each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 93 % water by weight . what is the new weight of the cucumbers , in pounds ?

Explanation: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 93 % water and 7 % of non - water , so now 1 pound of non - water composes 7 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.07 = 15 pounds . answer : b ."

multiply(divide(subtract(100, 99), subtract(100, 93)), 100)

<gadget id="calculator">100 - 99</gadget>
<output>1</output>
<gadget id="calculator">100 - 93</gadget>
<output>7</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/7) * 100</gadget>
<output>100/7 = around 14.285714</output>
<result>100/7 = around 14.285714</result>


the cost of the paint is rs . 50 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 20 feet each side

Explanation: "explanation : surface area of a cube = 6 x 20 ^ 2 = 2400 sq . ft quantity of paint required = ( 2400 / 20 ) = 120 kg cost of painting = 50 x 120 = rs . 6000 answer : b"

<gadget id="calculator">6 * (20 ** 2)</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 20</gadget>
<output>120</output>
<gadget id="calculator">120 * 50</gadget>
<output>6_000</output>
<result>6_000</result>


a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 160 meter length ?

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 160 = 520 meter time = distance / speed = 520 * ( 2 / 25 ) = 41.6 seconds answer : b"

divide(add(360, 160), divide(multiply(45, const_1000), const_3600))

<gadget id="calculator">360 + 160</gadget>
<output>520</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">520 / (25/2)</gadget>
<output>208/5 = around 41.6</output>
<result>208/5 = around 41.6</result>


the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2016 . the sum of the numbers is ?

Explanation: "let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2016 14 x ^ 2 = 2016 x ^ 2 = 144 x = 12 answer is b"

sqrt(divide(2016, add(power(3, 2), add(power(1, 2), power(2, 2)))))

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">9 + 5</gadget>
<output>14</output>
<gadget id="calculator">2_016 / 14</gadget>
<output>144</output>
<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<result>12</result>


a certain airline ' s fleet consisted of 90 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?

Explanation: "let x be the number of years . 4 x > 90 - 3 x 7 x > 90 x > 12 + 6 / 7 the answer is c ."

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">90 / 7</gadget>
<output>90/7 = around 12.857143</output>
<result>90/7 = around 12.857143</result>


john makes $ 60 a week from his job . he earns a raise andnow makes $ 78 a week . what is the % increase ?

Explanation: "increase = ( 18 / 60 ) * 100 = ( 3 / 10 ) * 100 = 30 % . c"

multiply(divide(subtract(78, 60), 60), const_100)

<gadget id="calculator">78 - 60</gadget>
<output>18</output>
<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>


a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?

Explanation: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 250 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : a"

divide(add(250, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

<gadget id="calculator">250 + 120</gadget>
<output>370</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">5 / 18</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">370 / 10</gadget>
<output>37</output>
<result>37</result>


two pipes a and b can separately fill a cistern in 60 minutes and 75 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 50 minutes . in how much time , the third pipe alone can empty the cistern ?

Explanation: "1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 third pipe can empty in 100 minutes answer : b"

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">1 / 75</gadget>
<output>1/75 = around 0.013333</output>
<gadget id="calculator">(1/60) + (1/75)</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(3/100) - (1/50)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">1 / (1/100)</gadget>
<output>100</output>
<result>100</result>


of the 20,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?

Explanation: the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e

multiply(multiply(divide(divide(divide(2, 7), const_2), add(divide(divide(2, 7), const_2), subtract(const_1, divide(2, 7)))), const_100), const_3)

<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(2/7) / 2</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 - (2/7)</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(1/7) + (5/7)</gadget>
<output>6/7 = around 0.857143</output>
<gadget id="calculator">(1/7) / (6/7)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 100</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 3</gadget>
<output>50</output>
<result>50</result>


if jimmy drinks 8 ounces of water each time for 8 times a day . how much gallons of water he would have to prepare ahead to drink for 5 days ? ( 1 ounce = 0.0078125 gallon )

Explanation: 8 ounces * 8 times / day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon . 5 days need 0.5 * 5 = 2.5 gallons . correct option : 2.5 answer : d

multiply(multiply(multiply(8, 8), 0.0078125), 5)

<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 * 0.007812</gadget>
<output>0.499968</output>
<gadget id="calculator">0.499968 * 5</gadget>
<output>2.49984</output>
<result>2.49984</result>


100 people are attending a newspaper conference . 45 of them are writers and more than 36 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 } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 45 + { editors } - x + 2 x - - > x = 55 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 37 , thus x = { both } = 55 - 37 = 18 . answer : c ."

subtract(100, add(add(36, const_1), 45))

<gadget id="calculator">36 + 1</gadget>
<output>37</output>
<gadget id="calculator">37 + 45</gadget>
<output>82</output>
<gadget id="calculator">100 - 82</gadget>
<output>18</output>
<result>18</result>


two trains , a and b , started simultaneously from opposite ends of a 120 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 120 - mile trip in 6 hours ; train b , traveling at a constant rate , completed the 120 - mile trip in 4 hours . how many miles had train a traveled when it met train b ?

Explanation: "as the ratio of the rates of a and b is 4 to 6 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 4 / ( 4 + 6 ) = 4 / 10 of 120 miles : 120 * 4 / 10 = 48 miles . answer : c ."

<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 120</gadget>
<output>48</output>
<result>48</result>


if a speaks the truth 55 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time

Explanation: "explanation : probability that a speaks truth is 55 / 100 = 0.55 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.55 × 0.6 = 0.33 answer : b"

multiply(divide(55, multiply(multiply(const_4, const_5), const_5)), divide(60, multiply(multiply(const_4, const_5), const_5)))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(11/20) * (3/5)</gadget>
<output>33/100 = around 0.33</output>
<result>33/100 = around 0.33</result>


the closest approximation of ( 69.28 × 0.004 ) / 0.03 is

Explanation: "( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . answer : c"

<gadget id="calculator">0.004 / 0.03</gadget>
<output>0.133333</output>
<gadget id="calculator">0.133333 * 69.28</gadget>
<output>9.23731</output>
<result>9.23731</result>


to complete a work a and b takes 8 days , b and c takes 12 days , a , b and c takes 6 days . how much time a and c will take

Explanation: explanation : a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + b + c 1 day work = 1 / 6 we can get a work by ( a + b + c ) - ( b + c ) and c by ( a + b + c ) - ( a + b ) so a 1 day work = 1 / 6 − 1 / 12 = 1 / 12 similarly c 1 day work = 1 / 6 − 1 / 8 = 4 − 3 / 24 = 1 / 24 so a and c 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 so a and c can together do this work in 8 days option d

divide(multiply(8, 6), add(subtract(8, 6), subtract(8, const_4)))

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


maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 34 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?

Explanation: "total distance = 34 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 30 / 10 = 3 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 3 = 12 + 4 = 16 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 16 / 4 = 4 hrs . . . answer b"

<gadget id="calculator">34 + 6</gadget>
<output>40</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>4</result>


the salary of a person was reduced by 25 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?

Explanation: "let the original salary be $ 100 new salary = $ 75 increase on 75 = 25 increase on 100 = [ ( 25 / 75 ) 100 ] % = 33.33 % answer is b"

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

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">100 * (1/4)</gadget>
<output>25</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">25 / 75</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


if ( x + 1 ) ( x + 3 ) = x ^ 2 + x , what is a possible value of x ?

Explanation: rearranging the given expression : ( x + 1 ) ( x + 3 ) = x ^ 2 + x i . e . x ^ 2 + 4 x + 3 = x ^ 2 + x i . e . 3 x = - 3 i . e . x = - 3 / 3 = - 1 answer : option e had it been a difficult expression to solve further , then we could have used options to check which one satisfies the expression after solving it as further as possible .

