a can do a piece of work 60 days . b can do work in 90 days . in how many days they will complete the work together ?

Explanation: lcm = 180 , ratio = 60 : 90 = 2 : 3 no of days = 180 / ( 2 + 3 ) = 180 / 5 = 36 days answer : a

divide(const_1, add(divide(const_1, 60), divide(const_1, 90)))

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/60) + (1/90)</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">1 / (1/36)</gadget>
<output>36</output>
<result>36</result>


what least number should be added to 1536 , so that the sum is completely divisible by 21 ?

Explanation: "1536 ÷ 21 = 73 reminder - 3 3 + 18 = 21 hence 18 should be added to 1536 so that the sum will be divisible by 21 answer : c"

<gadget id="calculator">1_536 % 21</gadget>
<output>3</output>
<gadget id="calculator">21 - 3</gadget>
<output>18</output>
<result>18</result>


gary drove from point a to point b at 60 km / h . on his way back he took a train travelling at 110 km / h and therefore his trip back lasted 5 hours less . what is the distance ( in km ) between a and b ?

Explanation: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 - 5 thus , s 1 t 1 = s 2 t 2 60 t 1 = s 2 ( t 1 - 5 ) t 1 = 11 60 * 11 = 660 answer : c

multiply(60, divide(multiply(110, 5), subtract(110, 60)))

<gadget id="calculator">110 * 5</gadget>
<output>550</output>
<gadget id="calculator">110 - 60</gadget>
<output>50</output>
<gadget id="calculator">550 / 50</gadget>
<output>11</output>
<gadget id="calculator">60 * 11</gadget>
<output>660</output>
<result>660</result>


when n is divided by 19 , the remainder is 7 . find thee difference between previous remainder and the remainder when 18 n is divided by 9 ?

Explanation: let n = 7 ( leaves a remainder of 7 when divided by 19 ) 18 n = 18 ( 7 ) = 126 , which leaves a remainder of 0 when divided by 9 . difference = 7 - 0 = 7 . answer a

<gadget id="calculator">18 % 9</gadget>
<output>0</output>
<gadget id="calculator">7 - 0</gadget>
<output>7</output>
<result>7</result>


solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 75 percent carbonated water , what percent of the volume of the mixture is p ?

Explanation: "75 % is 5 % - points below 80 % and 20 % - points above 55 % . so the ratio of solution p to solution q is 4 : 1 . mixture p is 4 / 5 = 80 % of the volume of mixture pq . the answer is d ."

multiply(divide(subtract(divide(75, const_100), divide(55, const_100)), add(subtract(divide(75, const_100), divide(55, const_100)), subtract(divide(80, const_100), divide(75, const_100)))), const_100)

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">(3/4) - (11/20)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) - (3/4)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/5) + (1/20)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/5) / (1/4)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>


the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 15 km / hr respectively . they will meet for the first time in ?

Explanation: "clearly , the two will meet when they are 1000 m apart to be 20 + 15 = 35 km apart , they take 1 hour to be 1000 m apart , they take 35 * 1000 / 1000 = 35 min . answer is c"

<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<result>35</result>


the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is :

Explanation: weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a

subtract(multiply(add(35, divide(400, const_1000)), add(24, const_1)), multiply(24, 35))

<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">35 + (2/5)</gadget>
<output>177/5 = around 35.4</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">(177/5) * 25</gadget>
<output>885</output>
<gadget id="calculator">24 * 35</gadget>
<output>840</output>
<gadget id="calculator">885 - 840</gadget>
<output>45</output>
<result>45</result>


the contents of a certain box consist of 14 apples and 24 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?

Explanation: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 24 oranges , so to get to 6 oranges , we should remove 24 - 6 = 18 oranges . answer a"

subtract(add(14, 24), divide(14, divide(70, const_100)))

<gadget id="calculator">14 + 24</gadget>
<output>38</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">14 / (7/10)</gadget>
<output>20</output>
<gadget id="calculator">38 - 20</gadget>
<output>18</output>
<result>18</result>


mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?

Explanation: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 96 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 96 ) is 96 % of juan ' s income ( 100 ) . answer : c"

multiply(multiply(subtract(const_1, divide(40, const_100)), add(const_1, divide(60, const_100))), const_100)

<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">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(3/5) * (8/5)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">(24/25) * 100</gadget>
<output>96</output>
<result>96</result>


a and b are two circles . the radius of a is four times as large as the diameter of b . what is the ratio between the areas of the circles ?

Explanation: given : the radius of a is 4 times as large as the diameter of b . = > r ( a ) = 4 * d ( b ) = 4 * 2 * r ( b ) = 8 r ( b ) . the radius are in ratio of 1 : 8 thus the area will be in the ratio of square of radius . 1 : 64 . hence d .

divide(power(const_1, const_2), power(multiply(const_2, const_4), const_2))

<gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">1 / 64</gadget>
<output>1/64 = around 0.015625</output>
<result>1/64 = around 0.015625</result>


a can run 192 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?

Explanation: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 192 / 32 = 6 m / s distance covered by b in 4 seconds = speed ã — time = 6 ã — 4 = 24 metre i . e . , a beat b by 24 metre answer is c"

subtract(192, multiply(divide(192, 32), 28))

<gadget id="calculator">192 / 32</gadget>
<output>6</output>
<gadget id="calculator">6 * 28</gadget>
<output>168</output>
<gadget id="calculator">192 - 168</gadget>
<output>24</output>
<result>24</result>


a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ?

Explanation: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1585.75 = > x = 791 e"

<gadget id="calculator">1_000 + 585.75</gadget>
<output>1_585.75</output>
<gadget id="calculator">1_585.75 / 2</gadget>
<output>792.875</output>
<result>792.875</result>


a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 550 ?

Explanation: "slope of 2 and a y - intercept of 2 y - coordinate is 550 y = 2 x + 2 548 = 2 x x = 274 answer : e . 274"

<gadget id="calculator">550 - 2</gadget>
<output>548</output>
<gadget id="calculator">548 / 2</gadget>
<output>274</output>
<result>274</result>


if xy = 4 , x / y = 16 , for positive numbers x and y , y = ?

Explanation: "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 16 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 16 - - - > y ^ 2 = 4 / 16 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a ."

<gadget id="calculator">4 / 16</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) ** (1/2)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


if a boat is rowed downstream for 24 km in 4 hours and upstream for 48 km in 24 hours , what is the speed of the boat and the river ?

Explanation: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 6 ; us = 2 x = ( 6 + 2 ) / 2 = 8 / 2 = 4 km / hr y = ( 6 - 2 ) / 2 = 4 / 2 = 2 km / hr answer : e"

divide(add(divide(48, 24), divide(24, 4)), const_2)

<gadget id="calculator">48 / 24</gadget>
<output>2</output>
<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<gadget id="calculator">2 + 6</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>


the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 86 , and the average of the female students ’ grades was 92 , how many female students took the test ?

Explanation: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 86 thus m = 688 - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 688 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 16 ans : e"

divide(subtract(multiply(90, 8), multiply(86, 8)), subtract(92, 90))

<gadget id="calculator">90 * 8</gadget>
<output>720</output>
<gadget id="calculator">86 * 8</gadget>
<output>688</output>
<gadget id="calculator">720 - 688</gadget>
<output>32</output>
<gadget id="calculator">92 - 90</gadget>
<output>2</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>


a cycle is bought for rs . 800 and sold for rs . 1080 , find the gain percent ?

