a certain high school has 500 students . of these students , 50 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?

Explanation: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 50 y = 20 z = 10 so , we have 50 students taking music , 20 taking art and 10 taking both music and art . 40 student taking just music 10 student taking just art 10 student taking both music and art total = 60 students we ' re asked for the total number of students who are taking neither course . that is 500 - 60 = 440 . b"

subtract(500, subtract(add(50, 20), 10))

<gadget id="calculator">50 + 20</gadget>
<output>70</output>
<gadget id="calculator">70 - 10</gadget>
<output>60</output>
<gadget id="calculator">500 - 60</gadget>
<output>440</output>
<result>440</result>


praveen starts business with rs . 3920 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?

Explanation: "let hari ’ s capital be rs . x . then , 3920 * 12 / 7 x = 2 / 3 = > 14 x = 141120 = > x = 10080 . answer : a"

divide(divide(3920, subtract(const_1, divide(5, const_12))), divide(2, 3))

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">1 - (5/12)</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">3_920 / (7/12)</gadget>
<output>6_720</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">6_720 / (2/3)</gadget>
<output>10_080</output>
<result>10_080</result>


a woman can do a piece of work in 40 days . man is 25 % more efficient than woman . in how many days a man can do the same piece of work ?

Explanation: the ratio of the efficiencies of a woman and man = 100 : 125 = 4 : 5 the ratio of the days taken by woman and man to finish the work = 5 : 4 woman takes 32 days to finish the work . = > 5 parts = 40 the number of days taken by man to finish the work = 4 parts = 40 / 5 x 4 = 32 days a

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

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">40 / 125</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<result>32</result>


the ratio between the present ages of a and b is 3.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?

Explanation: "let the present ages of a and b be 3.5 x and 3 x years respectively . then , ( 3.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 0.5 x = 8 = > x = 16 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 60 : 44 = 15 : 11 . answer : c"

divide(add(multiply(3.5, divide(add(3.5, 3.5), subtract(3.5, 3))), 3.5), subtract(multiply(3, divide(add(3.5, 3.5), subtract(3.5, 3))), 3.5))

<gadget id="calculator">3.5 + 3.5</gadget>
<output>7</output>
<gadget id="calculator">3.5 - 3</gadget>
<output>0.5</output>
<gadget id="calculator">7 / 0.5</gadget>
<output>14</output>
<gadget id="calculator">3.5 * 14</gadget>
<output>49</output>
<gadget id="calculator">49 + 3.5</gadget>
<output>52.5</output>
<gadget id="calculator">3 * 14</gadget>
<output>42</output>
<gadget id="calculator">42 - 3.5</gadget>
<output>38.5</output>
<gadget id="calculator">52.5 / 38.5</gadget>
<output>1.363636</output>
<result>1.363636</result>


ram , who is half as efficient as krish , will take 21 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?

Explanation: "number of days taken by ram to complete task = 21 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 24 days is 21 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 21 w / 3 w = 7 days answer d"

inverse(add(divide(const_1, 21), divide(const_1, divide(21, const_2))))

<gadget id="calculator">1 / 21</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">21 / 2</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">1 / (21/2)</gadget>
<output>2/21 = around 0.095238</output>
<gadget id="calculator">(1/21) + (2/21)</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / (1/7)</gadget>
<output>7</output>
<result>7</result>


Explanation: required l . c . m = l . c . m . of 7 , 8 , 3 , 5 / h . c . f . of 10 , 9 , 8 , 12 = 840 / 1 = 840 answer is a

multiply(multiply(7, 8), multiply(3, 5))

<gadget id="calculator">7 * 8</gadget>
<output>56</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">56 * 15</gadget>
<output>840</output>
<result>840</result>


a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?

Explanation: so we are looking for the area of the cloth over the area of the table area of the cloth = ( pi ) ( r ) ^ 2 which is about ( 3 ) ( 9 ) ( 9 ) area of the table = ( 24 ) ( 24 ) so the quick way to estimate is looking at the fraction like this : ( 3 / 24 ) ( 81 / 24 ) i hope this is easy to follow , so with some simplification i get ( 1 / 8 ) ( 3 ) = ( 3 / 8 ) answer is d

<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 24</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>


a man swims downstream 36 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?

Explanation: "36 - - - 3 ds = 12 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 12 + 6 ) / 2 = 9 answer : c"

divide(add(divide(18, 3), divide(36, 3)), const_2)

<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">36 / 3</gadget>
<output>12</output>
<gadget id="calculator">6 + 12</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>9</result>


the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is ?

Explanation: "cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : d"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">109.25 - (1/4)</gadget>
<output>109</output>
<result>109</result>


the price of maruti car rises by 30 percent while the sales of the car come down by 20 % . what is the percentage change in the total revenue ?

Explanation: solution : let initial price of maruti car be rs . 100 . as price increases 30 % , price of car will become , ( 100 + 30 % of 100 ) = rs . 130 . due to increase in price , sales is down by 20 % . it means , it is going make 20 % less revenue as expected after increment of price . so , new revenue = ( 130 - 20 % of 130 ) = rs . 104 . the initial revenue was rs . 100 which becomes rs . 104 at the end . it means there is 4 % increment in the total revenue . mind calculation method : 100 = = 30 % ↑ ( price effect ) = = > 130 = = 20 % ↓ ( sales effects ) = = > 104 . hence , 4 % rises . answer : option c

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

<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">20 * 130</gadget>
<output>2_600</output>
<gadget id="calculator">2_600 / 100</gadget>
<output>26</output>
<gadget id="calculator">130 - 26</gadget>
<output>104</output>
<gadget id="calculator">104 - 100</gadget>
<output>4</output>
<result>4</result>


if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 21 ( q + 1 ) , what is the least possible value of p + q ?

Explanation: "17 ( p + 1 ) = 21 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 21 / 17 - - > the least positive value of p + 1 is 21 , so the least value of p is 20 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 20 + 16 = 36 . answer : a ."

<gadget id="calculator">21 + 17</gadget>
<output>38</output>
<gadget id="calculator">38 - 2</gadget>
<output>36</output>
<result>36</result>


the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?

Explanation: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 5 / 4 ) * 4 = 2 / 5 the answer is b ."

multiply(divide(subtract(const_100, 60), add(const_100, 25)), divide(5, 4))

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">40 / 125</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(8/25) * (5/4)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>


three rugs have a combined area of 212 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?

Explanation: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 212 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 24 . answer : c ."

divide(subtract(subtract(212, 140), 24), const_2)

<gadget id="calculator">212 - 140</gadget>
<output>72</output>
<gadget id="calculator">72 - 24</gadget>
<output>48</output>
<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<result>24</result>


when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?

Explanation: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus q = 11 / 14 of the remaining votes must be against . answer : a ."

divide(subtract(divide(2, add(1, 2)), subtract(divide(2, 9), multiply(divide(2, 9), divide(3, 4)))), divide(subtract(9, 2), 9))

<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(2/9) * (3/4)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(2/9) - (1/6)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(2/3) - (1/18)</gadget>
<output>11/18 = around 0.611111</output>
<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">7 / 9</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">(11/18) / (7/9)</gadget>
<output>11/14 = around 0.785714</output>
<result>11/14 = around 0.785714</result>


tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 12 even numbers . his mother immediately worked out the answer . how much had he scored in math ?

Explanation: "a 156 sum = ( n x n ) + n hence , 12 x 12 = 144 + 12 = 156"

<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">13 * 12</gadget>
<output>156</output>
<result>156</result>


during a certain season , a team won 70 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?