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


as a treat for her two children , a mother runs to the freezer in which she has 3 cherry ice pops , 4 orange ice pops , and 4 lemon ice pops . she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one being jealous of the other and getting even more upset . what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?

Explanation: p ( 2 cherry ) = 3 / 11 * 2 / 10 = 6 / 110 p ( 2 orange ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 lemon ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 of the same flavor ) = 30 / 110 p ( 2 different flavors ) = 1 - 30 / 110 = 80 / 110 = 8 / 11 the answer is c .

subtract(const_1, divide(add(add(3, multiply(const_2, 3)), multiply(const_2, 3)), add(multiply(add(add(3, multiply(const_2, 3)), multiply(const_2, 3)), 3), const_10)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">9 + 6</gadget>
<output>15</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 + 10</gadget>
<output>55</output>
<gadget id="calculator">15 / 55</gadget>
<output>3/11 = around 0.272727</output>
<gadget id="calculator">1 - (3/11)</gadget>
<output>8/11 = around 0.727273</output>
<result>8/11 = around 0.727273</result>


a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 10 metres apart , how many poles will be needed ?

Explanation: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 10 ] = 28 m answer a"

<gadget id="calculator">2 * (90 + 50)</gadget>
<output>280</output>
<gadget id="calculator">280 / 10</gadget>
<output>28</output>
<result>28</result>


if in a race of 80 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :

Explanation: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 80 * 5 ) / 25 = 16 m hence , a beats b by 16 m . answer : a"

multiply(divide(subtract(25, 20), 25), 80)

<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 80</gadget>
<output>16</output>
<result>16</result>


when two dice are rolled , what is the probability that the sum of the two numbers is 6 ?

Explanation: we have 5 outcomes that satisfy the question : 1 - 5 2 - 4 3 - 3 4 - 2 5 - 1 the probability is ( 1 / 6 * 1 / 6 ) * 5 = 5 / 36 . i think the answer is b

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

<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">5 / 36</gadget>
<output>5/36 = around 0.138889</output>
<result>5/36 = around 0.138889</result>


two trains start from a & b and travel towards each other at speed of 50 kmph and 60 kmph resp . at the time of the meeting the second train has traveled 100 km more than the first . the distance between them .

Explanation: let the distance traveled by the first train be x km then distance covered by the second train is x + 100 km x / 50 = x + 100 / 60 x = 500 so the distance between a & b is x + x + 100 = 1100 km answer is d .

add(multiply(50, divide(100, subtract(60, 50))), multiply(60, divide(100, subtract(60, 50))))

<gadget id="calculator">60 - 50</gadget>
<output>10</output>
<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">50 * 10</gadget>
<output>500</output>
<gadget id="calculator">60 * 10</gadget>
<output>600</output>
<gadget id="calculator">500 + 600</gadget>
<output>1_100</output>
<result>1_100</result>


a dog takes 5 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :

Explanation: explanation : dog : hare = ( 5 * 3 ) leaps of hare : 7 leaps of hare = 15 : 7 answer : b

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 7</gadget>
<output>15/7 = around 2.142857</output>
<result>15/7 = around 2.142857</result>


if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value a of z - x ?

Explanation: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] a = z - x = x + 9 - x = 9 ans : d"

<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<result>9</result>


a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 m long ?

Explanation: "train length = 360 m platform length = 140 m time = ? length = speed * time total length = 360 + 140 = 500 m speed = 45 km / hr = 45 * ( 5 / 18 ) ( m / sec ) = 12.5 m / sec time = length / speed = 500 / 12.5 = 40 sec answer : d"

multiply(divide(add(divide(140, const_1000), divide(360, const_1000)), 45), const_3600)

<gadget id="calculator">140 / 1_000</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">360 / 1_000</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(7/50) + (9/25)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / 45</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/90) * 3_600</gadget>
<output>40</output>
<result>40</result>


two guys a and b leave point a and point b simultaneously and travel towards point b and point a on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will b take to cover the entire journey between point b and point a ?

Explanation: let x per minute be the speed of a and y per minute be the speed of b . after meeting at a point , a travels for 32 mins and b travels for 50 mins . so distance covered by each of them post point of crossing a = 32 x and b = 50 y the distance covered by a and b before they cross each would be distance covered by b and a post crossing respectively . therefore distance covered by b before he meets a = 32 x time taken by b cover 32 x distance = 32 x / y mins therefore total time taken by b = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of a and b = x + y therefore time taken before a and b meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by b reach destination after meeting a = 50 mins total travel time for b = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins b

add(50, multiply(add(const_4, const_1), add(const_4, const_4)))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<result>90</result>


if 63 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

Explanation: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 17 % = 33 % . the answer is d ."

subtract(add(add(63, 50), 20), const_100)

<gadget id="calculator">63 + 50</gadget>
<output>113</output>
<gadget id="calculator">113 + 20</gadget>
<output>133</output>
<gadget id="calculator">133 - 100</gadget>
<output>33</output>
<result>33</result>


for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 95 units raises the average to 55 units per day , what is the value of n ?

Explanation: "the average daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 95 - 55 = 40 n = 8 the answer is c ."

subtract(divide(subtract(95, 50), subtract(55, 50)), const_1)

<gadget id="calculator">95 - 50</gadget>
<output>45</output>
<gadget id="calculator">55 - 50</gadget>
<output>5</output>
<gadget id="calculator">45 / 5</gadget>
<output>9</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<result>8</result>


how many seconds will a 300 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 300 * 3 / 50 = 18 sec . answer : e"

divide(300, multiply(subtract(63, 3), const_0_2778))

<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">300 / (50/3)</gadget>
<output>18</output>
<result>18</result>


abcd is a parallelogram . bd = 2 . the angles of triangle bcd are all equal . what is the perimeter of the parallelogram ?

Explanation: so , bc = bd = cd = ba = ad = 2 the parallelogram has 4 equal sides bc = cd = ba = ad = 2 so the perimeter of the parallelogram will be 2 * 4 = 8 hence answer will be ( d ) 2

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


if the price of petrol increases by 40 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?

Explanation: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 40 ) i . e 140 . now , his consumption should be reduced to : - = ( 140 − 100 ) / 140 ∗ 100 . hence , the consumption should be reduced to 28.6 % . answer : d"

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

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">100 / 140</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">1 - (5/7)</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>


the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.8 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?

Explanation: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.8 * 2 ) + ( 3.85 * 2 ) ] = 8.4 . required average = ( 8.4 / 2 ) = 4.2 . a"

divide(subtract(multiply(6, 3.95), add(multiply(2, 3.8), multiply(2, 3.85))), 2)

<gadget id="calculator">6 * 3.95</gadget>
<output>23.7</output>
<gadget id="calculator">2 * 3.8</gadget>
<output>7.6</output>
<gadget id="calculator">2 * 3.85</gadget>
<output>7.7</output>
<gadget id="calculator">7.6 + 7.7</gadget>
<output>15.3</output>
<gadget id="calculator">23.7 - 15.3</gadget>
<output>8.4</output>
<gadget id="calculator">8.4 / 2</gadget>
<output>4.2</output>
<result>4.2</result>


the average of 7 numbers is 24 . if each number be multiplied by 5 . find the average of new set of numbers ?

Explanation: "explanation : average of new numbers = 24 * 5 = 120 answer : option c"

<gadget id="calculator">24 * 5</gadget>
<output>120</output>
<result>120</result>


a cycle is bought for rs . 900 and sold for rs . 1080 , find the gain percent ?