Explanation: "800 - - - - 180 100 - - - - ? = > 35 % answer : c"

multiply(divide(subtract(1080, 800), 800), const_100)

<gadget id="calculator">1_080 - 800</gadget>
<output>280</output>
<gadget id="calculator">280 / 800</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>35</result>


a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train .

Explanation: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : c"

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

<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>


laura took out a charge account at the general store and agreed to pay 8 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?

Explanation: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 8 % interest = ( 8 / 100 ) * 35 = 2.8 $ total amount that laura owes a year later = 35 + 2.8 = 37.8 $ answer d"

add(multiply(divide(8, const_100), 35), 35)

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 35</gadget>
<output>14/5 = around 2.8</output>
<gadget id="calculator">(14/5) + 35</gadget>
<output>189/5 = around 37.8</output>
<result>189/5 = around 37.8</result>


a man purchased 3 blankets @ rs . 100 each , 4 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?

Explanation: explanation : 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 a

subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(4, 150)))

<gadget id="calculator">10 * 150</gadget>
<output>1_500</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">4 * 150</gadget>
<output>600</output>
<gadget id="calculator">300 + 600</gadget>
<output>900</output>
<gadget id="calculator">1_500 - 900</gadget>
<output>600</output>
<result>600</result>


rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?

Explanation: "50 pages typed 1 x 40 pages typed 2 x ( original + one revision ) 10 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 40 ( 6 + 4 ) + 10 ( 6 + 4 + 4 ) = 300 + 400 + 140 = 840 answer - b"

add(add(multiply(100, 6), multiply(40, 4)), multiply(multiply(10, 4), const_2))

<gadget id="calculator">100 * 6</gadget>
<output>600</output>
<gadget id="calculator">40 * 4</gadget>
<output>160</output>
<gadget id="calculator">600 + 160</gadget>
<output>760</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">760 + 80</gadget>
<output>840</output>
<result>840</result>


a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?

Explanation: let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.7 x = 0.6 ( x + 30 ) 0.1 x = 6 x = 60 the answer is e .

divide(subtract(multiply(30, divide(60, const_100)), multiply(30, divide(40, const_100))), subtract(divide(70, const_100), divide(60, const_100)))

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">30 * (3/5)</gadget>
<output>18</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">30 * (2/5)</gadget>
<output>12</output>
<gadget id="calculator">18 - 12</gadget>
<output>6</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) - (3/5)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">6 / (1/10)</gadget>
<output>60</output>
<result>60</result>


a is 30 % more efficient than b . how much time they will working together take to complete a job which a alone could have done in 23 days ?

Explanation: "the ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b can do work in x days then 10 : 13 : : 23 : x x = ( 23 * 13 ) / 10 x = 299 / 10 a ' s 1 day ' s work = 1 / 23 b ' s 1 day ' s work = 10 / 299 ( a + b ) ' s 1 day ' s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 a and b together can do work in 13 days answer ( b )"

inverse(add(divide(const_1, 23), divide(const_1, multiply(add(divide(30, const_100), const_1), 23))))

<gadget id="calculator">1 / 23</gadget>
<output>1/23 = around 0.043478</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) + 1</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) * 23</gadget>
<output>299/10 = around 29.9</output>
<gadget id="calculator">1 / (299/10)</gadget>
<output>10/299 = around 0.033445</output>
<gadget id="calculator">(1/23) + (10/299)</gadget>
<output>1/13 = around 0.076923</output>
<gadget id="calculator">1 / (1/13)</gadget>
<output>13</output>
<result>13</result>


this year , mbb consulting fired 6 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?

Explanation: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 6 % reduction in employees lead to 94 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 94 employees is 94 * 1100 = 103400 now the new salary is more than previous salary by x % . x = ( 103400 / 100000 ) * 100 = 103.4 % so the answer is d"

divide(multiply(add(const_100, multiply(const_100, 10)), add(subtract(const_100, 6), const_4)), multiply(const_100, 10))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">100 + 1_000</gadget>
<output>1_100</output>
<gadget id="calculator">100 - 6</gadget>
<output>94</output>
<gadget id="calculator">94 + 4</gadget>
<output>98</output>
<gadget id="calculator">1_100 * 98</gadget>
<output>107_800</output>
<gadget id="calculator">107_800 / 1_000</gadget>
<output>539/5 = around 107.8</output>
<result>539/5 = around 107.8</result>


find the cost of fencing around a circular field of diameter 12 m at the rate of rs . 3.50 a meter ?

Explanation: "2 * 22 / 7 * 6 = 37.7 37.7 * 3 1 / 2 = rs . 131.95 answer : a"

<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">2 * pi * 6</gadget>
<output>12*pi = around 37.699112</output>
<gadget id="calculator">(12*pi) * 3.5</gadget>
<output>42.0*pi = around 131.946891</output>
<result>42.0*pi = around 131.946891</result>


a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .

Explanation: "explanation : as there is meal for 70 adults and 28 have their meal , the meal left can be catered to 42 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 42 adults = 54 children hence , the meal can be catered to 54 children . answer : b"

multiply(subtract(70, 28), divide(90, 70))

<gadget id="calculator">70 - 28</gadget>
<output>42</output>
<gadget id="calculator">90 / 70</gadget>
<output>9/7 = around 1.285714</output>
<gadget id="calculator">42 * (9/7)</gadget>
<output>54</output>
<result>54</result>


a side of beef lost 25 percent of its weight in processing . if the side of beef weighed 540 pounds after processing , how many pounds did it weigh before processing ?

Explanation: "let weight of side of beef before processing = x ( 75 / 100 ) * x = 540 = > x = ( 540 * 100 ) / 75 = 720 answer c"

divide(multiply(540, const_100), subtract(const_100, 25))

<gadget id="calculator">540 * 100</gadget>
<output>54_000</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">54_000 / 75</gadget>
<output>720</output>
<result>720</result>


when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?

Explanation: one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 2 ^ 3 / 3 ^ 5 we have 5 ! / 2 ! * 3 ! = 10 such cases so , 2 ^ 3 * 10 / 3 ^ 5 = 80 / 243 answer : d .

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


a reduction of 30 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 940 , what is the reduced price for kg ?

Explanation: "940 * ( 30 / 100 ) = 282 - - - - 6 ? - - - - 1 = > rs . 47 answer : b"

divide(divide(multiply(940, 30), const_100), 6)

<gadget id="calculator">940 * 30</gadget>
<output>28_200</output>
<gadget id="calculator">28_200 / 100</gadget>
<output>282</output>
<gadget id="calculator">282 / 6</gadget>
<output>47</output>
<result>47</result>


a certain company reported that the revenue on sales increased 30 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

Explanation: assume the revenue in 2000 to be 100 . then in 2003 it would be 130 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 130 ) / 130 = 50 / 130 = 39 % answer : e .

multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(30, const_100))), add(const_1, divide(30, const_100))), const_100)

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(9/5) - (13/10)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / (13/10)</gadget>
<output>5/13 = around 0.384615</output>
<gadget id="calculator">(5/13) * 100</gadget>
<output>500/13 = around 38.461538</output>
<result>500/13 = around 38.461538</result>


if a man lost 5 % by selling oranges at the rate of 8 a rupee at how many a rupee must he sell them to gain 52 % ?

Explanation: "95 % - - - - 8 152 % - - - - ? 95 / 152 * 8 = 5 answer : a"

divide(multiply(subtract(const_100, 5), 8), add(const_100, 52))

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 * 8</gadget>
<output>760</output>
<gadget id="calculator">100 + 52</gadget>
<output>152</output>
<gadget id="calculator">760 / 152</gadget>
<output>5</output>
<result>5</result>


there are 32 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?