Explanation: "we are first given that a team won 70 percent of its first 100 games . this means the team won 0.7 x 100 = 70 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 70 + 0.5 t – 50 = 0.7 t 20 = 0.2 t 200 = 2 t 100 = t answer is e ."

add(100, divide(subtract(70, 70), subtract(divide(70, 100), divide(50, 100))))

<gadget id="calculator">70 - 70</gadget>
<output>0</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(7/10) - (1/2)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">0 / (1/5)</gadget>
<output>0</output>
<gadget id="calculator">100 + 0</gadget>
<output>100</output>
<result>100</result>


if x 2 + kx - 3 , is divisible by ( x - 1 ) , what is the value of k

Explanation: explanation : if x 2 + kx - 3 is divisible by ( x - 1 ) then x = 1 ( 1 ) 2 + 1 ( k ) - 3 = 0 1 + k - 3 = 0 k = 2 answer : option c

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


if ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 then what is the least value of x + y + z ? if x , y , z are all integer no .

Explanation: ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 put x = 0 y = - 5 z = 12 then ( 0 - 10 ) ( - 5 - 5 ) ( 12 - 2 ) = 1000 ( - 10 ) ( - 10 ) ( 10 ) = 1000 1000 = 1000 answer : a

subtract(divide(multiply(10, 5), 5), const_3)

<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<result>7</result>


a can run 4 times as fast as b and gives b a start of 60 m . how long should the race course be so that a and b might reach in the same time ?

Explanation: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 60 m he gains 60 * ( 4 / 3 ) i . e 80 m answer : c"

add(multiply(4, divide(divide(60, 4), subtract(4, const_1))), 60)

<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 + 60</gadget>
<output>80</output>
<result>80</result>


a train 175 m long , running with a speed of 63 km / hr will pass a tree in ?

Explanation: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 175 * 2 / 35 = 10 sec answer : e"

multiply(divide(175, multiply(63, const_1000)), const_3600)

<gadget id="calculator">63 * 1_000</gadget>
<output>63_000</output>
<gadget id="calculator">175 / 63_000</gadget>
<output>1/360 = around 0.002778</output>
<gadget id="calculator">(1/360) * 3_600</gadget>
<output>10</output>
<result>10</result>


an 80 - liter solution of cool - drink is made from 10 % jasmine water . if 8 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?

Explanation: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 80 ) + 8 ) / 100 = 16 / 100 = 16 % the answer is c ."

multiply(divide(add(multiply(80, divide(10, const_100)), 8), const_100), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">80 * (1/10)</gadget>
<output>8</output>
<gadget id="calculator">8 + 8</gadget>
<output>16</output>
<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) * 100</gadget>
<output>16</output>
<result>16</result>


the length of rectangle is thrice its breadth and its perimeter is 120 m , find the area of the rectangle ?

Explanation: "2 ( 3 x + x ) = 120 l = 45 b = 15 lb = 45 * 15 = 675 answer : e"

multiply(multiply(divide(120, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(120, add(multiply(const_3, const_2), multiply(const_1, const_2))))

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">120 / 8</gadget>
<output>15</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 * 15</gadget>
<output>675</output>
<result>675</result>


at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?

Explanation: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 44.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 31 . in any case , there is no necessity to know each item ' s price , just the sum . answer : c"

<gadget id="calculator">164.5 - 120</gadget>
<output>44.5</output>
<gadget id="calculator">120 + 44.5</gadget>
<output>164.5</output>
<gadget id="calculator">44.5 * 3</gadget>
<output>133.5</output>
<gadget id="calculator">164.5 - 133.5</gadget>
<output>31</output>
<result>31</result>


65 % of x = 20 % of 682.50 . find the value of x ?

Explanation: "65 % of x = 20 % of 682.50 then , 65 / 100 * x = 20 / 100 * 6825 / 10 x = 210 answer is b"

divide(multiply(multiply(divide(682.50, const_100), 20), const_100), 65)

<gadget id="calculator">682.5 / 100</gadget>
<output>6.825</output>
<gadget id="calculator">6.825 * 20</gadget>
<output>136.5</output>
<gadget id="calculator">136.5 * 100</gadget>
<output>13_650</output>
<gadget id="calculator">13_650 / 65</gadget>
<output>210</output>
<result>210</result>


a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?

Explanation: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 120 kilometers ? 120 ÷ 40 = 3 × 1 gallon = 3 gallons correct answer d"

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


a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?

Explanation: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 4 = 25 . the minimum number of horses and ponies is 46 . the answer is d ."

add(add(lcm(7, multiply(divide(7, 2), 3)), 4), lcm(7, multiply(divide(7, 2), 3)))

<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) * 3</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">lcm(7, 21/2)</gadget>
<output>21</output>
<gadget id="calculator">21 + 4</gadget>
<output>25</output>
<gadget id="calculator">25 + 21</gadget>
<output>46</output>
<result>46</result>


on the first day of her vacation , louisa traveled 160 miles . on the second day , traveling at the same average speed , she traveled 280 miles . if the 160 - mile trip took 3 hours less than the 280 - mile trip , what was the average speed , in miles per hour ?

Explanation: ( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 160 / t = 280 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 160 / 4 = 40 answer : a

<gadget id="calculator">280 - 160</gadget>
<output>120</output>
<gadget id="calculator">120 / 3</gadget>
<output>40</output>
<result>40</result>


Explanation: "according to order of operations , inner brackets first . hence | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 5 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 5 + 72 | - | 5 - 11 | = | 77 | - | - 6 | = 77 - 6 = 71 correct answer d ) 71"

subtract(subtract(5, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))

<gadget id="calculator">3 - 12</gadget>
<output>-9</output>
<gadget id="calculator">8 * (-9)</gadget>
<output>-72</output>
<gadget id="calculator">5 - (-72)</gadget>
<output>77</output>
<gadget id="calculator">5 - 11</gadget>
<output>-6</output>
<gadget id="calculator">-(-6)</gadget>
<output>6</output>
<gadget id="calculator">77 - 6</gadget>
<output>71</output>
<result>71</result>


a 10 % stock yielding 8 % is quoted at ?

Explanation: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 10 , money invested = 100 × 10 / 8 = rs . 125 ie , market value of the stock = rs . 125 answer is a ."

<gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 10</gadget>
<output>125</output>
<result>125</result>


if a trader sold two cars each at rs . 325475 and gains 12 % on the first and loses 12 % on the second , then his profit or loss percent on the whole is ?

Explanation: sp of each car is rs . 325475 , he gains 12 % on first car and losses 12 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 12 ) ( 12 ) / 100 % = 1.44 % answer : a

<gadget id="calculator">12 * 12</gadget>
<output>144</output>
<gadget id="calculator">144 / 100</gadget>
<output>36/25 = around 1.44</output>
<result>36/25 = around 1.44</result>


i flew my tiny seaplane to visit my mother . on the flight up , i flew at 96 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?

Explanation: "( 96 mph + 88 mph ) / 2 = 92 mph correct answer is : c"

<gadget id="calculator">96 + 88</gadget>
<output>184</output>
<gadget id="calculator">184 / 2</gadget>
<output>92</output>
<result>92</result>


find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 20 cm ?

Explanation: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 20 ) = 380 cm 2 answer : b"

<gadget id="calculator">(20 + 18) * 20 / 2</gadget>
<output>380</output>
<result>380</result>


if x < y < z and y - x > 11 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?

Explanation: "we have : 1 ) x < y < z 2 ) y - x > 11 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 11 , the least value for y - x must be 13 , the least value for x must be 2 , and , thus , the least possible value for y must be 15 ( y - 2 = 13 , y = 15 ) 2 < 15 < z , since z is odd , the least possible value for z is 17 z - x = 17 - 2 = 15 answer e"

<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<gadget id="calculator">13 + 2</gadget>
<output>15</output>
<result>15</result>


Explanation: "since 24 / k = 4 and 24 / 6 = 4 , then k = 6 correct answer a"

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


a merchandise feedback online portal accords ‘ ratings ’ to a product by recording the percentage of customers who have reported their views as either ‘ satisfied ’ or ‘ unsatisfied ’ only . the portal rounds off the exact percentage value calculated to the closest integral value . if the percentage of unsatisfied customers as recorded by the portal is 57 % , what is the least possible number of people that could have reported their views as ‘ satisfied ’ ?

