be n . then , 50 % of n - 35 % of n = 24 50 / 100 n - 35 / 100 n = 24 n = ( 24 x 100 ) / 15 = 160 . answer c


Question: tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 5400 after completion of one year . what will be jose ' s share of profit ?

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

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

<gadget id="calculator">3_000 * 12</gadget>
<output>36_000</output>

<gadget id="calculator">12 - 2</gadget>
<output>10</output>

<gadget id="calculator">4_500 * 10</gadget>
<output>45_000</output>

<gadget id="calculator">45_000 + 36_000</gadget>
<output>81_000</output>

<gadget id="calculator">36_000 / 81_000</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">1 - (4/9)</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">5_400 * (5/9)</gadget>
<output>3_000</output>
<result>3_000</result>

Choices:
A. 3000
B. 2200
C. 2309
D. 2400
E. 3200

multiply(5400, subtract(const_1, divide(multiply(3000, multiply(2, multiply(2, const_3))), add(multiply(4500, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(3000, multiply(2, multiply(2, const_3)))))))

Explanation: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 5400 = 3000 a"


Question: there are 5 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?

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

<gadget id="calculator">6 * 5</gadget>
<output>30</output>

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

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

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

<gadget id="calculator">600 / 4</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 90
B. 120
C. 150
D. 180
E. 200

divide(multiply(multiply(5, const_4), multiply(6, 5)), power(factorial(const_2), const_2))

Explanation: number of ways of selecting 2 fiction books = 5 c 2 number of ways of selecting 2 non fiction books = 6 c 2 5 c 2 * 6 c 2 = 10 * 15 = 150 answer : c


Question: the area of a triangle is with base 4 m and height 6 m ?

<gadget id="calculator">(4 * 6) / 2</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 11 m 2
B. 10 m 2
C. 18 m 2
D. 19 m 2
E. 12 m 2

Explanation: "1 / 2 * 4 * 6 = 12 m 2 answer : e"


Question: if 40 sheep eat 40 bags of grass in 40 days . in how many days one sheep will eat one bag of grass ?

<gadget id="calculator">40 * 40</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 * 40</gadget>
<output>64_000</output>

<gadget id="calculator">64_000 / 40</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 / 40</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 1
B. 20
C. 40
D. 80
E. 70

divide(divide(multiply(multiply(40, 40), 40), 40), 40)

Explanation: explanation : let the required number of days be x . less sheep , more days ( indirect proportion ) less bags , less days ( direct proportion ) sheep 1 : 40 : : 40 : x bags 40 : 1 1 x 40 x x = 40 x 1 x 40 x = 40 . answer : c


Question: increasing the original price of an article by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by

<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">(6/5) * (6/5)</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>

<gadget id="calculator">100 * (11/25)</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 40 %
B. 41 %
C. 42 %
D. 43 %
E. 44 %

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

Explanation: "1.2 * 1.2 * x = 1.44 * x the answer is e ."


Question: the age of somu is one - third his father ' s . 6 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 * 6</gadget>
<output>30</output>

<gadget id="calculator">30 - 6</gadget>
<output>24</output>

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

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

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

divide(subtract(multiply(add(const_4, const_1), 6), 6), 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 - 6 = 3 x - 6 / 5 = x = 12 answer : option d"


Question: john builds a square with a side of 12 cm from some wire . if from the same wire , he builds a rectangle with a width of 6 cm , what will be the length of the rectangle ?

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

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

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

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

Choices:
A. 18 cm
B. 19 cm
C. 20 cm
D. 21 cm
E. none

divide(subtract(square_perimeter(12), multiply(6, const_2)), const_2)

Explanation: solution : if the side of the square is 12 cm , then its perimetre will be 48 cm . we build the rectangle from the same wire , so it will have the same perimetre . its width is 6 cm , so its length will be ( 48 - 12 ) ÷ 2 = 36 ÷ 2 = 18 cm answer a


Question: a train 560 m long , running with a speed of 63 km / hr will pass a tree in ?

<gadget id="calculator">63 * 1_000</gadget>
<output>63_000</output>

<gadget id="calculator">560 / 63_000</gadget>
<output>2/225 = around 0.008889</output>

<gadget id="calculator">(2/225) * 3_600</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 15
B. 16
C. 17
D. 28
E. 32

multiply(divide(560, multiply(63, const_1000)), const_3600)

Explanation: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 560 * 2 / 35 = 32 sec answer : option e"


Question: the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 180 . the banker â € ™ s discount is

<gadget id="calculator">180 * 100</gadget>
<output>18_000</output>

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

<gadget id="calculator">18_000 / 36</gadget>
<output>500</output>

<gadget id="calculator">500 + 180</gadget>
<output>680</output>
<result>680</result>

Choices:
A. rs . 960
B. rs . 840
C. rs . 1020
D. rs . 680
E. none

add(divide(multiply(180, const_100), multiply(3, 12)), 180)

Explanation: solution t . d = ( b . g x 100 / r x t ) = rs . ( 180 x 100 / 12 x 3 ) = rs . 500 . b . d = rs ( 500 + 180 ) = rs . 680 . answer d


Question: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 10 .