Explanation: the total number of stations = 34 from 34 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 34 p 2 ways . 34 p 2 = 34 * 33 = 1122 answer : d

multiply(add(32, const_2), subtract(add(32, const_2), const_1))

<gadget id="calculator">32 + 2</gadget>
<output>34</output>
<gadget id="calculator">34 - 1</gadget>
<output>33</output>
<gadget id="calculator">34 * 33</gadget>
<output>1_122</output>
<result>1_122</result>


a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 5 , ab = 5 and ac = 11 , what is the length of ae ?

Explanation: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 5 = 19 the answer is a ."

add(add(11, divide(subtract(11, 5), 2)), 5)

<gadget id="calculator">11 - 5</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">11 + 3</gadget>
<output>14</output>
<gadget id="calculator">14 + 5</gadget>
<output>19</output>
<result>19</result>


a can run 288 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?

Explanation: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 288 / 32 = 9 m / s distance covered by b in 4 seconds = speed ã — time = 9 ã — 4 = 36 metre i . e . , a beat b by 36 metre answer is e"

subtract(288, multiply(divide(288, 32), 28))

<gadget id="calculator">288 / 32</gadget>
<output>9</output>
<gadget id="calculator">9 * 28</gadget>
<output>252</output>
<gadget id="calculator">288 - 252</gadget>
<output>36</output>
<result>36</result>


Explanation: "any x and y satisfying x / y = 7 / 4 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 4 , then ( x + y ) / ( x - y ) = ( 7 + 4 ) / ( 7 - 4 ) = 11 / 3 . answer : b ."

<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">7 - 4</gadget>
<output>3</output>
<gadget id="calculator">11 / 3</gadget>
<output>11/3 = around 3.666667</output>
<result>11/3 = around 3.666667</result>


of the families in city x in 1956 , 25 percent owned a personal computer . the number of families in city x owning a computer in 1960 was 15 percent greater than it was in 1956 , and the total number of families in city x was 5 percent greater in 1956 than it was in 1960 . what percent of the families in city x owned a personal computer in 1960 ?

Explanation: "say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 number of families owning computer in 1960 = 25 * 115 / 100 = 28.75 number of families in 1960 = 105 the percentage = 28.75 / 105 * 100 = 27.38 % . option : e"

multiply(const_100, divide(divide(multiply(add(15, const_100), 25), const_100), add(const_100, 5)))

<gadget id="calculator">15 + 100</gadget>
<output>115</output>
<gadget id="calculator">115 * 25</gadget>
<output>2_875</output>
<gadget id="calculator">2_875 / 100</gadget>
<output>115/4 = around 28.75</output>
<gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">(115/4) / 105</gadget>
<output>23/84 = around 0.27381</output>
<gadget id="calculator">100 * (23/84)</gadget>
<output>575/21 = around 27.380952</output>
<result>575/21 = around 27.380952</result>


if the cost price is 91 % of sp then what is the profit %

Explanation: "sol . sp = rs 100 : then cp = rs 91 : profit = rs 9 . profit = { ( 9 / 91 ) * 100 } % = 9.89 % answer is a ."

multiply(divide(subtract(const_100, 91), 91), const_100)

<gadget id="calculator">100 - 91</gadget>
<output>9</output>
<gadget id="calculator">9 / 91</gadget>
<output>9/91 = around 0.098901</output>
<gadget id="calculator">(9/91) * 100</gadget>
<output>900/91 = around 9.89011</output>
<result>900/91 = around 9.89011</result>


a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 24 , find the sum of money ?

Explanation: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 24 41 - - - - ? = > rs . 123 answer : d"

multiply(divide(24, 40), add(add(const_100, 65), 40))

<gadget id="calculator">24 / 40</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">100 + 65</gadget>
<output>165</output>
<gadget id="calculator">165 + 40</gadget>
<output>205</output>
<gadget id="calculator">(3/5) * 205</gadget>
<output>123</output>
<result>123</result>


tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?

Explanation: number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e

<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<result>24</result>


a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 44000 . what is the share of c ?

Explanation: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 44000 ] = rs . 12000 answer : option a"

multiply(44000, inverse(add(add(divide(2, 3), multiply(divide(2, 3), 3)), const_1)))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 3</gadget>
<output>2</output>
<gadget id="calculator">(2/3) + 2</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">(8/3) + 1</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">1 / (11/3)</gadget>
<output>3/11 = around 0.272727</output>
<gadget id="calculator">44_000 * (3/11)</gadget>
<output>12_000</output>
<result>12_000</result>


a sum of rs . 100 is lent at simple interest of 3 % p . a . for the first month , 9 % p . a . for the second month , 27 % p . a . for the third month and so on . what is the total amount of interest earned at the end of the year approximately

Explanation: total amount of interest is i = p / 100 * 1 [ 3 / 12 + 9 / 12 + 27 / 12 … . 312 / 12 where p = 100 ; i = 1 / 12 ( 3 + 9 + … . . 312 ) i = 1 / 12 ( 3 ( 312 - 1 ) ) / 3 - 1 = 531440 * 3 / 12 * 2 = rs . 66430 answer : d

divide(multiply(subtract(power(3, const_12), const_1), 3), multiply(const_12, const_2))

<gadget id="calculator">3 ** 12</gadget>
<output>531_441</output>
<gadget id="calculator">531_441 - 1</gadget>
<output>531_440</output>
<gadget id="calculator">531_440 * 3</gadget>
<output>1_594_320</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">1_594_320 / 24</gadget>
<output>66_430</output>
<result>66_430</result>


suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?

Explanation: the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the “ back ” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b .

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<result>6</result>


a man bought 10 crates of mangoes for $ 40 total . if he lost 2 of the crates , at what price would he have to sell each of the remaining crates in order to earn a total profit of 20 percent of the total cost ?

Explanation: as given , after lost , the remaining 8 crates total cost = $ 40 so , 1 crate cost = 40 / 8 = 5 to get 20 % profit , 1 crate cost should be = 5 + 5 * 20 / 100 = $ 6 answer : a

divide(add(40, multiply(40, divide(20, const_100))), subtract(10, 2))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">40 * (1/5)</gadget>
<output>8</output>
<gadget id="calculator">40 + 8</gadget>
<output>48</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<result>6</result>


a number increased by 30 % gives 650 . the number is ?

Explanation: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 650 ( 130 ã — 5 = 650 ) 100 % - - - - - - - > 400 ( 100 ã — 5 = 500 ) option ' d '"

divide(650, add(const_1, divide(30, const_100)))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">650 / (13/10)</gadget>
<output>500</output>
<result>500</result>


arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 20 days .

Explanation: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 20 * 6 / 10 = 12 days . answer : a"

subtract(20, multiply(divide(20, 10), 4))

<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<result>12</result>


if ' x ' is a positive integer exactly divisible by 6 or 15 but not divisible by 12 . what could possibly be the value of ' x ' ?