Explanation: 57 % unsatisfied . so ~ 43 % satisfied but 100 % should be an integer only and since the above percentages are approximations 100 % should be as close as possible to an integer . now substitute value [ 1 ] if 43 % is 2 what is 100 % - > 200 / 43 is not giving a number which is closest to an integer . [ 2 ] if 43 % is 3 what is 100 % - > 300 / 43 [ 43 * 7 = 301 ] . . . therefore closest possible to an integer . [ it also satisfies the least possible and hence we need not check for other choices which are greater than 3 ] therefore ans is b .

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


a bag consists of 30 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?

Explanation: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 30 - 5 - 9 = 16 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 30 + 16 / 30 = 25 / 30 = 5 / 6 hence , answer will be a ."

divide(add(subtract(30, add(5, 9)), 9), 30)

<gadget id="calculator">5 + 9</gadget>
<output>14</output>
<gadget id="calculator">30 - 14</gadget>
<output>16</output>
<gadget id="calculator">16 + 9</gadget>
<output>25</output>
<gadget id="calculator">25 / 30</gadget>
<output>5/6 = around 0.833333</output>
<result>5/6 = around 0.833333</result>


a present value of a machine is $ 1000 . its value depletiation rate is 10 % per annum then find the machine value after 2 years ?

Explanation: "p = $ 1000 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1000 * 9 / 10 * 9 / 10 = $ 810 answer is b"

multiply(1000, power(subtract(const_1, divide(10, const_100)), 2))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>
<gadget id="calculator">1_000 * (81/100)</gadget>
<output>810</output>
<result>810</result>


in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 48 . what is the total number of students in the school ?

Explanation: "let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 48 + 2 / 3 of 48 ( 80 / 100 ) x = 80 x = 100 . answer d"

divide(add(48, multiply(48, divide(2, 3))), subtract(const_1, divide(20, const_100)))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">48 * (2/3)</gadget>
<output>32</output>
<gadget id="calculator">48 + 32</gadget>
<output>80</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">80 / (4/5)</gadget>
<output>100</output>
<result>100</result>


a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 756 find the share of a .

Explanation: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 756 = 288 answer : c"

multiply(divide(756, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>
<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>
<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>
<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>
<gadget id="calculator">756 / 84_000</gadget>
<output>9/1_000 = around 0.009</output>
<gadget id="calculator">(9/1_000) * 32_000</gadget>
<output>288</output>
<result>288</result>


100 people are attending a newspaper conference . 35 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?

Explanation: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 35 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 35 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : b ."

subtract(100, add(add(38, const_1), 35))

<gadget id="calculator">38 + 1</gadget>
<output>39</output>
<gadget id="calculator">39 + 35</gadget>
<output>74</output>
<gadget id="calculator">100 - 74</gadget>
<output>26</output>
<result>26</result>


there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 78 . how tall is the fourth person ?

Explanation: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 78 ) = 312 x = 74 and the fourth person has a height of 74 + 10 = 84 inches the answer is b ."

add(divide(subtract(multiply(78, 4), add(6, add(4, 6))), 4), add(4, 6))

<gadget id="calculator">78 * 4</gadget>
<output>312</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">6 + 10</gadget>
<output>16</output>
<gadget id="calculator">312 - 16</gadget>
<output>296</output>
<gadget id="calculator">296 / 4</gadget>
<output>74</output>
<gadget id="calculator">74 + 10</gadget>
<output>84</output>
<result>84</result>


if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability w that this product will be a multiple of 45 ?

Explanation: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability w = 1 / 24 . answer c ."

<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<result>1/24 = around 0.041667</result>


during a pizza buffet where a eats more times 1.8 than b , and b eats 8 times less than c . find the leat number of times all the 3 has to eat

Explanation: a eats more than b if b eats 1 times than the ratio of a and b is a : b is 1.8 : 1 or 9 : 5 and as b eat 8 times less the c the the ratio of b : c is 5 : 40 the the least number of times all three has eat is the lcm of a , b , c that is 360 . . answer : c

multiply(multiply(divide(multiply(1.8, const_10), 3), divide(multiply(1.8, const_10), 3)), const_10)

<gadget id="calculator">1.8 * 10</gadget>
<output>18</output>
<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 * 10</gadget>
<output>360</output>
<result>360</result>


ashok secured average of 72 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?

Explanation: explanation : number of subjects = 6 average of marks in 6 subjects = 72 therefore total marks in 6 subjects = 72 * 6 = 432 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 432 – 370 = 62 answer a

subtract(multiply(72, 6), multiply(74, 5))

<gadget id="calculator">72 * 6</gadget>
<output>432</output>
<gadget id="calculator">74 * 5</gadget>
<output>370</output>
<gadget id="calculator">432 - 370</gadget>
<output>62</output>
<result>62</result>


at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 85 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?

Explanation: "withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 85 customers per day . 30 / 5 = 6 days . choice ( a ) . withthe formula , we can set up the following : 90 = ( 85 x + 120 ) / ( x + 1 ) 90 x + 90 = 85 x + 120 5 x = 30 x = 6 answer choice ( c )"

subtract(divide(subtract(120, 90), subtract(90, 85)), divide(subtract(120, const_100), const_100))

<gadget id="calculator">120 - 90</gadget>
<output>30</output>
<gadget id="calculator">90 - 85</gadget>
<output>5</output>
<gadget id="calculator">30 / 5</gadget>
<output>6</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">6 - (1/5)</gadget>
<output>29/5 = around 5.8</output>
<result>29/5 = around 5.8</result>


two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction . what time will they take to be 20 km apart ?

Explanation: "explanation : relative speed = 7.5 - 5.5 = 2 kmph ( because they walk in the same direction ) distance = 20 km time = distance / speed = 20 / 2 = 10 hr answer : a"

<gadget id="calculator">7.5 - 5.5</gadget>
<output>2</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>


a man can row 6 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

Explanation: "m = 6 s = 2 ds = 8 us = 4 x / 8 + x / 4 = 1 x = 2.66 d = 2.66 * 2 = 5.32 answer : a"

multiply(divide(multiply(add(6, 2), subtract(6, 2)), add(add(6, 2), subtract(6, 2))), const_2)

<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">32 / 12</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">(8/3) * 2</gadget>
<output>16/3 = around 5.333333</output>
<result>16/3 = around 5.333333</result>


if 8 workers can build 8 cars in 8 days , then how many days would it take 6 workers to build 6 cars ?

Explanation: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 6 workers can build 6 / 8 car per day . the time required to build 6 cars is 6 / ( 6 / 8 ) = 8 days the answer is d ."

multiply(divide(multiply(8, 8), 8), divide(6, 6))

<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 / 8</gadget>
<output>8</output>
<gadget id="calculator">6 / 6</gadget>
<output>1</output>
<gadget id="calculator">8 * 1</gadget>
<output>8</output>
<result>8</result>


a person can swim in still water at 12 km / h . if the speed of water 10 km / h , how many hours will the man take to swim back against the current for 8 km ?

Explanation: "m = 12 s = 10 us = 12 - 10 = 2 d = 8 t = 8 / 2 = 4 answer : a"

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


the moon revolves around the earth at a speed of approximately 0.2 kilometers per second . this approximate speed is how many kilometers per hour ?

Explanation: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.2 * 3600 = 720 kilometers per hour . option b is correct"

<gadget id="calculator">0.2 * 3_600</gadget>
<output>720</output>
<result>720</result>


if 1.5 cm of a pencil is purple , 0.5 cm of the remaining is black and the remaining 2 cm is blue , what is the total length of the pencil ?

Explanation: purple is 1.5 cm black is 0.5 cm blue is 2 cm 1.5 + 0.5 + 2 = 4 cm answer is d ) 4 cm

<gadget id="calculator">1.5 + 0.5</gadget>
<output>2</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<result>4</result>


of the 130 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?

