a room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles . what will be the least number of square tiles required to cover the floor ?

Explanation: "length = 5 m 44 cm = 544 cm breadth = 3 m 74 cm = 374 cm area = 544 * 374 hcf = 34 area of square = 34 * 34 cm 2 no of tiles req = 544 * 374 / 34 * 34 = 16 * 11 = 176 answer a"

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

<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 + 44</gadget>
<output>544</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">300 + 74</gadget>
<output>374</output>
<gadget id="calculator">544 * 374</gadget>
<output>203_456</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">44 - 10</gadget>
<output>34</output>
<gadget id="calculator">34 * 34</gadget>
<output>1_156</output>
<gadget id="calculator">203_456 / 1_156</gadget>
<output>176</output>
<result>176</result>


the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 , is :

Explanation: "explanation : required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"

<gadget id="calculator">54 * 10</gadget>
<output>540</output>
<result>540</result>


jonathan can type a 30 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?

Explanation: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 30 / 40 + 30 / 30 + 30 / 24 = 30 / x if you solve this equation , you get the same answer b ( 10 )"

<gadget id="calculator">30 / 24</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">30 / 40</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">30 / 30</gadget>
<output>1</output>
<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">(5/4) + (7/4)</gadget>
<output>3</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<result>10</result>


a box contains 10 tablets of medicine a and 17 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .

Explanation: "the worst case scenario will be if we remove all 17 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17 + 2 = 19 tablets . answer : d ."

<gadget id="calculator">17 + 2</gadget>
<output>19</output>
<result>19</result>


the milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )

Explanation: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 25 * 1 / 2 = 750 feet ^ 3 of milk must be removed , which equals to 750 * 7.5 = 5625 gallons . answer : d ."

multiply(multiply(multiply(60, 25), divide(1, const_2)), 7.5)

<gadget id="calculator">60 * 25</gadget>
<output>1_500</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1_500 * (1/2)</gadget>
<output>750</output>
<gadget id="calculator">750 * 7.5</gadget>
<output>5_625</output>
<result>5_625</result>


rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? .

Explanation: since jill owns 5 of the pen , the subset from which the 2 pens hould be chosen are the 2 pens not owned by jill fom the universe of 7 . the first pen can be one of the 2 from the 7 with probability 2 / 7 . the second pen can be one of the 1 from the 6 remaining with probability 1 / 6 , the total probability will be 2 / 7 × 1 / 6 . on cancellation , this comes to 2 / 42 . thus , the answer is b - 2 / 42 .

multiply(divide(subtract(7, 5), 7), divide(subtract(subtract(7, 5), const_1), subtract(7, const_1)))

<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(2/7) * (1/6)</gadget>
<output>1/21 = around 0.047619</output>
<result>1/21 = around 0.047619</result>


country x taxes each of its citizens an amount equal to 13 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?

Explanation: "equation is correct , so math must be a problem . 0.13 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,200 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,800 - - > x = 54,000 . answer : a ."

add(multiply(multiply(const_4, const_10), const_1000), divide(subtract(multiply(multiply(const_4, const_2), const_1000), multiply(divide(13, const_100), multiply(multiply(const_4, const_10), const_1000))), divide(20, const_100)))

<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">40 * 1_000</gadget>
<output>40_000</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 1_000</gadget>
<output>8_000</output>
<gadget id="calculator">13 / 100</gadget>
<output>13/100 = around 0.13</output>
<gadget id="calculator">(13/100) * 40_000</gadget>
<output>5_200</output>
<gadget id="calculator">8_000 - 5_200</gadget>
<output>2_800</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">2_800 / (1/5)</gadget>
<output>14_000</output>
<gadget id="calculator">40_000 + 14_000</gadget>
<output>54_000</output>
<result>54_000</result>


the surface of a cube is 294 sq cm . find its volume ?

Explanation: "6 a 2 = 294 = 6 * 49 a = 7 = > a 3 = 343 cc answer : d"

<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">294 / 6</gadget>
<output>49</output>
<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<gadget id="calculator">7 ** 3</gadget>
<output>343</output>
<result>343</result>


the average marks of 20 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?

Explanation: "correct avg marks = 100 + ( 10 - 50 ) / 20 avg = 100 - 2 = 98 answer is c"

divide(add(subtract(multiply(100, 20), 50), 10), 20)

<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 - 50</gadget>
<output>1_950</output>
<gadget id="calculator">1_950 + 10</gadget>
<output>1_960</output>
<gadget id="calculator">1_960 / 20</gadget>
<output>98</output>
<result>98</result>


a parking garage rents parking spaces for $ 10 per week or $ 20 per month . how much does a person save in a year by renting by the month rather than by the week ?