<gadget id="calculator">17 * 9</gadget>
<output>153</output>

<gadget id="calculator">153 + 10</gadget>
<output>163</output>
<result>163</result>

Choices:
A. 150
B. 152
C. 154
D. 163
E. 144

Explanation: "d = d * q + r d = 17 * 9 + 10 d = 153 + 10 d = 163 answer d"


Question: a lady builds 8 cm length , 15 cm width , and 5 cm height box using 10 cubic cm cubes . what is the minimum number of cubes required to build the box ?

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

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

<gadget id="calculator">600 / 10</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 107
B. 60
C. 70
D. 89
E. 78

divide(multiply(multiply(8, 15), 5), 10)

Explanation: "number of cubes required = volume of box / volume of cube = 8 * 15 * 5 / 10 = 60 cubes answer : b"


Question: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total w of the book ?

<gadget id="calculator">3_000 + 3</gadget>
<output>3_003</output>
<result>3_003</result>

Choices:
A. 3003
B. 3027
C. 3024
D. 3021
E. 3018

Explanation: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) w 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."


Question: the population of a bacteria colony doubles every day . if it was started 8 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?

<gadget id="calculator">8 + 1</gadget>
<output>9</output>

<gadget id="calculator">2 ** 9</gadget>
<output>512</output>

<gadget id="calculator">512 - 1</gadget>
<output>511</output>
<result>511</result>

Choices:
A. 512
B. 768
C. 1024
D. 2048
E. 4096

subtract(power(2, add(8, const_1)), const_1)

Explanation: "8 days ago - 2 7 days ago - 4 6 days ago - 8 5 days ago - 16 4 days ago - 32 3 days ago - 64 2 days ago - 128 yesterday - 256 today - 512 ans : a"


Question: how many quarters are equal to 7 dollars ?

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

Choices:
A. 1
B. 28
C. 12
D. 9
E. 7

Explanation: "7 * 4 = 28 quarters answer : b"


Question: what is 0.1 percent of 12,356 ?

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

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

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

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

<gadget id="calculator">10 * 1_200</gadget>
<output>12_000</output>

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

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

<gadget id="calculator">35 * 10</gadget>
<output>350</output>

<gadget id="calculator">12_000 + 350</gadget>
<output>12_350</output>

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

<gadget id="calculator">12_350 + 6</gadget>
<output>12_356</output>

<gadget id="calculator">0.1 * 12_356</gadget>
<output>1_235.6</output>

<gadget id="calculator">1_235.6 / 100</gadget>
<output>12.356</output>
<result>12.356</result>

Choices:
A. 0.12356
B. 1.2356
C. 12.356
D. 0.012356
E. 0.0012356

divide(multiply(0.1, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)

Explanation: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.1 ( 1 / 100 ) 12,356 . the answer is 12.356 . hence , the correct answer is c .


Question: the difference between the value of a number increased by 25 % and the value of the original number decreased by 30 % is 22 . what is the original number ?

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

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

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(5/4) - (7/10)</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">22 / (11/20)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40
B. 50
C. 65
D. 70
E. 90

divide(22, subtract(add(const_1, divide(25, const_100)), subtract(const_1, divide(30, const_100))))

Explanation: "let the original # be x then 1.25 x − 0.7 x = 22 - - > x = 40 answer : a ."


Question: if a - b = 3 and a ^ 2 + b ^ 2 = 33 , find the value of ab .

Choices:
A. 12
B. 15
C. 10
D. 18
E. 13

multiply(multiply(add(3, divide(subtract(sqrt(33), 3), 2)), divide(subtract(sqrt(33), 3), 2)), 2)

Explanation: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 33 - 9 = 24 ab = 12 . answer is a ."


Question: 1 : 3 = 1 2 / 3 : x . the value of x is ?

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

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

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

<gadget id="calculator">(5/3) / (1/3)</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 1
B. 6
C. 7
D. 5
E. 8

divide(add(divide(2, 3), 1), divide(1, 3))

Explanation: x * 1 = 3 * 5 / 3 x = 5 answer : d


Question: how many figures are required to number the pages the pages of a book containing 709 pages ?