Explanation: "900 - - - - 180 100 - - - - ? = > 20 % answer : b"

multiply(divide(subtract(1080, 900), 900), const_100)

<gadget id="calculator">1_080 - 900</gadget>
<output>180</output>
<gadget id="calculator">180 / 900</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?

Explanation: "explanation : t = 15 / 45 * 60 = 20 answer : option c"

subtract(const_60, multiply(const_60, divide(30, 45)))

<gadget id="calculator">30 / 45</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">60 * (2/3)</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<result>20</result>


if rs . 544 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?

Explanation: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 544 * 2 / 17 = rs . 64 b ' s share = 544 * 3 / 17 = rs . 96 c ' s share = 544 * 12 / 17 = rs . 384 . answer : d"

divide(544, add(add(multiply(divide(2, 3), divide(1, 4)), divide(1, 4)), 1))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(2/3) * (1/4)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) + (1/4)</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">(5/12) + 1</gadget>
<output>17/12 = around 1.416667</output>
<gadget id="calculator">544 / (17/12)</gadget>
<output>384</output>
<result>384</result>


m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?

Explanation: we will have a negative product only if 1 , 2 , 3 , or 4 are selected from set t . p ( negative product ) = 4 / 8 = 1 / 2 the answer is d .

divide(multiply(5, 4), multiply(5, multiply(4, 2)))

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">20 / 40</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


a 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?

Explanation: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 489 = 50 / 3 3 x + 900 = 2400 = > x = 500 m . answer : a"

subtract(multiply(speed(300, 18), 48), 300)

<gadget id="calculator">300 / 18</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 48</gadget>
<output>800</output>
<gadget id="calculator">800 - 300</gadget>
<output>500</output>
<result>500</result>


the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years . find the average age of the women ?

Explanation: "20 + 22 + 8 * 2 = 58 / 2 = 29 answer : d"

divide(add(add(20, 22), multiply(8, 2)), const_2)

<gadget id="calculator">20 + 22</gadget>
<output>42</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">42 + 16</gadget>
<output>58</output>
<gadget id="calculator">58 / 2</gadget>
<output>29</output>
<result>29</result>


if 20 % of x is 15 less than 15 % of 1500 , then x is ?

Explanation: "20 % of x = x / 5 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 5 = 225 - 15 = > x / 5 = 210 = > x = 1050 . answer : e"

divide(subtract(multiply(1500, divide(15, const_100)), 15), divide(20, const_100))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1_500 * (3/20)</gadget>
<output>225</output>
<gadget id="calculator">225 - 15</gadget>
<output>210</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">210 / (1/5)</gadget>
<output>1_050</output>
<result>1_050</result>


if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?

Explanation: "sum of 5 integer ( a , b , c , d , e ) = 5 * 70 = 350 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 350 i . e . 5 a = 340 i . e . a = 68 i . e . largest e = 68 + 10 = 78 answer : option d"

add(divide(subtract(multiply(70, 5), 10), 5), 10)

<gadget id="calculator">70 * 5</gadget>
<output>350</output>
<gadget id="calculator">350 - 10</gadget>
<output>340</output>
<gadget id="calculator">340 / 5</gadget>
<output>68</output>
<gadget id="calculator">68 + 10</gadget>
<output>78</output>
<result>78</result>


what is the normal price of an article sold at $ 72 after two successive discounts of 10 % and 20 % ?

Explanation: 0.8 * 0.9 * cost price = $ 72 cost price = $ 100 the answer is c .

divide(72, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100)))

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(9/10) * (4/5)</gadget>
<output>18/25 = around 0.72</output>
<gadget id="calculator">72 / (18/25)</gadget>
<output>100</output>
<result>100</result>


of the 200 stamps in a collection , 80 are foreign and 50 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 . 60 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 60 + 30 ) = 90 the answer is b ."

subtract(200, subtract(add(80, 50), 20))

<gadget id="calculator">80 + 50</gadget>
<output>130</output>
<gadget id="calculator">130 - 20</gadget>
<output>110</output>
<gadget id="calculator">200 - 110</gadget>
<output>90</output>
<result>90</result>


joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 3 of the remaining paint . how many gallons of paint has joe used ?

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 3 ) * 270 = 90 gallons total paint used = 180 gallons . option b"

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 3))

<gadget id="calculator">360 / 4</gadget>
<output>90</output>
<gadget id="calculator">90 * 1</gadget>
<output>90</output>
<gadget id="calculator">360 - 90</gadget>
<output>270</output>
<gadget id="calculator">270 / 3</gadget>
<output>90</output>
<gadget id="calculator">90 + 90</gadget>
<output>180</output>
<result>180</result>


if a truck is traveling at a constant rate of 108 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )

Explanation: speed = 108 km / hr = > 108,000 m / hr in one minute = > 108000 / 60 = 1800 meters in one sec = > 1800 / 60 = 30 meters time = total distance need to be covered / avg . speed = > 600 / 30 = 20 and hence the answer : a

multiply(divide(divide(600, 1000), 108), const_3600)

<gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) / 108</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(1/180) * 3_600</gadget>
<output>20</output>
<result>20</result>


what is the least number that should be added to 1054 , so the sum of the number is divisible by 23 ?

Explanation: "( 1054 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."

multiply(subtract(add(const_1, floor(divide(1054, 23))), divide(1054, 23)), 23)

<gadget id="calculator">1_054 / 23</gadget>
<output>1_054/23 = around 45.826087</output>
<gadget id="calculator">floor(1_054/23)</gadget>
<output>45</output>
<gadget id="calculator">1 + 45</gadget>
<output>46</output>
<gadget id="calculator">46 - (1_054/23)</gadget>
<output>4/23 = around 0.173913</output>
<gadget id="calculator">(4/23) * 23</gadget>
<output>4</output>
<result>4</result>


two bullet trains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

Explanation: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 12 m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = 22 m / sec . required time = ( 120 + 120 ) / 22 sec = 11 sec . a"

<gadget id="calculator">120 + 120</gadget>
<output>240</output>
<gadget id="calculator">120 / 10</gadget>
<output>12</output>
<gadget id="calculator">120 / 12</gadget>
<output>10</output>
<gadget id="calculator">12 + 10</gadget>
<output>22</output>
<gadget id="calculator">240 / 22</gadget>
<output>120/11 = around 10.909091</output>
<result>120/11 = around 10.909091</result>


70 % of x is greater than 1 / 3 rd of x by 110 . what is x ?

Explanation: "7 x / 10 - x / 3 = 110 11 x / 30 = 110 x = 300 answer : c"

divide(110, subtract(divide(70, const_100), divide(1, 3)))

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(7/10) - (1/3)</gadget>
<output>11/30 = around 0.366667</output>
<gadget id="calculator">110 / (11/30)</gadget>
<output>300</output>
<result>300</result>


in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?

Explanation: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 80 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 80 = > total appeared candidates in state b = 80 x 100 = 8000 = > total appeared candidates in state a = total appeared candidates in state b = 8000"

divide(80, divide(subtract(7, 6), const_100))

<gadget id="calculator">7 - 6</gadget>
<output>1</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">80 / (1/100)</gadget>
<output>8_000</output>
<result>8_000</result>


the sector of a circle has perimeter of 144 cm and central angle 180 o . find its radius ?