Explanation: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 20 = 240 $ 520 - 240 = 280 ans e"

subtract(multiply(add(multiply(10, add(const_3, const_2)), const_2), 10), multiply(20, const_12))

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">50 + 2</gadget>
<output>52</output>
<gadget id="calculator">52 * 10</gadget>
<output>520</output>
<gadget id="calculator">20 * 12</gadget>
<output>240</output>
<gadget id="calculator">520 - 240</gadget>
<output>280</output>
<result>280</result>


jerry travels 8 miles at an average speed of 40 miles per hour , stops for 14 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?

Explanation: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 14 minutes + ( 20 / 60 ) * 60 minutes = 46 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 46 / 60 ) hours = 28 * 60 / 46 = 36 miles per hour answer : option a"

<gadget id="calculator">8 + 20</gadget>
<output>28</output>
<gadget id="calculator">8 / 40</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">14 / 60</gadget>
<output>7/30 = around 0.233333</output>
<gadget id="calculator">(1/5) + (7/30)</gadget>
<output>13/30 = around 0.433333</output>
<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(13/30) + (1/3)</gadget>
<output>23/30 = around 0.766667</output>
<gadget id="calculator">28 / (23/30)</gadget>
<output>840/23 = around 36.521739</output>
<result>840/23 = around 36.521739</result>


the total surface area of a cuboid length 12 m , breadth 10 m and height 8 m .

Explanation: total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c .

<gadget id="calculator">2 * (12 * 10 + 10 * 8 + 12 * 8)</gadget>
<output>592</output>
<result>592</result>


60 boys can complete a work in 24 days . how many men need to complete twice the work in 20 days

Explanation: "one man can complete the work in 24 * 60 = 1440 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1440 m = 144 workers answer : a"

divide(multiply(60, multiply(24, const_2)), 20)

<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">60 * 48</gadget>
<output>2_880</output>
<gadget id="calculator">2_880 / 20</gadget>
<output>144</output>
<result>144</result>


jill has 21 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?

Explanation: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 21 1 3 / 4 w = 21 w = 12 the total number of jars = 3 w = 36 answer : d

multiply(divide(21, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3)

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 + (3/4)</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">21 / (7/4)</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<result>36</result>


a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 20 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?

Explanation: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 20 = rs . 185 cp on 40 metres = 185 x 40 = rs . 7400 profit earned on 40 metres cloth = rs . 8200 – rs . 7400 = rs . 800 . answer : option a"

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


24 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?

Explanation: "required number of machines = 24 * 10 / 40 = 6 answer is b"

<gadget id="calculator">24 * 10</gadget>
<output>240</output>
<gadget id="calculator">240 / 40</gadget>
<output>6</output>
<result>6</result>


in a company of 170 employees , 110 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 25 employees are males with college degree only , how many employees are females with advanced degrees ?

Explanation: the number of males is 170 - 110 = 60 . the number of males with advanced degrees is 60 - 25 = 35 . the number of females with advanced degrees is 80 - 35 = 45 . the answer is b .

subtract(80, subtract(subtract(170, 110), 25))

<gadget id="calculator">170 - 110</gadget>
<output>60</output>
<gadget id="calculator">60 - 25</gadget>
<output>35</output>
<gadget id="calculator">80 - 35</gadget>
<output>45</output>
<result>45</result>


at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 36 males did not bring gifts to the party , how many females did bring gifts ?

Explanation: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 36 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"

divide(multiply(divide(multiply(subtract(subtract(300, divide(multiply(70, 300), const_100)), 36), const_100), subtract(const_100, 40)), 40), const_100)

<gadget id="calculator">70 * 300</gadget>
<output>21_000</output>
<gadget id="calculator">21_000 / 100</gadget>
<output>210</output>
<gadget id="calculator">300 - 210</gadget>
<output>90</output>
<gadget id="calculator">90 - 36</gadget>
<output>54</output>
<gadget id="calculator">54 * 100</gadget>
<output>5_400</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">5_400 / 60</gadget>
<output>90</output>
<gadget id="calculator">90 * 40</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 / 100</gadget>
<output>36</output>
<result>36</result>


if 8 a = 9 b and ab ≠ 0 , what is the ratio of a / 9 to b / 8 ?