Explanation: 120 and 60 are both divisible by 6 and 15 but also by 12 . so they are not the right answer . 36 and 54 are both clearly not divisible by 15 ( not correct ) 90 is both divisible by 6 and 15 but not by 12 . answer : ( d ) 90

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


on a sum of money , the simple interest for 2 years is rs . 324 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is

Explanation: "the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 324 = 16 ( r ã — si ) / ( 2 ã — 100 ) = 16 ( r ã — 324 ) / ( 2 ã — 100 ) = 16 r = 9.87 % answer : option c"

divide(multiply(const_100, subtract(subtract(340, divide(324, 2)), divide(324, 2))), divide(324, 2))

<gadget id="calculator">324 / 2</gadget>
<output>162</output>
<gadget id="calculator">340 - 162</gadget>
<output>178</output>
<gadget id="calculator">178 - 162</gadget>
<output>16</output>
<gadget id="calculator">100 * 16</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 / 162</gadget>
<output>800/81 = around 9.876543</output>
<result>800/81 = around 9.876543</result>


a taxi leaves point a 2 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .

Explanation: "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 4 hrs and taxi a total of 2 hrs . hence 4 * ( v - 20 ) = 2 v 4 v - 80 = 2 v 2 v = 80 v = 40 mph e"

divide(add(multiply(2, 20), multiply(2, 20)), subtract(add(2, 2), 2))

<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">40 + 40</gadget>
<output>80</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>40</result>


monica planned her birthday party . she prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra . after the party , it turned out that one of the guests did n ' t come but every one of the guests that did come ate 6 muffins and 6 muffins remained . how many guests did monica plan on ?

Explanation: let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a

<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">12 - 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<result>2</result>


a boy rides his bicycle 10 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately ?

Explanation: total distance traveled = 10 + 12 = 22 km / hr . total time taken = 10 / 12 + 12 / 10 = 61 / 30 hrs . average speed = 22 * 30 / 61 = 10.8 km / hr . answer : b

<gadget id="calculator">12 + 10</gadget>
<output>22</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<result>11</result>


Explanation: 3 ^ x = 2 3 ^ 4 x = 2 ^ 4 3 ^ 4 x = 16 3 ^ ( 4 x + 3 ) = 3 ^ 4 x * 3 ^ 3 = 16 * 27 = 432 answer : c

power(3, add(multiply(4, divide(log(const_2), log(const_3))), 3))

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<gadget id="calculator">log(3)</gadget>
<output>log(3) = around 1.098612</output>
<gadget id="calculator">log(2) / log(3)</gadget>
<output>log(2)/log(3) = around 0.63093</output>
<gadget id="calculator">4 * (log(2)/log(3))</gadget>
<output>4*log(2)/log(3) = around 2.523719</output>
<gadget id="calculator">(4*log(2)/log(3)) + 3</gadget>
<output>4*log(2)/log(3) + 3 = around 5.523719</output>
<gadget id="calculator">3 ** (4*log(2)/log(3) + 3)</gadget>
<output>3**(4*log(2)/log(3) + 3) = around 432</output>
<result>3**(4*log(2)/log(3) + 3) = around 432</result>


two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 360 meters , after what time will they meet at the starting point ?

Explanation: "they meet every 360 / 7 + 8 = 24 sec answer is d"

<gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">360 / 15</gadget>
<output>24</output>
<result>24</result>


a van takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?

Explanation: "time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )"

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 6</gadget>
<output>9</output>
<gadget id="calculator">540 / 9</gadget>
<output>60</output>
<result>60</result>


if an object travels 90 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )

Explanation: "90 feet / 2 seconds = 45 feet / second ( 45 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 30.68 ( approximately ) the answer is a ."

divide(divide(90, 5280), multiply(2, divide(1, const_3600)))

<gadget id="calculator">90 / 5_280</gadget>
<output>3/176 = around 0.017045</output>
<gadget id="calculator">1 / 3_600</gadget>
<output>1/3_600 = around 0.000278</output>
<gadget id="calculator">2 * (1/3_600)</gadget>
<output>1/1_800 = around 0.000556</output>
<gadget id="calculator">(3/176) / (1/1_800)</gadget>
<output>675/22 = around 30.681818</output>
<result>675/22 = around 30.681818</result>


the population of a village is 13400 . it increases annually at the rate of 21 % p . a . what will be its population after 2 years ?

Explanation: "formula : ( after = 100 denominator ago = 100 numerator ) 13400 × 121 / 100 × 121 / 100 = 19619 c"

multiply(13400, power(add(const_1, divide(21, const_100)), 2))


a box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?

Explanation: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is ."

divide(multiply(multiply(49, 21), 14), volume_cube(divide(14, const_2)))

<gadget id="calculator">49 * 21</gadget>
<output>1_029</output>
<gadget id="calculator">1_029 * 14</gadget>
<output>14_406</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">7 ** 3</gadget>
<output>343</output>
<gadget id="calculator">14_406 / 343</gadget>
<output>42</output>
<result>42</result>


sonika deposited rs . 7000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?

Explanation: "( 7000 * 3 * 2 ) / 100 = 420 9200 - - - - - - - - 9620 answer : c"

add(multiply(multiply(add(divide(2, const_100), divide(divide(subtract(9200, 7000), 3), 7000)), 7000), 3), 7000)

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">9_200 - 7_000</gadget>
<output>2_200</output>
<gadget id="calculator">2_200 / 3</gadget>
<output>2_200/3 = around 733.333333</output>
<gadget id="calculator">(2_200/3) / 7_000</gadget>
<output>11/105 = around 0.104762</output>
<gadget id="calculator">(1/50) + (11/105)</gadget>
<output>131/1_050 = around 0.124762</output>
<gadget id="calculator">(131/1_050) * 7_000</gadget>
<output>2_620/3 = around 873.333333</output>
<gadget id="calculator">(2_620/3) * 3</gadget>
<output>2_620</output>
<gadget id="calculator">2_620 + 7_000</gadget>
<output>9_620</output>
<result>9_620</result>


a ’ s speed is 20 / 13 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 ?

Explanation: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 13 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 13 meters ) to reach the finish line . so b should get a head start of 7 / 20 th of the race . answer ( d )"

<gadget id="calculator">20 - 13</gadget>
<output>7</output>
<gadget id="calculator">7 / 20</gadget>
<output>7/20 = around 0.35</output>
<result>7/20 = around 0.35</result>


what is the largest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?

Explanation: explanation : largest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , largest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : a

subtract(subtract(multiply(const_100, const_100), const_1), reminder(subtract(multiply(const_100, const_100), const_1), lcm(lcm(lcm(15, 25), 40), 75)))

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 - 1</gadget>
<output>9_999</output>
<gadget id="calculator">lcm(15, 25)</gadget>
<output>75</output>
<gadget id="calculator">lcm(75, 40)</gadget>
<output>600</output>
<gadget id="calculator">lcm(600, 75)</gadget>
<output>600</output>
<gadget id="calculator">9_999 % 600</gadget>
<output>399</output>
<gadget id="calculator">9_999 - 399</gadget>
<output>9_600</output>
<result>9_600</result>


what will be the cost of building a fence around a square plot with area equal to 64 sq ft , if the price per foot of building the fence is rs . 58 ?

Explanation: "let the side of the square plot be a ft . a 2 = 64 = > a = 8 length of the fence = perimeter of the plot = 4 a = 32 ft . cost of building the fence = 32 * 58 = rs . 1856 . answer : d"

<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">32 * 58</gadget>
<output>1_856</output>
<result>1_856</result>


a 6 litre sol is 20 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?

Explanation: "20 % of 6 = 1.2 50 % of 6 = 3 shortage is 1.8 so we need to have 1.8 / 50 % to get 50 % alcohol content . = 3.6 d"

subtract(6, multiply(const_2, multiply(divide(20, const_100), 6)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 6</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">2 * (6/5)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">6 - (12/5)</gadget>
<output>18/5 = around 3.6</output>
<result>18/5 = around 3.6</result>


if 45 % of z is 60 % of y and y is 75 % of x , what percent of x is z ?