Explanation: "let the radius is x cm perimeter of the sector = length of the arc + 2 ( radius ) 144 = ( 180 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 144 = 22 x / 7 + 2 x 144 = 36 x / 7 36 x = 1008 x = 28 answer : d"

divide(144, add(divide(multiply(multiply(const_2, divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), 180), divide(const_3600, const_10)), const_2))

<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">2 * (22/7)</gadget>
<output>44/7 = around 6.285714</output>
<gadget id="calculator">(44/7) * 180</gadget>
<output>7_920/7 = around 1_131.428571</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">(7_920/7) / 360</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) + 2</gadget>
<output>36/7 = around 5.142857</output>
<gadget id="calculator">144 / (36/7)</gadget>
<output>28</output>
<result>28</result>


the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is ?

Explanation: "area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d"

multiply(subtract(multiply(multiply(2, add(10, 7)), 5), add(add(multiply(2, 3), multiply(2, 1.5)), multiply(2, 1.5))), 3)

<gadget id="calculator">10 + 7</gadget>
<output>17</output>
<gadget id="calculator">2 * 17</gadget>
<output>34</output>
<gadget id="calculator">34 * 5</gadget>
<output>170</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * 1.5</gadget>
<output>3</output>
<gadget id="calculator">6 + 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">170 - 12</gadget>
<output>158</output>
<gadget id="calculator">158 * 3</gadget>
<output>474</output>
<result>474</result>


ravi and kavi start a business by investing â ‚ ¹ 2000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .

Explanation: "ratio of profit = ratio of investments = 2000 : 72000 = 1 : 36 answer : d"

<gadget id="calculator">2_000 / 72_000</gadget>
<output>1/36 = around 0.027778</output>
<result>1/36 = around 0.027778</result>


the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 125 ) = rs . 800 . answer : e"

divide(1000, add(const_1, divide(25, const_100)))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1_000 / (5/4)</gadget>
<output>800</output>
<result>800</result>


john makes $ 60 a week from his job . he earns a raise and now makes $ 100 a week . what is the % increase ?

Explanation: "increase = ( 40 / 60 ) * 100 = ( 4 / 6 ) * 100 = 66.67 % . b"

multiply(divide(subtract(100, 60), 60), const_100)

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>


a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 153 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?

Explanation: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 153 = > . 1 x + 3 / 4 x = 153 = > x = 180 180 - 153 = pure gala = 27 . d"

subtract(divide(153, add(divide(10, const_100), divide(3, 4))), 153)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/10) + (3/4)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">153 / (17/20)</gadget>
<output>180</output>
<gadget id="calculator">180 - 153</gadget>
<output>27</output>
<result>27</result>


a cistern 5 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :

Explanation: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 5 x 1.25 ) + 5 x 4 ] m 2 = 42.5 m 2 . answer : option b"

add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 4), multiply(add(divide(25, const_100), 1), 5))), multiply(4, 5))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 4</gadget>
<output>5</output>
<gadget id="calculator">(5/4) * 5</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">5 + (25/4)</gadget>
<output>45/4 = around 11.25</output>
<gadget id="calculator">2 * (45/4)</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">(45/2) + 20</gadget>
<output>85/2 = around 42.5</output>
<result>85/2 = around 42.5</result>


a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 63 , what is the total amount ?

Explanation: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 63 39 - - - ? = > 273 answer : b"

add(add(multiply(divide(const_100, 45), 63), multiply(divide(50, 45), 63)), 63)

<gadget id="calculator">100 / 45</gadget>
<output>20/9 = around 2.222222</output>
<gadget id="calculator">(20/9) * 63</gadget>
<output>140</output>
<gadget id="calculator">50 / 45</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">(10/9) * 63</gadget>
<output>70</output>
<gadget id="calculator">140 + 70</gadget>
<output>210</output>
<gadget id="calculator">210 + 63</gadget>
<output>273</output>
<result>273</result>


Explanation: 1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 b

divide(1, add(3, divide(1, add(3, divide(1, subtract(3, divide(1, 3)))))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">3 - (1/3)</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">1 / (8/3)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">3 + (3/8)</gadget>
<output>27/8 = around 3.375</output>
<gadget id="calculator">1 / (27/8)</gadget>
<output>8/27 = around 0.296296</output>
<gadget id="calculator">3 + (8/27)</gadget>
<output>89/27 = around 3.296296</output>
<gadget id="calculator">1 / (89/27)</gadget>
<output>27/89 = around 0.303371</output>
<result>27/89 = around 0.303371</result>


if a - b = 5 and a 2 + b 2 = 31 , find the value of ab .

Explanation: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 31 - 25 = 6 ab = 3 . answer : c"

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">31 - 25</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<result>3</result>


if circles x and y have the same area and circle x has a circumference of 18 π , half of the radius of circle y is :

Explanation: "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 18 * pi x = 9 thus y = 9 y / 2 = 4.5 ans : b"

<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>


the present population of a town is 2000 . population increase rate is 20 % p . a . find the population of town after 1 years ?

Explanation: "p = 2000 r = 20 % required population of town = p ( 1 + r / 100 ) ^ t = 2000 ( 1 + 20 / 100 ) = 2000 ( 6 / 5 ) = 2400 answer is b"

<gadget id="calculator">2_000 * 20</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">2_000 + 400</gadget>
<output>2_400</output>
<result>2_400</result>


the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 490 , krishan has ?

Explanation: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 490 : n & there n = 289 x 490 / 49 = rs . 2890 answer : a"

multiply(divide(multiply(divide(490, 7), 17), 7), 17)

<gadget id="calculator">490 / 7</gadget>
<output>70</output>
<gadget id="calculator">70 * 17</gadget>
<output>1_190</output>
<gadget id="calculator">1_190 / 7</gadget>
<output>170</output>
<gadget id="calculator">170 * 17</gadget>
<output>2_890</output>
<result>2_890</result>


by selling an article for $ 195 , a person gains $ 45 . what is the gain % ?

Explanation: s . p . = $ 195 gain = $ 45 c . p . = 195 - 45 = 150 gain % = 45 / 150 * 100 % = 30 % answer is b

divide(multiply(45, const_100), subtract(195, 45))

<gadget id="calculator">45 * 100</gadget>
<output>4_500</output>
<gadget id="calculator">195 - 45</gadget>
<output>150</output>
<gadget id="calculator">4_500 / 150</gadget>
<output>30</output>
<result>30</result>


by selling an article at rs . 600 , a profit of 60 % is made . find its cost price ?

Explanation: "sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 60 ) ] = 600 * [ 100 / 160 ] = rs . 375 answer : c"

divide(multiply(600, const_100), add(const_100, 60))

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>
<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">60_000 / 160</gadget>
<output>375</output>
<result>375</result>


ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the number .

Explanation: solution : let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y . . . . . . . ( 1 ) 10 x + y + 18 = 10 y + x . . . . ( 2 ) solving 1 st equation we get 2 x - y = 1 . . . . . ( 3 ) solving 2 nd equation we get y - x = 2 . . . . . ( 4 ) solving 3 and 4 , we get x = 3 and y = 5 answer : b

<gadget id="calculator">18 - 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<result>5</result>


how many 3 - digit integers between 311 and 401 , exclusive , are divisible by 3 when the tens digit and the hundered digit are switched ?

Explanation: answer is 30 no of digits between 311 and 401 ( exclusive ) = 401 - 311 - 1 = 89 no intergers divisble by 3 = ~ 89 / 3 ~ 30 divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . e . g 372 is divisble by 3 ( becae 3 + 7 + 2 = 12 ( divisble by 3 ) ) switch digits 732 also divisble by 3 ( becae 7 + 3 + 2 = 12 ( divisble by 3 ) ) divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . you have right . so it is enough to proceed like usual to find the numbers in a given range that are divisible by 3 . so 399 - 312 / 3 + 1 = 30 . answer : a

<gadget id="calculator">401 - 311</gadget>
<output>90</output>
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<result>30</result>


the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintain the original area ?