Explanation: "if ab ≠ 0 then a and b has two integer sets of pair if a = 9 then b = 8 and if a = - 9 then b = - 8 also in fraction if a = 1 / 8 then b = 1 / 9 any of the pair we check the ratio 8 a / 9 b = 1 answer : c"

<gadget id="calculator">8 * 9</gadget>
<output>72</output>
<gadget id="calculator">9 * 8</gadget>
<output>72</output>
<gadget id="calculator">72 / 72</gadget>
<output>1</output>
<result>1</result>


in a theater , the first row has 17 seats and each row has 3 more seats than previous row . if the last row has 44 seats , what is the total number of seats in the theater ?

Explanation: "the number of seats in the theater is 17 + ( 17 + 3 ) + . . . + ( 17 + 27 ) = 10 ( 17 ) + 3 ( 1 + 2 + . . . + 9 ) = 10 ( 17 ) + 3 ( 9 ) ( 10 ) / 2 = 170 + 135 = 305 the answer is e ."

multiply(divide(add(17, 44), const_2), divide(add(subtract(44, 17), 3), 3))

<gadget id="calculator">17 + 44</gadget>
<output>61</output>
<gadget id="calculator">61 / 2</gadget>
<output>61/2 = around 30.5</output>
<gadget id="calculator">44 - 17</gadget>
<output>27</output>
<gadget id="calculator">27 + 3</gadget>
<output>30</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<gadget id="calculator">(61/2) * 10</gadget>
<output>305</output>
<result>305</result>


the list price of an article is rs . 69 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

Explanation: "69 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 9.56 % answer : d"

multiply(divide(subtract(subtract(69, multiply(69, divide(10, const_100))), 56.16), subtract(69, multiply(69, divide(10, const_100)))), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">69 * (1/10)</gadget>
<output>69/10 = around 6.9</output>
<gadget id="calculator">69 - (69/10)</gadget>
<output>621/10 = around 62.1</output>
<gadget id="calculator">(621/10) - 56.16</gadget>
<output>5.94</output>
<gadget id="calculator">5.94 / (621/10)</gadget>
<output>0.095652</output>
<gadget id="calculator">0.095652 * 100</gadget>
<output>9.5652</output>
<result>9.5652</result>


how many seconds will a 200 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 = 200 * 3 / 50 = 12 sec . answer : c"

divide(200, 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">200 / (50/3)</gadget>
<output>12</output>
<result>12</result>


the radius of a semi circle is 70 cm then its perimeter is ?

Explanation: "diameter = 140 cm 1 / 2 * 22 / 7 * 140 + 140 = 360 answer : c"

add(divide(circumface(70), const_2), multiply(70, const_2))

<gadget id="calculator">2 * pi * 70</gadget>
<output>140*pi = around 439.822972</output>
<gadget id="calculator">(140*pi) / 2</gadget>
<output>70*pi = around 219.911486</output>
<gadget id="calculator">70 * 2</gadget>
<output>140</output>
<gadget id="calculator">(70*pi) + 140</gadget>
<output>140 + 70*pi = around 359.911486</output>
<result>140 + 70*pi = around 359.911486</result>


running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets .

Explanation: i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 36 days to doing 6 w widgets . answer : b

<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<result>36</result>


the cost price of a radio is rs . 1500 and it was sold for rs . 1230 , find the loss % ?

Explanation: "1500 - - - - 270 100 - - - - ? = > 18 % answer : a"

multiply(divide(subtract(1500, 1230), 1500), const_100)

<gadget id="calculator">1_500 - 1_230</gadget>
<output>270</output>
<gadget id="calculator">270 / 1_500</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">(9/50) * 100</gadget>
<output>18</output>
<result>18</result>


the sale price sarees listed for rs . 500 after successive discount is 10 % and 5 % is ?

Explanation: "500 * ( 90 / 100 ) * ( 95 / 100 ) = 427.5 answer : a"

subtract(subtract(500, divide(multiply(500, 10), const_100)), divide(multiply(subtract(500, divide(multiply(500, 10), const_100)), 5), const_100))

<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>
<gadget id="calculator">500 - 50</gadget>
<output>450</output>
<gadget id="calculator">450 * 5</gadget>
<output>2_250</output>
<gadget id="calculator">2_250 / 100</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">450 - (45/2)</gadget>
<output>855/2 = around 427.5</output>
<result>855/2 = around 427.5</result>


the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 350 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?

Explanation: let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 350 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 3 / 5 x = 3 / 5 ( 250 ) = 150 the correct answer is d

add(divide(multiply(350, 2), 5), multiply(2, 5))

<gadget id="calculator">350 * 2</gadget>
<output>700</output>
<gadget id="calculator">700 / 5</gadget>
<output>140</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">140 + 10</gadget>
<output>150</output>
<result>150</result>


a can do a piece of work in 8 days and b alone can do it in 12 days . how much time will both take to finish the work ?