Explanation: full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 30 answer : option b

<gadget id="calculator">130 - 80</gadget>
<output>50</output>
<gadget id="calculator">50 - 20</gadget>
<output>30</output>
<result>30</result>


what is the rate percent when the simple interest on rs . 810 amount to rs . 155 in 4 years ?

Explanation: "155 = ( 810 * 4 * r ) / 100 r = 4.78 % answer : a"

divide(multiply(const_100, 155), multiply(810, 4))

<gadget id="calculator">100 * 155</gadget>
<output>15_500</output>
<gadget id="calculator">810 * 4</gadget>
<output>3_240</output>
<gadget id="calculator">15_500 / 3_240</gadget>
<output>775/162 = around 4.783951</output>
<result>775/162 = around 4.783951</result>


a pharmaceutical company received $ 4 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?

Explanation: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 4 / 20 = 1 / 5 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 4 / 20 ) x 60 = 12 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 12 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 12 ) / 12 ] x 100 - 175 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 175 / 3 is just a bit less than ½ , we know that - 175 / 3 x 100 is about a 58 % decrease . answer e ."

multiply(divide(subtract(multiply(divide(4, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(4, 20), const_100)), const_100)

<gadget id="calculator">4 / 20</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">20 - (25/3)</gadget>
<output>35/3 = around 11.666667</output>
<gadget id="calculator">(35/3) / 20</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">(7/12) * 100</gadget>
<output>175/3 = around 58.333333</output>
<result>175/3 = around 58.333333</result>


a father said to his son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 52 years now , the son ' s age 5 years back was :

Explanation: let the son ' s present age be x years . then , ( 52 - x ) = x 2 x = 52 . x = 26 . son ' s age 5 years back ( 26 - 5 ) = 21 years . answer : d

<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<gadget id="calculator">26 - 5</gadget>
<output>21</output>
<result>21</result>


at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 20 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 20 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?

Explanation: "let number of apples = a number of oranges = b a + b = 20 - - - 1 . 56 = ( . 4 a + . 6 b ) / 20 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 16 let the number of oranges put back = c 52 * ( 20 - c ) = 40 * 4 + 60 ( 16 - c ) = > c = 10 answer e"

divide(subtract(multiply(56, 20), multiply(52, 20)), subtract(60, 52))

<gadget id="calculator">56 * 20</gadget>
<output>1_120</output>
<gadget id="calculator">52 * 20</gadget>
<output>1_040</output>
<gadget id="calculator">1_120 - 1_040</gadget>
<output>80</output>
<gadget id="calculator">60 - 52</gadget>
<output>8</output>
<gadget id="calculator">80 / 8</gadget>
<output>10</output>
<result>10</result>


there are 20 cm , 21 cm , 22 cm , 23 cm , 24 cm , 25 cm rods of quantities 23 , 64 , 32 respectively . find average of this data .

Explanation: average = ( 20 * 2 + 21 * 3 + 22 * 6 + 23 * 4 + 24 * 3 + 25 * 2 ) / 20 = 22.45 answer : d

divide(add(add(add(add(add(multiply(20, 23), multiply(21, 23)), multiply(22, 64)), multiply(23, 64)), multiply(24, 32)), multiply(25, 32)), multiply(add(add(23, 64), 32), const_2))

<gadget id="calculator">20 * 23</gadget>
<output>460</output>
<gadget id="calculator">21 * 23</gadget>
<output>483</output>
<gadget id="calculator">460 + 483</gadget>
<output>943</output>
<gadget id="calculator">22 * 64</gadget>
<output>1_408</output>
<gadget id="calculator">943 + 1_408</gadget>
<output>2_351</output>
<gadget id="calculator">23 * 64</gadget>
<output>1_472</output>
<gadget id="calculator">2_351 + 1_472</gadget>
<output>3_823</output>
<gadget id="calculator">24 * 32</gadget>
<output>768</output>
<gadget id="calculator">3_823 + 768</gadget>
<output>4_591</output>
<gadget id="calculator">25 * 32</gadget>
<output>800</output>
<gadget id="calculator">4_591 + 800</gadget>
<output>5_391</output>
<gadget id="calculator">23 + 64</gadget>
<output>87</output>
<gadget id="calculator">87 + 32</gadget>
<output>119</output>
<gadget id="calculator">119 * 2</gadget>
<output>238</output>
<gadget id="calculator">5_391 / 238</gadget>
<output>5_391/238 = around 22.651261</output>
<result>5_391/238 = around 22.651261</result>


a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together what part of the same work they can finish in a day ?

Explanation: 1 days work of a + b = ( 18 + 9 ) / 18 * 9 = 1 / 6 answer is c

add(divide(const_1, 18), divide(const_1, divide(18, const_2)))

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/18) + (1/9)</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


if n is a positive integer and n ^ 2 is divisible by 18 , then what is the largest positive integer that must divide n ?

Explanation: "18 = 2 * 3 ^ 2 if 18 divides n ^ 2 , then n must be divisible by 2 * 3 = 6 the answer is c ."

<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<result>6</result>


an employee ’ s annual salary was increased $ 25000 . if her new annual salary now equals $ 90000 , what was the percent increase ?

Explanation: new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d .

<gadget id="calculator">90_000 - 25_000</gadget>
<output>65_000</output>
<gadget id="calculator">25_000 / 65_000</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>


in a class of 45 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?

Explanation: "total = english + german - both + neither - - > 45 = english + 22 - 12 + 0 - - > english = 35 - - > only english = english - both = 35 - 12 = 23 . answer : d ."

<gadget id="calculator">45 + 12</gadget>
<output>57</output>
<gadget id="calculator">57 - 22</gadget>
<output>35</output>
<gadget id="calculator">35 - 12</gadget>
<output>23</output>
<result>23</result>


mr . parkin invested in fund z and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund z paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund z . how much did ms . morris invest in fund z ?

Explanation: 0.17 b - 0.23 z = 200 | * 100 17 b - 23 z = 20000 z + b = 100000 b = 100000 - z 17 ( 100000 - z ) - 23 z = 20000 1 , 700000 - 17 z - 23 z = 20000 1 , 680000 = 40 z divide by 40 first two digits : 42 . . . so answer is d .

<gadget id="calculator">23 + 17</gadget>
<output>40</output>
<gadget id="calculator">40 * 100_000</gadget>
<output>4_000_000</output>
<gadget id="calculator">4_000_000 / 100</gadget>
<output>40_000</output>
<result>40_000</result>


a train 100 meters long completely crosses a 300 meters long bridge in 36 seconds . what is the speed of the train is ?

Explanation: "s = ( 100 + 300 ) / 36 = 400 / 36 * 18 / 5 = 40 answer : e"

divide(divide(add(100, 300), const_1000), divide(36, const_3600))

<gadget id="calculator">100 + 300</gadget>
<output>400</output>
<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">36 / 3_600</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(2/5) / (1/100)</gadget>
<output>40</output>
<result>40</result>


a school has 11 maths 8 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required

Explanation: "total subjects = 11 + 8 + 5 = 24 max subjects by 1 teacher = 3 so , min of teachers required = 24 / 3 = 8 answer : d"

<gadget id="calculator">11 + 8</gadget>
<output>19</output>
<gadget id="calculator">19 + 5</gadget>
<output>24</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>8</result>


trapezoid jklm in the x - y plane has coordinates j = ( – 3 , – 4 ) , k = ( – 3 , 1 ) , l = ( 5 , 7 ) , and m = ( 5 , – 4 ) . what is its perimeter ?

Explanation: jk = 5 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 34 a

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">15 + 8</gadget>
<output>23</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">23 + 11</gadget>
<output>34</output>
<result>34</result>


| - 2 | ( | - 25 | - | 5 | ) = ? ? source : preparation material mba center

Explanation: absolute value will turn negatives into their positive ' equivalents ' , and will leave positives unchanged , so | - 2 | = 2 , | - 25 | = 25 , and | 5 | = 5 . getting rid of our absolute values we have : | - 2 | ( | - 25 | - | 5 | ) = ( 2 ) ( 25 - 5 ) = 2 * 20 = 40

<gadget id="calculator">25 - 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<result>40</result>


at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 30 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 30 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?