Explanation: "sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28.2 % c"

multiply(divide(subtract(const_1, divide(subtract(const_100, 22), const_100)), divide(subtract(const_100, 22), const_100)), const_100)

<gadget id="calculator">100 - 22</gadget>
<output>78</output>
<gadget id="calculator">78 / 100</gadget>
<output>39/50 = around 0.78</output>
<gadget id="calculator">1 - (39/50)</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">(11/50) / (39/50)</gadget>
<output>11/39 = around 0.282051</output>
<gadget id="calculator">(11/39) * 100</gadget>
<output>1_100/39 = around 28.205128</output>
<result>1_100/39 = around 28.205128</result>


a car drives 60 miles on local roads at 20 mph , and 195 miles on the highway at 65 mph , what is the average speed of the entire trip ?

Explanation: "so the answer is plainly d . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 195 to 65 to find the needed time to cover 195 miles , so t = 3 hours so the total time for covering total distance would be 3 + 3 = 6 hours and total distance is 60 + 195 = 255 miles final stage : average speed is total distance divide to total time : 255 / 6 = 42.5 miles per hour rounded up to 43 mph . . . ."

<gadget id="calculator">60 + 195</gadget>
<output>255</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<gadget id="calculator">195 / 65</gadget>
<output>3</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">255 / 6</gadget>
<output>85/2 = around 42.5</output>
<result>85/2 = around 42.5</result>


if x > 3000 , then the value of ( 1.2 x ) / ( 0.5 x - 406 ) is closest to ?

Explanation: assume x = 3002 ( 1.2 x ) / ( 0.5 x - 406 ) = 3602.4 / ( 3002 * 0.5 - 406 ) = 3602.4 / 1095 = = 3 / 1 e

<gadget id="calculator">2 - 0.5</gadget>
<output>1.5</output>
<gadget id="calculator">1.5 * 2</gadget>
<output>3</output>
<result>3</result>


a train passes a platform in 32 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is

Explanation: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 32 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 32 = > 300 + l = 15 × 32 = 480 = > l = 480 - 300 = 180 meter answer : option a"

multiply(multiply(const_0_2778, 54), subtract(32, 20))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<gadget id="calculator">32 - 20</gadget>
<output>12</output>
<gadget id="calculator">15 * 12</gadget>
<output>180</output>
<result>180</result>


the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % ?

Explanation: c 37.5 % let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 88 gain % = 24 / 64 * 100 = 37.5 % .

multiply(subtract(multiply(divide(const_100, 64), divide(subtract(const_100, 12), const_100)), const_1), const_100)

<gadget id="calculator">100 / 64</gadget>
<output>25/16 = around 1.5625</output>
<gadget id="calculator">100 - 12</gadget>
<output>88</output>
<gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">(25/16) * (22/25)</gadget>
<output>11/8 = around 1.375</output>
<gadget id="calculator">(11/8) - 1</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>


3 numbers are in the ratio 3 : 5 : 7 . the largest number value is 70 . find difference between smallest & largest number is ?

Explanation: = = 3 : 5 : 7 total parts = 15 = the largest number value is 70 = the largest number is = 7 = then 7 parts - - - - - > 70 ( 7 * 10 = 70 ) = smallest number = 3 & largest number = 7 = difference between smallest number & largest number is = 7 - 3 = 4 = then 4 parts - - - - - > 40 ( 4 * 10 = 40 ) a

subtract(70, multiply(divide(70, 7), 3))

<gadget id="calculator">70 / 7</gadget>
<output>10</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">70 - 30</gadget>
<output>40</output>
<result>40</result>


in a 80 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :

Explanation: "b runs 56 m in 7 sec . = > b runs 80 m in 7 / 56 * 80 = 10 seconds since a beats b by 7 seconds , a runs 80 m in ( 10 - 7 ) = 3 seconds hence , a ' s time over the course = 3 seconds answer : a"

subtract(multiply(divide(7, 56), 80), 7)

<gadget id="calculator">7 / 56</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 80</gadget>
<output>10</output>
<gadget id="calculator">10 - 7</gadget>
<output>3</output>
<result>3</result>


there are 5 people who can build 5 houses in just 5 days . increase the amount of people to 100 . how long would it take these 100 people to build 100 houses ?

Explanation: it will take 5 days for 100 people to build 100 houses . 1 person can build 1 house in 5 days . so , 100 people can build 100 houses in 5 days . answer d

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


the smallest number which when diminished by 2 , is divisible by 12 , 16 , 18 , 21 and 28 is

Explanation: required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 2 = 1008 + 2 = 1010 answer : b

add(multiply(multiply(power(const_3, 2), power(2, const_4)), add(const_3, const_4)), const_2)

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">9 * 16</gadget>
<output>144</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">144 * 7</gadget>
<output>1_008</output>
<gadget id="calculator">1_008 + 2</gadget>
<output>1_010</output>
<result>1_010</result>


45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours ?

Explanation: "45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers the answer is d ."

subtract(multiply(multiply(45, divide(8, 6)), divide(55, 30)), 45)

<gadget id="calculator">8 / 6</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">45 * (4/3)</gadget>
<output>60</output>
<gadget id="calculator">55 / 30</gadget>
<output>11/6 = around 1.833333</output>
<gadget id="calculator">60 * (11/6)</gadget>
<output>110</output>
<gadget id="calculator">110 - 45</gadget>
<output>65</output>
<result>65</result>


in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 12 feet between each tree . how many trees can be planted if the road is 157 feet long ?

Explanation: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 12 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 12 feet spaces will be t - 1 . then , the length of sidewalk required for 12 feet spaces will be 12 * ( t - 1 ) it is given that total lenght of sidewalk is 157 feet . or 12 ( t - 1 ) + t = 157 or 12 t - 12 + t = 157 or 13 t = 169 or t = 13 answer : - e"

add(divide(subtract(157, const_1), add(12, const_1)), const_1)

<gadget id="calculator">157 - 1</gadget>
<output>156</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">156 / 13</gadget>
<output>12</output>
<result>13</result>


a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 150 m long ?

Explanation: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 150 = 510 meter time taken to cross the platform = 510 / ( 25 / 2 ) = 510 ã — 2 / 25 = 40.8 seconds answer : d"

multiply(divide(add(divide(150, const_1000), divide(360, const_1000)), 45), const_3600)

<gadget id="calculator">150 / 1_000</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">360 / 1_000</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(3/20) + (9/25)</gadget>
<output>51/100 = around 0.51</output>
<gadget id="calculator">(51/100) / 45</gadget>
<output>17/1_500 = around 0.011333</output>
<gadget id="calculator">(17/1_500) * 3_600</gadget>
<output>204/5 = around 40.8</output>
<result>204/5 = around 40.8</result>


two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 7 . find the probability that both of them are selected .

Explanation: explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 7 ) = 2 / 21 answer : b ) 2 / 21

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(1/3) * (2/7)</gadget>
<output>2/21 = around 0.095238</output>
<result>2/21 = around 0.095238</result>


a box contains 22 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is

Explanation: "solution p ( none is defective ) = 18 c 2 / 22 c 2 = 51 / 77 p ( at least one is defective ) = ( 1 - 51 / 77 ) = 26 / 77 . answer e"

subtract(const_1, divide(choose(subtract(22, 4), const_2), choose(22, const_2)))

<gadget id="calculator">22 - 4</gadget>
<output>18</output>
<gadget id="calculator">binomial(18, 2)</gadget>
<output>153</output>
<gadget id="calculator">binomial(22, 2)</gadget>
<output>231</output>
<gadget id="calculator">153 / 231</gadget>
<output>51/77 = around 0.662338</output>
<gadget id="calculator">1 - (51/77)</gadget>
<output>26/77 = around 0.337662</output>
<result>26/77 = around 0.337662</result>


the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 8 times the probability that both events a and b occur . what is the probability that event a occurs ?