<gadget id="calculator">709 / 10</gadget>
<output>709/10 = around 70.9</output>

<gadget id="calculator">(709/10) / 10</gadget>
<output>709/100 = around 7.09</output>

<gadget id="calculator">(709/100) - 1</gadget>
<output>609/100 = around 6.09</output>

<gadget id="calculator">(709/10) - 1</gadget>
<output>699/10 = around 69.9</output>

<gadget id="calculator">(699/10) - (609/100)</gadget>
<output>6_381/100 = around 63.81</output>

<gadget id="calculator">(609/100) + (6_381/100)</gadget>
<output>699/10 = around 69.9</output>

<gadget id="calculator">709 - 1</gadget>
<output>708</output>

<gadget id="calculator">708 - (699/10)</gadget>
<output>6_381/10 = around 638.1</output>

<gadget id="calculator">(6_381/10) * 3</gadget>
<output>19_143/10 = around 1_914.3</output>

<gadget id="calculator">(699/10) + (19_143/10)</gadget>
<output>9_921/5 = around 1_984.2</output>
<result>9_921/5 = around 1_984.2</result>

Choices:
A. 2020
B. 2019
C. 1019
D. 2029
E. 2039

add(add(subtract(divide(divide(709, const_10), const_10), const_1), subtract(subtract(divide(709, const_10), const_1), subtract(divide(divide(709, const_10), const_10), const_1))), multiply(subtract(subtract(709, const_1), subtract(divide(709, const_10), const_1)), const_3))

Explanation: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 709 = 610 * 3 = 1830 - - - - - - - - - - - 2019 answer : b"


Question: a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :

<gadget id="calculator">4/3 * pi * (9 ** 3)</gadget>
<output>972*pi = around 3_053.628059</output>

<gadget id="calculator">pi * (9 ** 2) * 9 / 3</gadget>
<output>243*pi = around 763.407015</output>

<gadget id="calculator">(972*pi) - (243*pi)</gadget>
<output>729*pi = around 2_290.221044</output>

<gadget id="calculator">(729*pi) / (972*pi)</gadget>
<output>3/4 = around 0.75</output>

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

Choices:
A. 45 %
B. 56 %
C. 67 %
D. 75 %
E. none of these

multiply(divide(subtract(volume_sphere(9), volume_cone(9, 9)), volume_sphere(9)), const_100)

Explanation: explanation : we will first subtract the cone volume from wood volume to get the wood wasted . then we can calculate its percentage . sphere volume = 4 / 3 π r 3 cone volume = 1 / 3 π r 2 h volume of wood wasted = ( 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ) − ( 1 / 3 π ∗ 9 ∗ 9 ∗ 9 ) = π ∗ 9 ∗ 9 ∗ 9 cm 3 required percentage = π ∗ 9 ∗ 9 ∗ 9 / 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ∗ 100 % = 3 / 4 ∗ 100 % = 75 % option d


Question: of the votes cast on a certain proposal , 66 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )

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

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

<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">66 / (1/5)</gadget>
<output>330</output>
<result>330</result>

Choices:
A. 290
B. 310
C. 330
D. 350
E. 370

divide(66, subtract(subtract(const_1, divide(40, const_100)), divide(40, const_100)))

Explanation: "let x be the total number of votes cast . 0.6 x = 0.4 x + 66 0.2 x = 66 x = 330 the answer is c ."


Question: the average earning of amechanic for the first 4 days of a week is rs . 25 and for the last 4 days is rs . 22 . if heearns rs . 20 on the fourth day , his average earning forthe whole week is ?

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

<gadget id="calculator">4 * 22</gadget>
<output>88</output>

<gadget id="calculator">100 + 88</gadget>
<output>188</output>

<gadget id="calculator">188 - 20</gadget>
<output>168</output>

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

<gadget id="calculator">168 / 7</gadget>
<output>24</output>
<result>24</result>

Choices:
A. s . 10
B. s . 24
C. s . 30
D. s . 40
E. s . 50

divide(subtract(add(multiply(4, 25), multiply(4, 22)), 20), add(const_3, const_4))

Explanation: total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 25 + 4 x 22 - 20 = rs . 168 â ˆ ´ average earning = 168 / 7 = rs . 24 b


Question: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3025 in 3 years . find the rate percent ?

<gadget id="calculator">3_025 - 2_420</gadget>
<output>605</output>

<gadget id="calculator">605 / 2_420</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 11
B. 10
C. 28
D. 25
E. 82

multiply(divide(subtract(3025, 2420), 2420), const_100)

Explanation: "explanation : 2420 - - - 605 100 - - - ? = > 25 % answer : option d"