Explanation: "let number of apples = a number of oranges = b a + b = 30 - - - 1 . 56 = ( . 4 a + . 6 b ) / 30 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 24 let the number of oranges put back = c 52 * ( 30 - c ) = 40 * 6 + 60 ( 24 - c ) = > c = 15 answer e"

divide(subtract(multiply(56, 30), multiply(52, 30)), subtract(60, 52))

<gadget id="calculator">56 * 30</gadget>
<output>1_680</output>
<gadget id="calculator">52 * 30</gadget>
<output>1_560</output>
<gadget id="calculator">1_680 - 1_560</gadget>
<output>120</output>
<gadget id="calculator">60 - 52</gadget>
<output>8</output>
<gadget id="calculator">120 / 8</gadget>
<output>15</output>
<result>15</result>


a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12 % while buying and by 30 % while selling . what is his percentage profit ?

Explanation: "the owner buys 100 kg but actually gets 112 kg ; the owner sells 100 kg but actually gives 70 kg ; profit : ( 112 - 70 ) / 70 * 100 = ~ 60 % answer : d ."

divide(multiply(subtract(add(const_100, 12), subtract(const_100, 30)), const_100), subtract(const_100, 30))

<gadget id="calculator">100 + 12</gadget>
<output>112</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">112 - 70</gadget>
<output>42</output>
<gadget id="calculator">42 * 100</gadget>
<output>4_200</output>
<gadget id="calculator">4_200 / 70</gadget>
<output>60</output>
<result>60</result>


a statue is being carved by a sculptor . the original piece of marble weighed 180 kg . in the first week 28 percent is cut away . in the second week 18 percent of the remainder is cut away . in the third week the statue is completed when 20 percent of the remainder is cut away . what is the weight of the final statue ?

Explanation: "b 85 kg 180 ã — 0.72 ã — 0.82 ã — 0.8 = 85 kg ."

multiply(subtract(const_1, divide(20, const_100)), multiply(subtract(const_1, divide(18, const_100)), multiply(180, subtract(const_1, divide(28, const_100)))))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">1 - (9/50)</gadget>
<output>41/50 = around 0.82</output>
<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">1 - (7/25)</gadget>
<output>18/25 = around 0.72</output>
<gadget id="calculator">180 * (18/25)</gadget>
<output>648/5 = around 129.6</output>
<gadget id="calculator">(41/50) * (648/5)</gadget>
<output>13_284/125 = around 106.272</output>
<gadget id="calculator">(4/5) * (13_284/125)</gadget>
<output>53_136/625 = around 85.0176</output>
<result>53_136/625 = around 85.0176</result>


there are 22 kids in a classroom . 12 kids are wearing socks and 8 are wearing shoes . 6 kids are wearing both . how many are bare feet ?

Explanation: 12 kids wear socks 8 kids wear shoes 6 wear both . 12 â € “ 6 = 6 ( wear only socks ) 8 â € “ 6 = 2 ( wear only shoes ) 6 ( wear both ) hence , 22 - 14 = 8 8 kids are with bare feet . e

subtract(22, add(add(subtract(12, 6), subtract(8, 6)), 6))

<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">8 - 6</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">22 - 14</gadget>
<output>8</output>
<result>8</result>


a and b together can do a piece of work in 6 days and a alone can do it in 13 days . in how many days can b alone can do it ?

Explanation: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 13 work in 1 day b alone can do ( 1 / 6 - 1 / 13 ) = 7 / 78 work in 1 day = > complete work can be done in 78 / 7 days by b answer : option c"

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 13</gadget>
<output>1/13 = around 0.076923</output>
<gadget id="calculator">(1/6) - (1/13)</gadget>
<output>7/78 = around 0.089744</output>
<gadget id="calculator">1 / (7/78)</gadget>
<output>78/7 = around 11.142857</output>
<result>78/7 = around 11.142857</result>


the length of a side of a hexagon is 4 inches . what is the perimeter ?

Explanation: hexagon . it means 6 equal sides . p = 6 ( 4 ) = 24 inches answer c

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<result>24</result>


how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 112 m length ?

Explanation: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 112 = 222 m . required time = 222 / 20 = 11.1 sec . answer : d"

<gadget id="calculator">110 + 112</gadget>
<output>222</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">222 / 20</gadget>
<output>111/10 = around 11.1</output>
<result>111/10 = around 11.1</result>


ketchup , mustard and mayo bottles at a hot dog stand are in the ratio of 3 : 3 : 2 . if there are 6 ketchup bottles , the number of mayo bottles at the hot dog stand is :

Explanation: explanation : let ketchup = 3 x , mustard = 3 x & mayo = 2 x . now , 3 x = 6 hence x = 2 . number of mayo bottles = 2 x which is 4 . answer : e

<gadget id="calculator">6 / 3</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<result>4</result>


at a certain university , 65 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?

Explanation: "total women = 65 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 25 % but question wants to know the percent of men that are tenured 25 % / 40 % = 62.5 % d"

add(subtract(const_100, 65), subtract(90, 65))

<gadget id="calculator">100 - 65</gadget>
<output>35</output>
<gadget id="calculator">90 - 65</gadget>
<output>25</output>
<gadget id="calculator">35 + 25</gadget>
<output>60</output>
<result>60</result>


a can do a work in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is

Explanation: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 5 days they work 35 * 5 = 175 remaining work is 300 - 175 = 125 remaining fraction of work is = 125 / 300 = 5 / 12 answer d"

subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 5))

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(7/60) * 5</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">1 - (7/12)</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>


of the 200 stamps in a collection , 90 are foreign and 80 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?

Explanation: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 60 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 60 ) = 50 the answer is a ."

subtract(200, subtract(add(90, 80), 20))

<gadget id="calculator">90 + 80</gadget>
<output>170</output>
<gadget id="calculator">170 - 20</gadget>
<output>150</output>
<gadget id="calculator">200 - 150</gadget>
<output>50</output>
<result>50</result>


find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm .

Explanation: volume = pier 2 h = pie x 72 x 60 = 9240 cm 3 curved surface area = 2 pierh = ( 2 x 3.14 x 7 x 60 ) cm 2 = 2640 cm 2 answer : d

<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">2 * pi * 7</gadget>
<output>14*pi = around 43.982297</output>
<gadget id="calculator">(14*pi) * 60</gadget>
<output>840*pi = around 2_638.937829</output>
<result>840*pi = around 2_638.937829</result>


a car traveled 560 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?

Explanation: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 560 / h = > 336 / c = 560 / ( c + 6 ) = > 336 c + 336 * 6 = 560 c = > c = 336 * 6 / 224 = 9 answer a ."

divide(336, divide(subtract(560, 336), 6))

<gadget id="calculator">560 - 336</gadget>
<output>224</output>
<gadget id="calculator">224 / 6</gadget>
<output>112/3 = around 37.333333</output>
<gadget id="calculator">336 / (112/3)</gadget>
<output>9</output>
<result>9</result>


a hall 36 m long and 15 m broad is to be paved with stones , each measuring 2 dm by 5 dm . the number of stones required is :

Explanation: area of the hall = 3600 * 1500 area of each stone = ( 20 * 50 ) therefore , number of stones = ( 3600 * 1500 / 20 * 50 ) = 5400 answer : c

divide(multiply(36, 15), divide(multiply(2, 5), const_100))

<gadget id="calculator">36 * 15</gadget>
<output>540</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">540 / (1/10)</gadget>
<output>5_400</output>
<result>5_400</result>


by selling an article at rs . 900 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?