Explanation: "( 45 / 100 ) z = ( 60 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 60 / 100 ) * ( 3 / 4 ) x i . e . z = ( 60 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1 ) x = ( 100 / 100 ) x i . e . z is 100 % of x answer : option c"

multiply(divide(divide(75, const_100), divide(divide(45, const_100), divide(60, const_100))), const_100)

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(9/20) / (3/5)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) / (3/4)</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>100</result>


how many odd 3 - digit integers greater than 800 are there such that all their digits are different ?

Explanation: in the range 800 - 900 : 1 choice for the first digit : 8 ; 5 choices for the third digit : 1 , 3 , 5 , 7 , 9 ( as the number is odd ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 5 * 8 = 40 . in the range 900 - 999 : 1 choice for the first digit : 9 ; 4 choices for the third digit : 1 , 3 , 5 , 7 ( 9 is out as it ' s the first digit ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 4 * 8 = 32 . total : 40 + 32 = 72 . answer : c

add(multiply(add(3, add(const_3, const_2)), const_4), multiply(multiply(const_1, add(const_3, const_2)), add(3, add(const_3, const_2))))

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">1 * 5</gadget>
<output>5</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">32 + 40</gadget>
<output>72</output>
<result>72</result>


the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?

Explanation: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 40 x = 8 and the number of spinsters is 2 ( 8 ) = 16 . the answer is b ."

<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>16</result>


Explanation: "33 1 / 3 % = 1 / 3 1 / 3 × 240 = 80 a )"

divide(multiply(add(33, divide(1, 3)), 240), const_100)

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">33 + (1/3)</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">(100/3) * 240</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 / 100</gadget>
<output>80</output>
<result>80</result>


one pump drains one - half of a pond in 7 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?

Explanation: "first pump drains 1 / 2 of the tank in 7 hours so 14 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 14 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 14 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 14 + 1 / a ) = 1 / 2 solving u get a = 14 / 13 = 1.1 hence answer is b"

divide(const_1, subtract(const_1, divide(const_1, multiply(7, const_2))))

<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">1 / 14</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">1 - (1/14)</gadget>
<output>13/14 = around 0.928571</output>
<gadget id="calculator">1 / (13/14)</gadget>
<output>14/13 = around 1.076923</output>
<result>14/13 = around 1.076923</result>


what is the area of square field whose side of length 18 m ?

Explanation: "18 * 18 = 324 sq m answer : d"

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


how much is 80 % of 40 is greater than 4 / 5 of 30 ?

Explanation: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 32 - 24 = 8 answer : c"

subtract(multiply(40, divide(80, const_100)), multiply(divide(4, 5), 30))

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">40 * (4/5)</gadget>
<output>32</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 30</gadget>
<output>24</output>
<gadget id="calculator">32 - 24</gadget>
<output>8</output>
<result>8</result>


how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ?

Explanation: "the odd numbers less than 60 are 1 , 3,5 , . . . 59 some of them are equal to product of 5 and odd number hence odd multiples of 5 which are less than 60 are 5,15 , 25,35 , 45,55 ( total = 6 ) ; answer : b"

<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>6</result>


in a sports club with 30 members , 17 play badminton and 18 play tennis and 2 do not play either . how many members play both badminton and tennis ?

Explanation: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 18 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"

<gadget id="calculator">17 + 18</gadget>
<output>35</output>
<gadget id="calculator">35 + 2</gadget>
<output>37</output>
<gadget id="calculator">37 - 30</gadget>
<output>7</output>
<result>7</result>


working at their respective constant rates , machine a makes 100 copies in 15 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?

Explanation: "machine a can produce 100 * 30 / 15 = 200 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 650 copies . c is the answer"

<gadget id="calculator">100 / 15</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">150 / 10</gadget>
<output>15</output>
<gadget id="calculator">(20/3) + 15</gadget>
<output>65/3 = around 21.666667</output>
<gadget id="calculator">(65/3) * 30</gadget>
<output>650</output>
<result>650</result>


one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .

Explanation: "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a"

rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2))))

<gadget id="calculator">17 ** 2</gadget>
<output>289</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">289 - 225</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<gadget id="calculator">15 * 8</gadget>
<output>120</output>
<result>120</result>


a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scale ?

Explanation: first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c

add(multiply(subtract(24, 6), divide(subtract(100, 60), subtract(60, 30))), 24)

<gadget id="calculator">24 - 6</gadget>
<output>18</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">60 - 30</gadget>
<output>30</output>
<gadget id="calculator">40 / 30</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">18 * (4/3)</gadget>
<output>24</output>
<gadget id="calculator">24 + 24</gadget>
<output>48</output>
<result>48</result>


the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number .

Explanation: let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 .

divide(add(multiply(184, const_3), multiply(multiply(add(const_3, const_4), const_3), 8)), add(add(const_3, const_4), const_3))

<gadget id="calculator">184 * 3</gadget>
<output>552</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 * 8</gadget>
<output>168</output>
<gadget id="calculator">552 + 168</gadget>
<output>720</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">720 / 10</gadget>
<output>72</output>
<result>72</result>


the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ?

Explanation: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b"

multiply(divide(add(200, 102), const_2), add(divide(subtract(200, 102), const_2), const_1))

<gadget id="calculator">200 + 102</gadget>
<output>302</output>
<gadget id="calculator">302 / 2</gadget>
<output>151</output>
<gadget id="calculator">200 - 102</gadget>
<output>98</output>
<gadget id="calculator">98 / 2</gadget>
<output>49</output>
<gadget id="calculator">49 + 1</gadget>
<output>50</output>
<gadget id="calculator">151 * 50</gadget>
<output>7_550</output>
<result>7_550</result>


how many litres of pure acid are there in 15 litres of a 20 % solution

Explanation: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 15 * 20 / 100 = 3 answer : option d

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 15</gadget>
<output>3</output>
<result>3</result>


rs . 385 were divided among x , y , z in such a way that x had rs . 20 more than y and z had rs 15 more than x . how much was y ’ s share ?

Explanation: let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r ’ s share = rs ( 110 + 35 ) = rs . 145 b

<gadget id="calculator">20 + 20</gadget>
<output>40</output>
<gadget id="calculator">15 + 40</gadget>
<output>55</output>
<gadget id="calculator">385 - 55</gadget>
<output>330</output>
<gadget id="calculator">330 / 3</gadget>
<output>110</output>
<gadget id="calculator">110 + 20</gadget>
<output>130</output>
<gadget id="calculator">15 + 130</gadget>
<output>145</output>
<result>145</result>


when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16

Explanation: case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a

floor(divide(add(add(const_12, const_3), add(const_2, const_4)), 16))

<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">15 + 6</gadget>
<output>21</output>
<gadget id="calculator">21 / 16</gadget>
<output>21/16 = around 1.3125</output>
<gadget id="calculator">floor(21/16)</gadget>
<output>1</output>
<result>1</result>


a group of men decided to do a work in 20 days , but 8 of them became absent . if the rest of the group did the work in 28 days , find the original number of men ?

Explanation: "original number of men = 8 * 28 / ( 28 - 20 ) = 28 answer is b"

divide(multiply(8, 28), subtract(28, 20))

<gadget id="calculator">8 * 28</gadget>
<output>224</output>
<gadget id="calculator">28 - 20</gadget>
<output>8</output>
<gadget id="calculator">224 / 8</gadget>
<output>28</output>
<result>28</result>


three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ?