Explanation: "let us say probability of a occurring is a . let us say probability of b occurring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 8 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 8 * 2 b * b 3 b - 2 b ^ 2 = 16 b ^ 2 3 b = 18 b ^ 2 b = 3 / 18 = 1 / 6 so , a = 2 b = 1 / 3 answer : d"

multiply(divide(add(const_2, const_1), add(multiply(8, const_2), const_2)), const_2)

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<gadget id="calculator">3 / 18</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 2</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


if - 2 and - 3 are negative integers , then - 2 * - 3 + 2 is

Explanation: answer : b

<gadget id="calculator">-2</gadget>
<output>-2</output>
<gadget id="calculator">-3</gadget>
<output>-3</output>
<gadget id="calculator">(-2) * (-3)</gadget>
<output>6</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<result>8</result>


a can give b 50 meters start and c 100 meters start in a kilometer race . how much start can b give c in a kilometer race ?

Explanation: "a runs 1000 m while b runs 950 m and c runs 900 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 900 ) / 950 = 947.37 m . b can give c = 1000 - 947.37 = 52.63 m . answer : d"

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 100)), subtract(multiply(const_100, const_10), 50)))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>
<gadget id="calculator">1_000 * 900</gadget>
<output>900_000</output>
<gadget id="calculator">1_000 - 50</gadget>
<output>950</output>
<gadget id="calculator">900_000 / 950</gadget>
<output>18_000/19 = around 947.368421</output>
<gadget id="calculator">1_000 - (18_000/19)</gadget>
<output>1_000/19 = around 52.631579</output>
<result>1_000/19 = around 52.631579</result>


how many seconds will a 800 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?

Explanation: "explanation : here distance d = 800 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = 800 x 18 / 60 x 5 = 48 sec . answer is a"

divide(800, multiply(subtract(63, 3), const_0_2778))

<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">800 / (50/3)</gadget>
<output>48</output>
<result>48</result>


if a - b = 8 and a ^ 2 + b ^ 2 = 164 , find the value of ab

Explanation: 2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 164 - 64 = 100 = > ab = 50 answer : c

multiply(multiply(add(8, divide(subtract(sqrt(164), 8), 2)), divide(subtract(sqrt(164), 8), 2)), 2)

<gadget id="calculator">164 ** (1/2)</gadget>
<output>2*sqrt(41) = around 12.806248</output>
<gadget id="calculator">(2*sqrt(41)) - 8</gadget>
<output>-8 + 2*sqrt(41) = around 4.806248</output>
<gadget id="calculator">(-8 + 2*sqrt(41)) / 2</gadget>
<output>-4 + sqrt(41) = around 2.403124</output>
<gadget id="calculator">8 + (-4 + sqrt(41))</gadget>
<output>4 + sqrt(41) = around 10.403124</output>
<gadget id="calculator">(4 + sqrt(41)) * (-4 + sqrt(41))</gadget>
<output>(-4 + sqrt(41))*(4 + sqrt(41)) = around 25</output>
<gadget id="calculator">((-4 + sqrt(41))*(4 + sqrt(41))) * 2</gadget>
<output>2*(-4 + sqrt(41))*(4 + sqrt(41)) = around 50</output>
<result>2*(-4 + sqrt(41))*(4 + sqrt(41)) = around 50</result>


a sum fetched a total simple interest of rs . 929.20 at the rate of 8 p . c . p . a . in 5 years . what is the sum ?

Explanation: "explanation : si = rs . 929.20 p = ? t = 5 years r = 8 % p = 100 × si / rt = 100 × 929.20 / 8 × 5 = rs . 2323 answer : option a"

divide(divide(multiply(929.20, const_100), 8), 5)

<gadget id="calculator">929.2 * 100</gadget>
<output>92_920</output>
<gadget id="calculator">92_920 / 8</gadget>
<output>11_615</output>
<gadget id="calculator">11_615 / 5</gadget>
<output>2_323</output>
<result>2_323</result>


Explanation: "? % of 360 = 151.2 or , ? = 151.2 × 100 / 360 = 42 answer a"

<gadget id="calculator">151.2 * 100</gadget>
<output>15_120</output>
<gadget id="calculator">15_120 / 360</gadget>
<output>42</output>
<result>42</result>


the radius of a wheel is 22.5 cm . what is the distance covered by the wheel in making 500 resolutions ?

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.5 = 70714 cm = 707.14 m answer : b"

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.5), const_2), 500), const_100)

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) * 22.5</gadget>
<output>70.714286</output>
<gadget id="calculator">70.714286 * 2</gadget>
<output>141.428572</output>
<gadget id="calculator">141.428572 * 500</gadget>
<output>70_714.286</output>
<gadget id="calculator">70_714.286 / 100</gadget>
<output>707.14286</output>
<result>707.14286</result>


how many cubes of 10 cm edge can be put in a cubical box of 1 m edge ?

Explanation: "sol . number of cubes = [ 100 * 100 * 100 / 10 * 10 * 10 ] = 1000 . answer d"

<gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) ** 3</gadget>
<output>1/1_000 = around 0.001</output>
<gadget id="calculator">1 / (1/1_000)</gadget>
<output>1_000</output>
<result>1_000</result>


12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required ?

Explanation: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 10 = 8 days . a )"

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

<gadget id="calculator">12 * 10</gadget>
<output>120</output>
<gadget id="calculator">120 * 8</gadget>
<output>960</output>
<gadget id="calculator">8 * 15</gadget>
<output>120</output>
<gadget id="calculator">960 / 120</gadget>
<output>8</output>
<result>8</result>


if a man lost 10 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?

Explanation: 90 % - - - - 12 144 % - - - - ? 90 / 144 * 12 = 7.50 answer : b

divide(multiply(subtract(const_100, 10), 12), add(const_100, 44))

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 12</gadget>
<output>1_080</output>
<gadget id="calculator">100 + 44</gadget>
<output>144</output>
<gadget id="calculator">1_080 / 144</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>


jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

Explanation: "explanation : indian stamps are common to both ratios . multiply both ratios by factors such that the indian stamps are represented by the same number . us : indian = 5 : 2 , and indian : british = 5 : 1 . multiply the first by 5 , and the second by 2 . hence the two ratios can be combined and us : british = 25 : 2 now us : indian = 25 : 10 , and indian : british = 10 : 2 answer : d"

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


a canteen requires 13 dozen bananas per day . how many bananas will it require for 9 weeks ?

Explanation: requirement of bananas for 1 day in the canteen = 13 dozens ∴ requirement of bananas for 9 weeks i . e . 63 days = 63 × 13 dozens = 63 × 13 × 12 = 9828 . answer d

multiply(multiply(13, multiply(9, add(const_3, const_4))), multiply(const_3, const_4))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">9 * 7</gadget>
<output>63</output>
<gadget id="calculator">13 * 63</gadget>
<output>819</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">819 * 12</gadget>
<output>9_828</output>
<result>9_828</result>


an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 11 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?

Explanation: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 11 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 3300 . hence , ( r - p ) = ( 3300 - 900 ) = 2400 answer : e"

multiply(divide(1500, 5), subtract(11, 3))

<gadget id="calculator">1_500 / 5</gadget>
<output>300</output>
<gadget id="calculator">11 - 3</gadget>
<output>8</output>
<gadget id="calculator">300 * 8</gadget>
<output>2_400</output>
<result>2_400</result>


a shipment of 230 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?