Explanation: "sp = 900 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 900 * [ 100 / 125 ] = 720 loss = 25 % = 25 % of 720 = rs . 180 sp = cp - loss = 720 - 180 = rs . 540 answer : d"

subtract(divide(multiply(900, const_100), add(25, const_100)), divide(multiply(divide(multiply(900, const_100), add(25, const_100)), 25), const_100))

<gadget id="calculator">900 * 100</gadget>
<output>90_000</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">90_000 / 125</gadget>
<output>720</output>
<gadget id="calculator">720 * 25</gadget>
<output>18_000</output>
<gadget id="calculator">18_000 / 100</gadget>
<output>180</output>
<gadget id="calculator">720 - 180</gadget>
<output>540</output>
<result>540</result>


a train 220 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?

Explanation: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 220 * 3 / 55 ] sec = 12 sec answer : option d"

multiply(const_3600, divide(divide(220, const_1000), add(60, 6)))

<gadget id="calculator">220 / 1_000</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">(11/50) / 66</gadget>
<output>1/300 = around 0.003333</output>
<gadget id="calculator">3_600 * (1/300)</gadget>
<output>12</output>
<result>12</result>


assume that f ( 1 ) = 0 and f ( m + n ) = f ( m ) + f ( n ) + 4 ( 9 mn - 1 ) . for all natural numbers ( integers > 0 ) m and n . what is the value of f ( 17 ) ?

Explanation: explanation : f ( 1 ) = 0 f ( 2 ) = f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 4 ( 9 × 1 × 1 – 1 ) = 0 + 0 + 4 × 8 = 32 f ( 4 ) = f ( 2 + 2 ) = f ( 2 ) + f ( 2 ) + 4 ( 9 × 2 × 2 – 1 ) = 32 + 32 + 4 × 35 = 204 f ( 8 ) = f ( 4 + 4 ) = f ( 4 ) + f ( 4 ) + 4 ( 9 × 4 × 4 – 1 ) = 204 + 204 + 4 × 143 = 980 f ( 16 ) = f ( 8 + 8 ) = f ( 8 ) + f ( 8 ) + 4 ( 9 × 8 × 8 – 1 ) = 980 + 980 + 4 × 575 = 4260 f ( 17 ) = f ( 1 + 16 ) = f ( 16 ) + f ( 1 ) + 4 ( 9 × 16 × 1 – 1 ) = 4260 + 0 + 4 × 143 = 4832 answer : a

add(add(add(add(add(add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4)), add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4))), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4)), add(add(add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4)), add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4))), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4))), multiply(add(multiply(add(const_4, const_1), const_100), subtract(add(multiply(17, const_4), 9), const_2)), const_4)), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4))

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">32 + 32</gadget>
<output>64</output>
<gadget id="calculator">32 + 3</gadget>
<output>35</output>
<gadget id="calculator">35 * 4</gadget>
<output>140</output>
<gadget id="calculator">64 + 140</gadget>
<output>204</output>
<gadget id="calculator">204 + 204</gadget>
<output>408</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">40 + 3</gadget>
<output>43</output>
<gadget id="calculator">100 + 43</gadget>
<output>143</output>
<gadget id="calculator">143 * 4</gadget>
<output>572</output>
<gadget id="calculator">408 + 572</gadget>
<output>980</output>
<gadget id="calculator">980 + 980</gadget>
<output>1_960</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">17 * 4</gadget>
<output>68</output>
<gadget id="calculator">68 + 9</gadget>
<output>77</output>
<gadget id="calculator">77 - 2</gadget>
<output>75</output>
<gadget id="calculator">500 + 75</gadget>
<output>575</output>
<gadget id="calculator">575 * 4</gadget>
<output>2_300</output>
<gadget id="calculator">1_960 + 2_300</gadget>
<output>4_260</output>
<gadget id="calculator">4_260 + 572</gadget>
<output>4_832</output>
<result>4_832</result>


allay ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning allay makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?

Explanation: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now allay can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional paymentsi . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c

<gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">12 / 0.5</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>25</result>


if ( 2 ^ 16 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?

Explanation: given 2 ^ 16 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 16 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans d on comparing the power of 2 = > m = 16

<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<result>16</result>


Explanation: "explanation : 90 + 5 * 12 / ( 180 / 3 ) = 90 + 5 * 12 / ( 60 ) = 90 + ( 5 * 12 ) / 60 = 90 + 1 = 91 . answer : d"

add(90, divide(multiply(5, 12), divide(180, 3)))

<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">180 / 3</gadget>
<output>60</output>
<gadget id="calculator">60 / 60</gadget>
<output>1</output>
<gadget id="calculator">90 + 1</gadget>
<output>91</output>
<result>91</result>


if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is

Explanation: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"

divide(subtract(350, 340), divide(5, const_100))

<gadget id="calculator">350 - 340</gadget>
<output>10</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">10 / (1/20)</gadget>
<output>200</output>
<result>200</result>


a welder received an order to make a 1 million liter cube - shaped tank . if he has only 2 x 3 meter sheets of metal that can be cut , how many metal sheets will be required for this order ? ( 1 cubic meter = 1000 liters )

Explanation: the question say : a welder received an order to make a 1 million liter cube - shaped tank . ( 1 cubic meter = 1,000 liters ) in other words , the tank is going to have a volume of 1000 cubic meters . that would equal 1 million liters . a cube with a volume of 1000 cubic meters must be ( 10 meters ) x ( 10 meters ) x ( 10 meters ) . the question does n ' t specify whether this tank should have a closed top or an open top . ( the real gmat is good about specifying things like that . ) here , we are going to assume a closed top , only because if the top is open , we do n ' t use enough metal - - - we get an answer smaller than any of the answer choices . a closed - top cube , a full cube , has 6 sides , each of which is ( 10 meters ) x ( 10 meters ) . that ' s a total surface area of 600 sq m . the question tells us : he has only 2 x 3 meter sheets of metal that can be cut . each sheet has an area of 6 sq m . how many of these need to fill up 600 sq m ? 600 / 6 = 100 . he needs 100 sheets . answer = e

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

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">600 / 6</gadget>
<output>100</output>
<result>100</result>


if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is .

Explanation: explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x = > 140 * 30 * x = 100 * 18 * 42 = > or x = 18 answer : a

divide(multiply(multiply(18, 100), 42), multiply(140, 30))

<gadget id="calculator">18 * 100</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 * 42</gadget>
<output>75_600</output>
<gadget id="calculator">140 * 30</gadget>
<output>4_200</output>
<gadget id="calculator">75_600 / 4_200</gadget>
<output>18</output>
<result>18</result>


when x is multiplied by 3 , the result is 10 more than the result of subtracting x from 26 . what is the value of x ?

Explanation: "the equation that can be formed is : 3 x - 10 = 26 - x or , 4 x = 36 or , x = 9 . b answer ."

<gadget id="calculator">26 + 10</gadget>
<output>36</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">36 / 4</gadget>
<output>9</output>
<result>9</result>


if the l . c . m of two numbers is 560 and their product is 42000 , find the h . c . f of the numbers .

Explanation: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 42000 / 560 = 75 . answer : c"

<gadget id="calculator">42_000 / 560</gadget>
<output>75</output>
<result>75</result>


Explanation: interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1004 ^ 2 - > 16 total - > * 30 answer d .

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


in a room filled with 6 people , all 6 people have exactly 1 sibling in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?

Explanation: the 6 people consist of three sets of 2 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the second group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the third group of siblings is 2 c 2 = 1 . the number of ways to choose 2 people who are siblings is 1 + 1 + 1 = 3 . the number of ways to choose 2 people who are not siblings is 15 - 3 = 12 . p ( the two people are not siblings ) = 12 / 15 = 4 / 5 the answer is b .

divide(multiply(6, subtract(subtract(6, const_1), const_1)), multiply(6, subtract(6, const_1)))

<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">24 / 30</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


find the least number of complete years in which a sum of money put out at 50 % compound interest will be more than double of itself ?