Explanation: "280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) ."

divide(subtract(subtract(280, 180), 36), const_2)

<gadget id="calculator">280 - 180</gadget>
<output>100</output>
<gadget id="calculator">100 - 36</gadget>
<output>64</output>
<gadget id="calculator">64 / 2</gadget>
<output>32</output>
<result>32</result>


mr . x , a mathematician , defines a number as ' connected with 6 if it is divisible by 6 or if the sum of its digits is 6 , or if 6 is one of the digits of the number . other numbers are all ' not connected with 6 ' . as per this definition , the number of integers from 1 to 60 ( both inclusive ) which are not connected with 6 is

Explanation: explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such uncommon numbers . numbers from 1 to 60 , which have 6 as one of the digits are 6 , 16 , 26 , 36 , 46 , 56 , 60 . clearly , there are 4 such uncommon numbers . so , numbers ' not connected with 6 ' = 60 - ( 10 + 3 + 4 ) = 43 . answer : d

subtract(60, add(add(const_10, const_3), const_4))

<gadget id="calculator">10 + 3</gadget>
<output>13</output>
<gadget id="calculator">13 + 4</gadget>
<output>17</output>
<gadget id="calculator">60 - 17</gadget>
<output>43</output>
<result>43</result>


a camera lens filter kit containing 5 filters sells for $ 67.50 . if the filters are purchased individually , 2 of them are priced at $ 7.45 each , 2 at $ 10.05 each , 1 at $ 14.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?

Explanation: "cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b ."

<gadget id="calculator">2 * 7.45</gadget>
<output>14.9</output>
<gadget id="calculator">2 * 10.05</gadget>
<output>20.1</output>
<gadget id="calculator">14.9 + 20.1</gadget>
<output>35</output>
<gadget id="calculator">14.5 + 35</gadget>
<output>49.5</output>
<gadget id="calculator">67.5 - 49.5</gadget>
<output>18</output>
<gadget id="calculator">18 * 100</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 67.5</gadget>
<output>26.666667</output>
<result>26.666667</result>


if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ? .

Explanation: 20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d

add(add(add(divide(20, 2), divide(20, power(2, const_2))), floor(divide(20, power(power(2, const_2), 2)))), floor(divide(20, power(2, const_3))))

<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">20 / 16</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">floor(5/4)</gadget>
<output>1</output>
<gadget id="calculator">15 + 1</gadget>
<output>16</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">floor(5/2)</gadget>
<output>2</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<result>18</result>


a man performs 1 / 2 of the total journey by rail , 1 / 4 by bus and the remaining 4 km on foot . his total journey is

Explanation: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b"

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


what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?

Explanation: "explanation : since every third number starting from 10 will be divisible by 3 , so total number of numbers divisible by 3 are 90 / 3 = 30 numbers which are divisible by 3 and 5 both are numbers which are multiple of 15 . for the range 10 to 99 , 15 is the first number divisible by 15 and 90 is the last number . so total number of numbers divisible by 15 are : ( 90 - 15 ) / 15 + 1 = 5 + 1 = 6 number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6 . so number of numbers divisible by 3 and not by 5 are : 30 - 6 = 24 so total probability = 24 / 90 = 4 / 15 answer : c"

divide(subtract(multiply(multiply(5, const_2), 3), multiply(3, const_2)), multiply(multiply(5, const_2), multiply(3, 3)))

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">30 - 6</gadget>
<output>24</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">10 * 9</gadget>
<output>90</output>
<gadget id="calculator">24 / 90</gadget>
<output>4/15 = around 0.266667</output>
<result>4/15 = around 0.266667</result>


bhanu spends 30 % of his income on petrol on scooter 21 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?

Explanation: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 21 % ( 700 ) = rs . 147 answer : e"

multiply(subtract(divide(300, divide(30, const_100)), 300), divide(21, const_100))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">300 / (3/10)</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 300</gadget>
<output>700</output>
<gadget id="calculator">21 / 100</gadget>
<output>21/100 = around 0.21</output>
<gadget id="calculator">700 * (21/100)</gadget>
<output>147</output>
<result>147</result>


one - third less than 25 % of 180 is equal to :

Explanation: "lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b"

subtract(multiply(divide(25, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(25, const_100), 180)))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 180</gadget>
<output>45</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 45</gadget>
<output>15</output>
<gadget id="calculator">45 - 15</gadget>
<output>30</output>
<result>30</result>


in arun ’ s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun ’ s weight is greater than 60 kg but less than 70 kg . his mother ’ s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what is the average of different probable weights of arun ?

Explanation: explanation : let arun ’ s weight by x kg . according to arun , 65 < x < 72 according to arun ’ s brother , 60 < x < 70 . according to arun ’ s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b

divide(add(add(subtract(68, const_1), subtract(subtract(68, const_1), const_1)), 68), const_3)

<gadget id="calculator">68 - 1</gadget>
<output>67</output>
<gadget id="calculator">67 - 1</gadget>
<output>66</output>
<gadget id="calculator">67 + 66</gadget>
<output>133</output>
<gadget id="calculator">133 + 68</gadget>
<output>201</output>
<gadget id="calculator">201 / 3</gadget>
<output>67</output>
<result>67</result>


there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?

Explanation: approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e

<gadget id="calculator">binomial(8, 4)</gadget>
<output>70</output>
<gadget id="calculator">binomial(5, 4)</gadget>
<output>5</output>
<gadget id="calculator">70 - 5</gadget>
<output>65</output>
<result>65</result>


rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 500 . then his monthly salary is

Explanation: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 500 â ‡ ” 20 / 100 x = 500 â ‡ ” x = 500 ã — 5 = 2500 . answer a"

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">500 * 5</gadget>
<output>2_500</output>
<result>2_500</result>


robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert borrowed rs . 7280 / - from company . but robert forget that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the incentive amount given to robert ?

Explanation: "total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c"

<gadget id="calculator">18_500 - 7_280</gadget>
<output>11_220</output>
<result>11_220</result>


the food in a camp lasts for 40 men for 20 days . if 10 more men join , how many days will the food last ?

Explanation: one man can consume the same food in 40 * 20 = 800 days . 10 more men join , the total number of men = 50 the number of days the food will last = 800 / 50 = 16 days . answer : d

<gadget id="calculator">40 * 20</gadget>
<output>800</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">800 / 50</gadget>
<output>16</output>
<result>16</result>


a trader bought a car at 30 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 70 s = 70 * ( 150 / 100 ) = 105 100 - 105 = 5 % answer : e"

multiply(subtract(divide(divide(multiply(subtract(const_100, 30), add(const_100, 50)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">70 * 150</gadget>
<output>10_500</output>
<gadget id="calculator">10_500 / 100</gadget>
<output>105</output>
<gadget id="calculator">105 / 100</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) - 1</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>5</result>


in a weight - lifting competition , the total weight of joe ' s two lifts was 450 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?

Explanation: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 450 pounds . we sum the two variables to obtain : f + s = 450 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 450 3 f = 750 f = 250 answer is a ."