Explanation: "probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = ( 84 / 230 ) probability of chosing one defective phone from a lot of 229 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 229 ) combined probability of series of events = product of the probabilities = ( 84 / 230 ) * ( 83 / 229 ) 84 / 230 is close to ( 23 / 63 ) and ( 83 / 229 ) = ( 29 / 80 ) so answer is ( 23 / 63 ) * ( 29 / 80 ) = ( 9 / 68 ) so , answer will be d"

divide(multiply(84, subtract(84, const_1)), multiply(230, subtract(230, const_1)))

<gadget id="calculator">84 - 1</gadget>
<output>83</output>
<gadget id="calculator">84 * 83</gadget>
<output>6_972</output>
<gadget id="calculator">230 - 1</gadget>
<output>229</output>
<gadget id="calculator">230 * 229</gadget>
<output>52_670</output>
<gadget id="calculator">6_972 / 52_670</gadget>
<output>3_486/26_335 = around 0.132371</output>
<result>3_486/26_335 = around 0.132371</result>


a large box contains 20 small boxes and each small box contains 32 chocolate bars . how many chocolate bars are in the large box ?

Explanation: "the only thing you have to do is a simple multiply we have : 20 * 32 = 640 correct answer is : e ) 640"

<gadget id="calculator">20 * 32</gadget>
<output>640</output>
<result>640</result>


in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25000 votes how many votes did candidate x received ?

Explanation: z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b .

multiply(multiply(add(const_1, divide(1, 2)), subtract(const_1, divide(2, 5))), 25000)

<gadget id="calculator">1 / 2</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">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/2) * (3/5)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * 25_000</gadget>
<output>22_500</output>
<result>22_500</result>


a train 800 m long can cross a pole in 10 sec and then find the speed of the train ?

Explanation: "length = speed * time speed = l / t s = 800 / 10 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 288 kmph answer : e"

divide(divide(800, const_1000), divide(10, const_3600))

<gadget id="calculator">800 / 1_000</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">10 / 3_600</gadget>
<output>1/360 = around 0.002778</output>
<gadget id="calculator">(4/5) / (1/360)</gadget>
<output>288</output>
<result>288</result>


a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is two times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?

Explanation: water : soap = 3 : 2 soap : salt = 6 : 2 = > for 6 soap , salt = 2 = > for 2 soap , salt = ( 2 / 6 ) * 2 = 2 / 3 so , water : soap : salt = 3 : 2 : 2 / 3 = 18 : 12 : 4 after open container , water : soap : salt = 9 : 18 : 4 so , water : salt = 9 : 4 = 18 : 8 e

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

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">18 / 8</gadget>
<output>9/4 = around 2.25</output>
<result>9/4 = around 2.25</result>


a string of 30 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.1 , what is the probability that the string of light bulbs will fail during the time period t ?

Explanation: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 30 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.1 = 0.90 the the probability that none of the 30 light bulbs fails is 0.90 ^ 30 . hence , the probability that at least one light bulb fails is 1 - 0.90 ^ 30 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 30 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.1 = 10 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."

subtract(const_1, power(subtract(const_1, 0.1), 30))

<gadget id="calculator">1 - 0.1</gadget>
<output>0.9</output>
<gadget id="calculator">0.9 ** 30</gadget>
<output>0.042391</output>
<gadget id="calculator">1 - 0.042391</gadget>
<output>0.957609</output>
<result>0.957609</result>


for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?

Explanation: from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive there are 8 * 12 = 96 five - minute intervals , thus total of 96 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 96 * 30 - - > x = 24 * 30 and 3 x = 3 * ( 24 * 30 ) = 24 * 90 . therefore , the total revenue from ticket sales that day was 24 * 30 * 6 + 24 * 90 * 10 = $ 25,920 . answer : b .

add(multiply(multiply(divide(multiply(multiply(add(subtract(add(const_12, const_4), 9), const_1), const_12), 30), add(3, const_1)), 3), 10), multiply(divide(multiply(multiply(add(subtract(add(const_12, const_4), 9), const_1), const_12), 30), add(3, const_1)), 6))

<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">16 - 9</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">96 * 30</gadget>
<output>2_880</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">2_880 / 4</gadget>
<output>720</output>
<gadget id="calculator">720 * 3</gadget>
<output>2_160</output>
<gadget id="calculator">2_160 * 10</gadget>
<output>21_600</output>
<gadget id="calculator">720 * 6</gadget>
<output>4_320</output>
<gadget id="calculator">21_600 + 4_320</gadget>
<output>25_920</output>
<result>25_920</result>


during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 105 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?

Explanation: "easy 280 is the answer . 3 / 4 ( x / 2 ) = 105 x = 105 * 8 / 3 = 280 . answer a"

divide(105, subtract(1, add(divide(1, 2), multiply(divide(1, 2), divide(1, 4)))))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) * (1/4)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/2) + (1/8)</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">105 / (3/8)</gadget>
<output>280</output>
<result>280</result>


if 2 / 3 rd of the contents of a container evaporated on the 1 st day . and 1 / 4 th of the remaining evaporated on the second day . what part of the contents of the container is left at the end of the second day ?

Explanation: after first day , 1 / 3 of the contents remain . after second day , ( 1 / 3 ) - ( 1 / 4 ( 2 / 3 ) ) = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 of the contents remain answer : d

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

<gadget id="calculator">4 * 1</gadget>
<output>4</output>
<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/4) * (2/3)</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


the average of first 7 prime numbers is ?

Explanation: "sum of 7 prime no . = 58 average = 58 / 7 = 8.29 answer : c"

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


in a group of 28 junior high school students , 5 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?

Explanation: b 13 add 1 + 10 + 4 to get 15 . then subtract 21 from the total students ⇒ 28 – 15 = 13 . answer is b

<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">28 - 15</gadget>
<output>13</output>
<result>13</result>


a , b , c can complete a piece of work in 3,9 and 15 days respectively . working together , they will complete the same work in how many days ?

Explanation: ( a + b + c ) ' s 1 day work = ( 1 / 3 ) + ( 1 / 9 ) + ( 1 / 115 ) = 23 / 45 a , b , c together will complete the work in 45 / 23 days answer is a

inverse(add(inverse(15), add(inverse(const_3), inverse(add(add(const_4, const_4), const_1)))))

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/3) + (1/9)</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">(1/15) + (4/9)</gadget>
<output>23/45 = around 0.511111</output>
<gadget id="calculator">1 / (23/45)</gadget>
<output>45/23 = around 1.956522</output>
<result>45/23 = around 1.956522</result>


in a group of cows and chickens , the number of legs was 12 more than twice the number of heads . the number of cows was :

Explanation: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 12 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 12 = 4 x + 2 y . or , 2 x + 12 = 4 x [ subtracting 2 y from both sides ] . or , 12 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 12 = 2 x . or , x = 6 [ dividing by 2 on both sides ] . therefore , the number of cows = 6 . correct answer : a ) 6"

<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>6</result>


a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?

Explanation: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 320 ) / 320 ] x 100 65 / 320 x 100 13 / 64 x 100 ≈ 13 / 65 x 100 ≈ 1 / 5 x 100 ≈ 20 % . the answer is c ."

multiply(divide(subtract(385, 320), 320), const_100)

<gadget id="calculator">385 - 320</gadget>
<output>65</output>
<gadget id="calculator">65 / 320</gadget>
<output>13/64 = around 0.203125</output>
<gadget id="calculator">(13/64) * 100</gadget>
<output>325/16 = around 20.3125</output>
<result>325/16 = around 20.3125</result>


if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab .

Explanation: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 ab = 10 . b )"

multiply(multiply(add(3, divide(subtract(sqrt(29), 3), 2)), divide(subtract(sqrt(29), 3), 2)), 2)


students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 182 cms . what was the ratio of men to women ?

Explanation: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 182 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 182 m ) / ( w + m ) = 180 170 w + 182 m = 180 w + 180 m 2 m = 10 w m = 5 w m / w = 5 / 1 the ratio of men to women is 5 to 1 . b"

divide(subtract(180, 170), subtract(182, 180))

<gadget id="calculator">180 - 170</gadget>
<output>10</output>
<gadget id="calculator">182 - 180</gadget>
<output>2</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 400 , by what percent is the price to be reduced ?

Explanation: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 400 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 400 ) * 100 / 500 = 80 % answer : option e"

<gadget id="calculator">400 / 500</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>


jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the number ' s sum will be 13 ?

Explanation: both dice addition result is 13 = ( 6 + 7 ) probability that the number on first die is 6 = 1 / 6 probability that the number on second die is 7 = 1 / 7 probability that both dice addition result is 13 = 1 / 6 * 1 / 7 = 1 / 42 d

multiply(divide(const_1, 6), divide(1, 7))

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/6) * (1/7)</gadget>
<output>1/42 = around 0.02381</output>
<result>1/42 = around 0.02381</result>


if a = 105 and a ^ 3 = 21 * 25 * 315 * b , what is the value of b ?

Explanation: first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 315 = 3 * 3 * 5 * 7 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 3 * 5 * 7 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 3 * 7 ^ 2 b = 7 correct answer b .

divide(power(105, 3), multiply(multiply(21, 25), 315))

<gadget id="calculator">105 ** 3</gadget>
<output>1_157_625</output>
<gadget id="calculator">21 * 25</gadget>
<output>525</output>
<gadget id="calculator">525 * 315</gadget>
<output>165_375</output>
<gadget id="calculator">1_157_625 / 165_375</gadget>
<output>7</output>
<result>7</result>


boy sells a book for rs . 540 he gets a loss of 10 % , to gain 10 % , what should be the sp ?

Explanation: "cost price = 540 / 90 x 100 = 600 to gain 10 % = 600 x 10 / 100 = 60 sp = cp + gain = 600 + 60 = 660 answer : e"

add(divide(540, subtract(const_1, divide(10, const_100))), multiply(divide(540, subtract(const_1, divide(10, const_100))), divide(10, const_100)))

<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">540 / (9/10)</gadget>
<output>600</output>
<gadget id="calculator">600 * (1/10)</gadget>
<output>60</output>
<gadget id="calculator">600 + 60</gadget>
<output>660</output>
<result>660</result>


xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?

Explanation: "p ( xavier will solve ) = 1 / 3 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 3 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 16 . ans . a ."

multiply(multiply(divide(1, 3), divide(1, 2)), subtract(1, divide(5, 8)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/3) * (1/2)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(1/6) * (3/8)</gadget>
<output>1/16 = around 0.0625</output>
<result>1/16 = around 0.0625</result>


if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers i

Explanation: "sol . 0.2 a = 0.08 b â ‡ ” a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 â ˆ ´ a : b = 2 : 5 . answer b"

divide(multiply(0.08, const_100), multiply(0.2, const_100))

<gadget id="calculator">0.08 * 100</gadget>
<output>8</output>
<gadget id="calculator">0.2 * 100</gadget>
<output>20</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>


a person want to give his money of $ 1800 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?

Explanation: "b ' s share = 1800 * 3 / 9 = $ 600 answer is b"

multiply(divide(3, add(add(2, 3), 4)), 1800)

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 1_800</gadget>
<output>600</output>
<result>600</result>


in what time will a train 240 metres long cross an electric pole , if its speed be 126 km / hr ?

Explanation: "solution speed = ( 126 x 5 / 18 ) m / sec = 35 m / sec time taken = ( 240 / 35 ) sec = 6.85 sec . answer b"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">126 * (5/18)</gadget>
<output>35</output>
<gadget id="calculator">240 / 35</gadget>
<output>48/7 = around 6.857143</output>
<result>48/7 = around 6.857143</result>


a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 7 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?

Explanation: correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.07 ( $ 1120 ) = $ 78.40 . the correct answer is b .

divide(multiply(subtract(1720, 600), 7), const_100)

<gadget id="calculator">1_720 - 600</gadget>
<output>1_120</output>
<gadget id="calculator">1_120 * 7</gadget>
<output>7_840</output>
<gadget id="calculator">7_840 / 100</gadget>
<output>392/5 = around 78.4</output>
<result>392/5 = around 78.4</result>


how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 200 m in length ?

Explanation: "a 18.6 sec d = 110 + 200 = 310 m s = 60 * 5 / 18 = 50 / 3 t = 310 * 3 / 50 = 18.6 sec answer is a"

<gadget id="calculator">110 + 200</gadget>
<output>310</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">310 / (50/3)</gadget>
<output>93/5 = around 18.6</output>
<result>93/5 = around 18.6</result>


excepting ‘ seldom ’ which means – rarely , infrequently and not often , is the antonym .

Explanation: answer : d

add(const_100, add(multiply(add(const_3, const_4), const_10), add(const_3, const_3)))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">70 + 6</gadget>
<output>76</output>
<gadget id="calculator">100 + 76</gadget>
<output>176</output>
<result>176</result>


two pipes a and b can fill a tank in 24 minutes and 32 minutes respectively . if both the pipes are opened simultaneously , after how much time should b be closed so that the tank is full in 18 minutes ?

Explanation: pipe a will work for 18 minutes . suppose pipe b is closed after x minutes than we have 18 / 24 + x / 32 = 1 x = 8 minute . answer : d

multiply(subtract(const_1, multiply(divide(const_1, 24), 18)), 32)

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/24) * 18</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 32</gadget>
<output>8</output>
<result>8</result>


the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?

Explanation: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"

floor(divide(add(subtract(multiply(35, 181), 166), 106), 35))

<gadget id="calculator">35 * 181</gadget>
<output>6_335</output>
<gadget id="calculator">6_335 - 166</gadget>
<output>6_169</output>
<gadget id="calculator">6_169 + 106</gadget>
<output>6_275</output>
<gadget id="calculator">6_275 / 35</gadget>
<output>1_255/7 = around 179.285714</output>
<gadget id="calculator">floor(1_255/7)</gadget>
<output>179</output>
<result>179</result>


in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 280 vote ’ s majority . what is the total number of votes polled ?

Explanation: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 7 = 280 ) 100 % - - - - - > 700 ( 100 * 7 = 700 ) answer : option b"

divide(multiply(const_100, 280), subtract(70, subtract(const_100, 70)))

<gadget id="calculator">100 * 280</gadget>
<output>28_000</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">70 - 30</gadget>
<output>40</output>
<gadget id="calculator">28_000 / 40</gadget>
<output>700</output>
<result>700</result>


a dishonest dealer professes to sell goods at the cost price but uses a weight of 990 grams per kg , what is his percent ?

Explanation: "990 - - - 10 100 - - - ? = > 1.01 % answer : a"

subtract(multiply(divide(const_100, 990), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

<gadget id="calculator">100 / 990</gadget>
<output>10/99 = around 0.10101</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">(10/99) * 1_000</gadget>
<output>10_000/99 = around 101.010101</output>
<gadget id="calculator">(10_000/99) - 100</gadget>
<output>100/99 = around 1.010101</output>
<result>100/99 = around 1.010101</result>