Explanation: 2 years answer : a

floor(add(divide(log(const_2), log(add(const_1, divide(50, const_100)))), const_1))

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">log(3/2)</gadget>
<output>log(3/2) = around 0.405465</output>
<gadget id="calculator">log(2) / log(3/2)</gadget>
<output>log(2)/log(3/2) = around 1.709511</output>
<gadget id="calculator">(log(2)/log(3/2)) + 1</gadget>
<output>1 + log(2)/log(3/2) = around 2.709511</output>
<gadget id="calculator">floor(1 + log(2)/log(3/2))</gadget>
<output>2</output>
<result>2</result>


excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

Explanation: "in 1 hr , the bus covers 60 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 60 - 40 ) km i . e 20 km at 60 km / hr . stoppage time = 20 / 60 hrs = 20 min . answer : d"

subtract(multiply(const_1, const_60), multiply(divide(40, 60), const_60))

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 60</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<result>20</result>


in an office , 50 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?

Explanation: ( 10 / 100 ) workers = 16 = > number of workers = 160 ( 50 / 100 ) * workers = x + 16 = > x = 8 answer a

divide(subtract(divide(multiply(divide(16, divide(10, const_100)), 90), const_100), multiply(divide(16, divide(10, const_100)), divide(const_1, const_2))), multiply(const_2, const_4))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">16 / (1/10)</gadget>
<output>160</output>
<gadget id="calculator">160 * 90</gadget>
<output>14_400</output>
<gadget id="calculator">14_400 / 100</gadget>
<output>144</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">160 * (1/2)</gadget>
<output>80</output>
<gadget id="calculator">144 - 80</gadget>
<output>64</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">64 / 8</gadget>
<output>8</output>
<result>8</result>


bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many d hours does it currently take anne to clean the house on her own ?

Explanation: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in d = 3 hours ) solving these 2 equations we can find b as 12 so , d"

inverse(subtract(divide(const_1, 3), divide(const_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>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?

Explanation: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 8 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 640 = 200 answer : b"

subtract(multiply(add(20, const_1), add(8, 32)), multiply(20, 32))

<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">8 + 32</gadget>
<output>40</output>
<gadget id="calculator">21 * 40</gadget>
<output>840</output>
<gadget id="calculator">20 * 32</gadget>
<output>640</output>
<gadget id="calculator">840 - 640</gadget>
<output>200</output>
<result>200</result>


a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 17 , the how old is b ? a . 7 b . 8 c . 9 d . 10 explanation :

Explanation: let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 17 5 x = 15 x = 3 . hence , b ' s age = 2 x = 6 years . answer : option a

multiply(divide(subtract(17, const_2), add(const_4, const_1)), const_2)

<gadget id="calculator">17 - 2</gadget>
<output>15</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<result>6</result>


two pipes can fill a tank in 12 minutes and 20 minutes respectively . both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes . for how many minutes was first pipe open ?

Explanation: second pipe is opened for 10 minutes . so , part of tank filled by the second pipe = 10 / 20 = 1 / 2 . so , 1 - 1 / 2 = 1 / 2 tank is filled by first pipe . first pipe can fill 1 / 2 of tank in 1 * 12 / 2 = 6 minutes . so , the first pipe is opened for 6 minutes . answer : b

subtract(10, divide(subtract(multiply(add(inverse(12), inverse(20)), 10), const_1), inverse(12)))

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/12) + (1/20)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(2/15) * 10</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) / (1/12)</gadget>
<output>4</output>
<gadget id="calculator">10 - 4</gadget>
<output>6</output>
<result>6</result>


the average of 50 numbers id 20 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :

Explanation: "explanation : total of 50 numbers = ( 50 × 20 ) = 1000 total of 48 numbers = ( 1000 - ( 45 + 55 ) ] = 900 required average = 900 / 48 = 18.75 answer : e"

divide(subtract(multiply(50, 20), add(45, 55)), subtract(50, const_2))

<gadget id="calculator">50 * 20</gadget>
<output>1_000</output>
<gadget id="calculator">45 + 55</gadget>
<output>100</output>
<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">900 / 48</gadget>
<output>75/4 = around 18.75</output>
<result>75/4 = around 18.75</result>


the area of a triangle is with base 10 m and height 10 m ?

Explanation: "1 / 2 * 10 * 10 = 50 m 2 answer : c"

<gadget id="calculator">(10 * 10) / 2</gadget>
<output>50</output>
<result>50</result>


in what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

Explanation: "t = 40 / 36 * 18 / 5 = 4 sec answer : b"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>4</result>


find remainder if ( 67 ^ 67 + 67 ) is divided by 68

Explanation: = > ( 6767 + 1 ) is divisible by ( 67 + 1 ) = > ( 6767 + 1 ) is divisible by 68 = > ( 6767 + 1 ) ÷ 68 gives a remainder of 0 = > [ ( 6767 + 1 ) + 66 ] ÷ 68 gives a remainder of 66 = > ( 6767 + 67 ) ÷ 68 gives a remainder of 66 c

<gadget id="calculator">67 - 1</gadget>
<output>66</output>
<result>66</result>


last year a worker saved 6 % of her annual salary . this year , she made 20 % more money than last year and she saved 5 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?

Explanation: let x be the worker ' s salary last year . last year , she saved 0.06 x . this year , she saved 0.05 ( 1.2 x ) = 0.06 x 0.06 x / 0.06 x = 100 % the answer is b .

multiply(const_100, divide(6, multiply(add(20, const_100), divide(5, const_100))))

<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">120 * (1/20)</gadget>
<output>6</output>
<gadget id="calculator">6 / 6</gadget>
<output>1</output>
<gadget id="calculator">100 * 1</gadget>
<output>100</output>
<result>100</result>


a walks at 10 kmph and 4 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?

Explanation: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . x / 10 - x / 20 = 4 x = 80 km answer is c"

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


a man can swim in still water at 12 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?

Explanation: "m = 12 s = x ds = 12 + x us = 12 + x 12 + x = ( 12 - x ) 2 12 + x = 24 - 2 x 3 x = 12 x = 4 answer : e"

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


nitin ranks 24 th in a class of 58 students . what is rank from the last ?

Explanation: "explanation : number students behind the nitin in rank = ( 58 - 24 ) = 34 nitin is 34 nd from the last answer : b ) 34"

<gadget id="calculator">58 - 24</gadget>
<output>34</output>
<result>34</result>


a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 4 volts , what was the smallest possible recording in volts ?

Explanation: if average of 3 is 4 so sum of 3 should be 12 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 5 and 5 so a has to be 2 a

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<result>2</result>


5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 12 days . how many additional pipes q , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?

Explanation: this is an inverse proportional problem . . . . . . 5 pipes in 12 days ; so for 4 days , it will be = 12 x 5 / 4 = 15 so , q = 15 - 5 = 10 . c

<gadget id="calculator">12 * 5</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<result>10</result>


set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 3 ?

Explanation: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"

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


a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 45 % . staff are allowed a further 40 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?

Explanation: effective discount = a + b + ab / 100 = - 45 - 40 + ( - 45 ) ( - 40 ) / 100 = - 67 sale price = d * ( 1 - 67 / 100 ) sale price = . 33 * d answer ( e )

subtract(divide(subtract(const_100, 45), const_100), multiply(divide(subtract(const_100, 45), const_100), divide(40, const_100)))

<gadget id="calculator">100 - 45</gadget>
<output>55</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(11/20) * (2/5)</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">(11/20) - (11/50)</gadget>
<output>33/100 = around 0.33</output>
<result>33/100 = around 0.33</result>


the average weight of 4 person ' s increases by 8.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?

Explanation: "total weight increased = ( 4 x 8.5 ) kg = 34 kg . weight of new person = ( 95 + 34 ) kg = 129 kg option a"

<gadget id="calculator">4 * 8.5</gadget>
<output>34</output>
<gadget id="calculator">34 + 95</gadget>
<output>129</output>
<result>129</result>


the s . i . on a certain sum of money for 2 years at 8 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?