<gadget id="calculator">450 + 300</gadget>
<output>750</output>
<gadget id="calculator">750 / 3</gadget>
<output>250</output>
<result>250</result>


a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 108 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

Explanation: "the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 108 books , thus the number of un - returned books is 150 - 108 = 42 books . 0.35 x = 42 x = 120 the answer is e ."

divide(subtract(150, 108), subtract(const_1, divide(65, const_100)))

<gadget id="calculator">150 - 108</gadget>
<output>42</output>
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">1 - (13/20)</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">42 / (7/20)</gadget>
<output>120</output>
<result>120</result>


ramu rides his bike at an average speed of 45 km / hr and reaches his desitination in 4 hours . somu covers the same distance in 6 hours . if ramu covered his journey at an average speed which was 9 km / hr less and somu covered his journey at an average speed which was 10 km / hr more , then the difference in their times taken to reach the destination would be ( in minutes ) .

Explanation: distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b

multiply(subtract(divide(multiply(45, 4), subtract(45, 9)), divide(multiply(45, 4), add(divide(multiply(45, 4), 6), 10))), const_60)

<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">180 / 36</gadget>
<output>5</output>
<gadget id="calculator">180 / 6</gadget>
<output>30</output>
<gadget id="calculator">30 + 10</gadget>
<output>40</output>
<gadget id="calculator">180 / 40</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">5 - (9/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 60</gadget>
<output>30</output>
<result>30</result>


elena purchased brand x pens for $ 5.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?

Explanation: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c ."

<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<gadget id="calculator">48 - 42</gadget>
<output>6</output>
<result>6</result>


in order to fence a square manish fixed 48 poles . if the distance between two poles , is 2 metres then what will be the area of the square so formed ?

Explanation: let the side of the square be x m . ∴ perimeter of the square = 48 × 2 = 4 x ∴ x = 24 m ∴ area = ( 24 ) 2 = 576 m 2 answer d

<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<gadget id="calculator">24 ** 2</gadget>
<output>576</output>
<result>576</result>


find the area of a parallelogram with base 20 cm and height 10 cm ?

Explanation: area of a parallelogram = base * height = 20 * 10 = 200 cm 2 answer : e

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


a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 84 liters of drink a to convert it to drink b ?

Explanation: "in 84 liters of drink a , there are 48 liters of milk and 36 liters of juice . with 48 liters of milk , we need a total of 64 liters of juice to make drink b . we need to add 28 liters of juice . the answer is b ."

subtract(divide(multiply(multiply(divide(4, add(4, 3)), 84), 4), 3), multiply(divide(3, add(4, 3)), 84))

<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">(4/7) * 84</gadget>
<output>48</output>
<gadget id="calculator">48 * 4</gadget>
<output>192</output>
<gadget id="calculator">192 / 3</gadget>
<output>64</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(3/7) * 84</gadget>
<output>36</output>
<gadget id="calculator">64 - 36</gadget>
<output>28</output>
<result>28</result>


in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ?

Explanation: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b"

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


in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is

Explanation: "sol . let the number of grils be x . then , number of boys = ( 620 - x ) . then , ( 11 3 / 4 × 620 ) ⇔ 11 x + 12 ( 620 - x ) ⇔ x = 7440 - 7285 ⇔ 155 . answer c"

subtract(multiply(12, 620), multiply(add(11, divide(9, 12)), 620))

<gadget id="calculator">12 * 620</gadget>
<output>7_440</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">11 + (3/4)</gadget>
<output>47/4 = around 11.75</output>
<gadget id="calculator">(47/4) * 620</gadget>
<output>7_285</output>
<gadget id="calculator">7_440 - 7_285</gadget>
<output>155</output>
<result>155</result>


two trains are moving in opposite directions with speed of 60 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds

Explanation: "relative speed = 60 + 90 = 150 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 150 hr = 1 / / 75 hr = 3600 / 75 seconds = 1200 / 25 = 240 / 5 = 48 seconds answer is e ."

<gadget id="calculator">1.1 + 0.9</gadget>
<output>2</output>
<gadget id="calculator">60 + 90</gadget>
<output>150</output>
<gadget id="calculator">2 / 150</gadget>
<output>1/75 = around 0.013333</output>
<gadget id="calculator">(1/75) * 3_600</gadget>
<output>48</output>
<result>48</result>


the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 14 km / hr respectively . they will meet for the first time in ?

Explanation: clearly , the two will meet when they are 1000 m apart to be 20 + 14 = 34 km apart , they take 1 hour to be 1000 m apart , they take 34 * 1000 / 1000 = 34 min . answer is c

<gadget id="calculator">20 + 14</gadget>
<output>34</output>
<result>34</result>


the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 90 and rs . 80 respectively . the sum is :

Explanation: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 90 * 80 / ( 90 - 80 ) = rs . 720 . answer c"

divide(multiply(90, 80), subtract(90, 80))

<gadget id="calculator">90 * 80</gadget>
<output>7_200</output>
<gadget id="calculator">90 - 80</gadget>
<output>10</output>
<gadget id="calculator">7_200 / 10</gadget>
<output>720</output>
<result>720</result>


if shreehari walks in the speed of 4.5 km / hr from his house , in what time will he reach his school which is 750 m long from his house ?

Explanation: speed = 4.5 * 5 / 18 = 1.25 m / sec time taken = 750 / 1.25 = 600 sec ie . 10 mins . answer : c

multiply(divide(divide(750, const_1000), 4.5), const_60)

<gadget id="calculator">750 / 1_000</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) / 4.5</gadget>
<output>0.166667</output>
<gadget id="calculator">0.166667 * 60</gadget>
<output>10.00002</output>
<result>10.00002</result>


if x is a number such that x ^ 2 + 2 x - 24 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =

Explanation: x ^ 2 + 2 x - 24 = ( x + 6 ) ( x - 4 ) = 0 then x = - 6 or x = 4 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 4 . the answer is a .

<gadget id="calculator">4 + 24</gadget>
<output>28</output>
<gadget id="calculator">2 + 5</gadget>
<output>7</output>
<gadget id="calculator">28 / 7</gadget>
<output>4</output>
<result>4</result>


a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is

Explanation: sol . since the month begins with a sunday , so there will be five sundays in the month . ∴ required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d

divide(add(multiply(add(const_4, const_1), 510), multiply(multiply(add(const_4, const_1), add(const_4, const_1)), 240)), 30)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 510</gadget>
<output>2_550</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 240</gadget>
<output>6_000</output>
<gadget id="calculator">2_550 + 6_000</gadget>
<output>8_550</output>
<gadget id="calculator">8_550 / 30</gadget>
<output>285</output>
<result>285</result>


a horse chases a pony 8 hours after the pony runs . horse takes 12 hours to reach the pony . if the average speed of the horse is 320 kmph , what s the average speed of the pony ?

Explanation: pony take 20 hours and horse take 12 hours . . . then distance chased by them is 320 * 12 . so speed of pony is ( 320 * 12 ) / 20 = 192 kmph . answer is b

<gadget id="calculator">12 * 320</gadget>
<output>3_840</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">3_840 / 20</gadget>
<output>192</output>
<result>192</result>


a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 10 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?

Explanation: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.10 x = 50 x = 39.52 hence , the correct option is a"

divide(50, add(divide(add(10, 15), const_100), const_1))

<gadget id="calculator">10 + 15</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">50 / (5/4)</gadget>
<output>40</output>
<result>40</result>


what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150 ?

Explanation: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 150 / 2 = 75 answer is d"

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


a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?

Explanation: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 15 ) / ( 15 - 0 ) = 3 / 1 1 / x = 3 / 1 x = 1 / 3 answer : b"

<gadget id="calculator">60 - 15</gadget>
<output>45</output>
<gadget id="calculator">15 / 45</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


a certain car uses one gallon of gasoline every 32 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?