Explanation: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 8 ) = rs . 2625 answer : e"

divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(8, const_100)))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>
<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">2 * (2/25)</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">420 / (4/25)</gadget>
<output>2_625</output>
<result>2_625</result>


two trains 120 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

Explanation: relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 160 = 280 m . required time = 280 * 9 / 250 = 252 / 25 = 10.08 sec . ' answer : d

<gadget id="calculator">120 + 160</gadget>
<output>280</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">280 / (250/9)</gadget>
<output>252/25 = around 10.08</output>
<result>252/25 = around 10.08</result>


in the first 20 overs of a cricket game , the run rate was only 4.6 . what should be the run rate in the remaining 30 overs to reach the target of 396 runs ?

Explanation: required run rate = 396 - ( 4.6 x 20 ) / 30 = 304 / 30 = 10.13 option a

divide(subtract(396, multiply(20, 4.6)), 30)

<gadget id="calculator">20 * 4.6</gadget>
<output>92</output>
<gadget id="calculator">396 - 92</gadget>
<output>304</output>
<gadget id="calculator">304 / 30</gadget>
<output>152/15 = around 10.133333</output>
<result>152/15 = around 10.133333</result>


a club wants to mix 10 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?

Explanation: "let number of pounds of 5 $ candy to be used be w 6 = ( 10 * 8 + 5 * w ) / ( 10 + w ) = > 60 + 6 w = 80 + 5 w = > w = 20 answer a"

subtract(multiply(10, 8.00), multiply(6.00, 10))

<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">80 - 60</gadget>
<output>20</output>
<result>20</result>


if the annual increase in the population of a town is 10 % and the present number of people is 15000 , what will the population be in 2 years ?

Explanation: "the required population is = 15000 ( 1 + 10 / 100 ) ^ 2 = 15000 * 11 / 10 * 11 / 10 = 18150 answer is c"

multiply(multiply(divide(add(10, const_100), const_100), 15000), divide(add(10, const_100), const_100))

<gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) * 15_000</gadget>
<output>16_500</output>
<gadget id="calculator">16_500 * (11/10)</gadget>
<output>18_150</output>
<result>18_150</result>


a plant manager must assign 8 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?

Explanation: "whatever : my take selecting team of 2 out of 8 to assign to the shifts = 8 c 2 = 28 ways . now 2 out of 8 means total of 4 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 4 * 3 * 2 * 1 = 24 here alt and alt are the same : so 24 / 2 = 12 ways . total ways of selecting = ( selecting 2 out of 8 ) * arranging those teams in shifts = 28 * 12 = 336 ans : b"

multiply(divide(factorial(divide(8, 2)), const_2), divide(factorial(8), multiply(factorial(subtract(8, 2)), factorial(2))))

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>
<gadget id="calculator">40_320 / 1_440</gadget>
<output>28</output>
<gadget id="calculator">12 * 28</gadget>
<output>336</output>
<result>336</result>


Explanation: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b

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


find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 10 as quotient and the 10 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 10 x + 10 9 x = 990 x = 110 large number = 110 + 1000 = 1110 b"

multiply(divide(subtract(1000, 10), subtract(10, const_1)), 10)

<gadget id="calculator">1_000 - 10</gadget>
<output>990</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">990 / 9</gadget>
<output>110</output>
<gadget id="calculator">110 * 10</gadget>
<output>1_100</output>
<result>1_100</result>


the average height of 30 girls out of a class of 40 is 160 cm . and that of the remaining girls is 156 cm . the average height of the whole class is :

Explanation: explanation : average height of the whole class = ( 36 × 160 + 10 × 156 / 40 ) = 159 cms answer c

divide(add(multiply(160, 30), multiply(156, const_10)), 40)

<gadget id="calculator">160 * 30</gadget>
<output>4_800</output>
<gadget id="calculator">156 * 10</gadget>
<output>1_560</output>
<gadget id="calculator">4_800 + 1_560</gadget>
<output>6_360</output>
<gadget id="calculator">6_360 / 40</gadget>
<output>159</output>
<result>159</result>


a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 15000 rs , what is the value of buzness ?

Explanation: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 15000 - > x = 75000 answer : b"

divide(15000, multiply(divide(1, 3), divide(3, 5)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(1/3) * (3/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">15_000 / (1/5)</gadget>
<output>75_000</output>
<result>75_000</result>


jaylen was planning to save all summer for a pair of jordan 12 s . they cost $ 250 . jaylen figured that he could cut grass to help with the cost of the sneakers . how many yards would jaylen have to cut if he charges $ 2.15 per yard ?

<gadget id="calculator">250 / 2.15</gadget>
<output>116.27907</output>
<result>116.27907</result>


at the end of the month , a certain ocean desalination plant ’ s reservoir contained 30 million gallons of water . this amount is twice the normal level . if this amount represents 75 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?

Explanation: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 30 mg = 75 % of total . . total = 30 / . 75 = 40 mg . . normal level = 1 / 2 of 40 = 20 mg . . shortage of normal level = 40 - 20 = 20 mg . . c"

divide(divide(30, const_2), divide(75, const_100))

<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">15 / (3/4)</gadget>
<output>20</output>
<result>20</result>


matt gets a $ 1000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?

Explanation: let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d

divide(subtract(1000, subtract(250, 150)), 150)

<gadget id="calculator">250 - 150</gadget>
<output>100</output>
<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>
<gadget id="calculator">900 / 150</gadget>
<output>6</output>
<result>6</result>


the present worth of $ 169 due in 2 years at 4 % per annum compound interest is ?

Explanation: "present worth = 169 / ( 1 + 4 / 100 ) ^ 2 = 169 * 25 / 26 * 25 / 26 = $ 156.25 answer is c"

divide(169, power(add(divide(4, const_100), const_1), 2))

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) + 1</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">169 / (676/625)</gadget>
<output>625/4 = around 156.25</output>
<result>625/4 = around 156.25</result>


an urn contains 10 black and 5 white balls . two balls are drawn from the urn one after the other without replacement . what is the probability that both drawn balls are black ?

Explanation: let e and f denote respectively the events that first and second ball drawn are black . we have to find p ( e n f ) or p ( ef ) . now p ( e ) = p ( black ball in first draw ) = 10 / 15 also given that the first ball drawn is black , i . e . , event e has occurred , now there are 9 black balls and five white balls left in the urn . therefore , the probability that the second ball drawn is black , given that the ball in the first draw is black , is nothing but the conditional probability of f given that e has occurred . that is p ( f | e ) = 9 / 14 by multiplication rule of probability , we have p ( e n f ) = p ( e ) p ( f | e ) = 10 / 15 × 9 / 14 = 3 / 7 b

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

<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">10 / 15</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">9 / 14</gadget>
<output>9/14 = around 0.642857</output>
<gadget id="calculator">(2/3) * (9/14)</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>


by selling 11 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ?

Explanation: 90 % - - - 11 120 % - - - ? 90 / 120 * 11 = 8.25 answer : a

multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 10)))), 11)

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">120 * (1/90)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">1 / (4/3)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 11</gadget>
<output>33/4 = around 8.25</output>
<result>33/4 = around 8.25</result>


in the first 10 overs of a cricket game , the run rate was only 4.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?

Explanation: "10 overs - run rate = 4.2 runs scored in first 10 overs = 42 remaining overs 40 total runs to be scored = 282 42 runs already scored 282 - 42 = 240 240 runs to be scored in 40 overs let required runrate be x 40 * x = 240 x = 240 / 40 x = 6.0 the required runrate is 6.0 answer : e"

divide(subtract(282, multiply(10, 4.2)), 40)

<gadget id="calculator">10 * 4.2</gadget>
<output>42</output>
<gadget id="calculator">282 - 42</gadget>
<output>240</output>
<gadget id="calculator">240 / 40</gadget>
<output>6</output>
<result>6</result>