Explanation: "4 miles on the highway = 4 / 32 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 32 + 4 / 20 = 13 / 40 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 13 / 40 - 8 / 32 ) / ( 8 / 32 ) = 0.30 . answer : e ."

multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 32))), multiply(8, divide(const_1, 32))), multiply(8, divide(const_1, 32))), const_100)

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 4</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 32</gadget>
<output>1/32 = around 0.03125</output>
<gadget id="calculator">4 * (1/32)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/5) + (1/8)</gadget>
<output>13/40 = around 0.325</output>
<gadget id="calculator">8 * (1/32)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(13/40) - (1/4)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(3/40) / (1/4)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>


a retailer sold an appliance for $ 100 . if the retailer ' s gross profit on the appliance was 25 percent of the retailer ' s cost for the appliance , how many dollars was the retailer ' s gross profit ?

Explanation: let p be the original price paid by the retailer . 1.25 * p = 100 p = 80 the profit is $ 20 . the answer is c .

subtract(100, multiply(divide(const_1, add(divide(25, 100), const_1)), 100))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1 / (5/4)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<result>20</result>


24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?

Explanation: easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to t ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice t will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice t = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice v = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d

subtract(24, divide(subtract(multiply(4, 25), 24), subtract(multiply(4, 5), 1)))

<gadget id="calculator">4 * 25</gadget>
<output>100</output>
<gadget id="calculator">100 - 24</gadget>
<output>76</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">76 / 19</gadget>
<output>4</output>
<gadget id="calculator">24 - 4</gadget>
<output>20</output>
<result>20</result>


if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 15 percent of the test takers answered neither question correctly , what percent answered both correctly ?

Explanation: { total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 75 - { both correctly } + 15 { both correctly } = 75 . answer : d .

subtract(add(add(85, 75), 15), const_100)

<gadget id="calculator">85 + 75</gadget>
<output>160</output>
<gadget id="calculator">160 + 15</gadget>
<output>175</output>
<gadget id="calculator">175 - 100</gadget>
<output>75</output>
<result>75</result>


find the least number of complete years in which a sum of money put out at 25 % compound interest will be more than double of itself ?

Explanation: "4 years answer : d"

floor(add(divide(log(const_2), log(add(const_1, divide(25, const_100)))), const_1))

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<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">log(5/4)</gadget>
<output>log(5/4) = around 0.223144</output>
<gadget id="calculator">log(2) / log(5/4)</gadget>
<output>log(2)/log(5/4) = around 3.106284</output>
<gadget id="calculator">(log(2)/log(5/4)) + 1</gadget>
<output>1 + log(2)/log(5/4) = around 4.106284</output>
<gadget id="calculator">floor(1 + log(2)/log(5/4))</gadget>
<output>4</output>
<result>4</result>


mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 24 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?

Explanation: "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : c"

<gadget id="calculator">24 + 22</gadget>
<output>46</output>
<gadget id="calculator">46 + 5</gadget>
<output>51</output>
<gadget id="calculator">51 - 29</gadget>
<output>22</output>
<result>22</result>


7 m - 20 = 2 m , then m + 7 is equal to ?

Explanation: 7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c

<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">4 + 7</gadget>
<output>11</output>
<result>11</result>


the smallest value of n , for which 2 n + 1 is not a prime number is

Explanation: "sol . = ( 2 × 1 + 1 ) = 3 , = ( 2 × 3 + 1 ) = 7 , = ( 2 × 4 + 1 ) = 9 , which is not prime . therefore n = 4 . answer b"

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


two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ?

Explanation: two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a

<gadget id="calculator">100 / 500</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 1 / 4 of the way by bus , and the remaining 5 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?

Explanation: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 5 x - 1 / 2 x - 3 / 5 x = 5 x = 12 km option : e"

multiply(5, inverse(subtract(1, add(divide(1, 3), divide(1, 4)))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) + (1/4)</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">1 - (7/12)</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">1 / (5/12)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">5 * (12/5)</gadget>
<output>12</output>
<result>12</result>


tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 10 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?

Explanation: ( 1 mph + 10 mph ) / 2 = 5.5 mph correct option is : b

<gadget id="calculator">1 + 10</gadget>
<output>11</output>
<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>
<result>11/2 = around 5.5</result>


j is 25 % less than p and 20 % less than t . t is x % less than p . what is the value of x ?

Explanation: "let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d"

<gadget id="calculator">25 * 25</gadget>
<output>625</output>
<gadget id="calculator">625 / 100</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>


denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination .

Explanation: when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 39263999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well . we ' ll get 3925 / 4000 = 157 / 160 . answer : c .

<gadget id="calculator">4_000 - 75</gadget>
<output>3_925</output>
<gadget id="calculator">3_925 / 4_000</gadget>
<output>157/160 = around 0.98125</output>
<result>157/160 = around 0.98125</result>


in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]

Explanation: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d"

multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">8 / (1/2)</gadget>
<output>16</output>
<gadget id="calculator">16 / 12</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">0.33 * 100</gadget>
<output>33</output>
<gadget id="calculator">(4/3) * 33</gadget>
<output>44</output>
<result>44</result>


two spheres of their radios in the ratio 4 : 3 . find its volumes ratio ?

Explanation: sphere volume ( v ) = 4 / 3 π r ( power 3 ) : 4 / 3 π r ( power 3 ) = 4 ( power 3 ) : 3 ( power 3 ) = 64 : 27 answer is d .

<gadget id="calculator">4/3 * pi * (4 ** 3)</gadget>
<output>256*pi/3 = around 268.082573</output>
<gadget id="calculator">4/3 * pi * (3 ** 3)</gadget>
<output>36*pi = around 113.097336</output>
<gadget id="calculator">(256*pi/3) / (36*pi)</gadget>
<output>64/27 = around 2.37037</output>
<result>64/27 = around 2.37037</result>


danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ?

Explanation: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer"

divide(power(multiply(const_3, power(1536, const_2)), divide(const_1, const_3)), 1.5)

<gadget id="calculator">1_536 ** 2</gadget>
<output>2_359_296</output>
<gadget id="calculator">3 * 2_359_296</gadget>
<output>7_077_888</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">7_077_888 ** (1/3)</gadget>
<output>192</output>
<gadget id="calculator">192 / 1.5</gadget>
<output>128</output>
<result>128</result>


sum of the squares of 3 no . is 276 and the sum of their products taken two at a time is 150 . find the sum ?

Explanation: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = â ˆ š 576 = 24 answer d"

<gadget id="calculator">150 * 2</gadget>
<output>300</output>
<gadget id="calculator">276 + 300</gadget>
<output>576</output>
<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<result>24</result>


zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 14 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 14 questions did zachary answer correctly ?

Explanation: i got two equations : 3 x - 2 y = 25 x + y = 14 3 x - 2 ( 14 - x ) = 25 3 x - 28 + 2 x = 25 5 x = 53 x = 10.6 or between 10 and 11 . ( ans e )

divide(add(subtract(multiply(2, subtract(14, 2)), multiply(3, 2)), 31), add(3, 2))

<gadget id="calculator">14 - 2</gadget>
<output>12</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">24 - 6</gadget>
<output>18</output>
<gadget id="calculator">18 + 31</gadget>
<output>49</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">49 / 5</gadget>
<output>49/5 = around 9.8</output>
<result>49/5 = around 9.8</result>