Explanation: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 8 x 12 / ( 8 + 12 ) = 96 / 20 = 4.8 days answer : a"

divide(const_1, add(divide(const_1, 8), divide(const_1, 12)))

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/8) + (1/12)</gadget>
<output>5/24 = around 0.208333</output>
<gadget id="calculator">1 / (5/24)</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>


the measurement of a rectangular box with lid is 25 cmx 6 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )

Explanation: d = 6 , r = 2 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 3 * 3 * 3 = 36 π cm 3 answer : c

multiply(divide(const_4, const_3), power(3, const_3))

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">(4/3) * 27</gadget>
<output>36</output>
<result>36</result>


a and b go around a circular track of length 150 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?

Explanation: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 150 / ( 36 * 5 / 18 ) , 150 / ( 54 * 5 / 18 ) } = lcm ( 15 , 10 ) = 30 sec . answer : a"

divide(150, subtract(multiply(54, const_0_2778), multiply(36, const_0_2778)))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">54 * (5/18)</gadget>
<output>15</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">150 / 5</gadget>
<output>30</output>
<result>30</result>


two trains of length 150 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?

Explanation: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 150 + 280 = 430 m . the time required = d / s = 430 / 20 = 21.5 sec . answer : d"

<gadget id="calculator">150 + 280</gadget>
<output>430</output>
<gadget id="calculator">42 + 30</gadget>
<output>72</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">430 / 20</gadget>
<output>43/2 = around 21.5</output>
<result>43/2 = around 21.5</result>


source : knewton a cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . what is the maximum distance , in miles , that the cyclist could travel in 5 hours ?

Explanation: we are told that : generallya cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . is it possible the cyclist to travel with maximum speed for some time ? why not , if there is right terrain for that . so , if there is long enough terrain for the maximum speed of 14 mph then the maximum distance , in miles , that the cyclist could travel in 5 hours would be 5 * 14 = 70 miles . answer : c .

<gadget id="calculator">14 * 5</gadget>
<output>70</output>
<result>70</result>


the length of a rectangle is two - seventh of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 5929 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 25 units ?

Explanation: given that the area of the square = 5929 sq . units = > side of square = â ˆ š 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d

rectangle_area(25, multiply(sqrt(5929), divide(const_2, add(const_3, const_4))))

<gadget id="calculator">5_929 ** (1/2)</gadget>
<output>77</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">77 * (2/7)</gadget>
<output>22</output>
<gadget id="calculator">25 * 22</gadget>
<output>550</output>
<result>550</result>


if 20 men take 15 days to to complete a job , in how many days can 25 men finish that work ?

Explanation: ans . 12 days

<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">300 / 25</gadget>
<output>12</output>
<result>12</result>


on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?

Explanation: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.2 t x = 0.4 t the answer is b ."

divide(20, subtract(const_1, divide(50, const_100)))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">20 / (1/2)</gadget>
<output>40</output>
<result>40</result>


the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 7 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?

Explanation: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 7 = 35 km imo , correct answer is ` ` b . ' '"

multiply(60, divide(multiply(5, 7), 60))

<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">35 / 60</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">60 * (7/12)</gadget>
<output>35</output>
<result>35</result>


the fuel indicator in a car shows 1 / 5 th of the fuel tank as full . when 22 more liters of fuel are poured in to the tank , the indicator rests at the 3 / 4 of the full mark . find the capacity of the tank .

Explanation: x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d

divide(22, subtract(divide(3, 4), divide(1, 5)))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(3/4) - (1/5)</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">22 / (11/20)</gadget>
<output>40</output>
<result>40</result>


a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 450 kilograms of pears that day , how many kilograms did he sell in the afternoon ?

Explanation: 3 x = 450 x = 150 therefore , the salesman sold 150 kg in the morning and 2 ⋅ 150 = 300 kg in the afternoon . so answer is c .

<gadget id="calculator">450 / 3</gadget>
<output>150</output>
<gadget id="calculator">150 * 2</gadget>
<output>300</output>
<result>300</result>


find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 30 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 30 5 x = 1335 x = 267 large number = 267 + 1365 = 1632 d"

add(multiply(divide(subtract(1365, 30), subtract(6, const_1)), 6), 30)

<gadget id="calculator">1_365 - 30</gadget>
<output>1_335</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_335 / 5</gadget>
<output>267</output>
<gadget id="calculator">267 * 6</gadget>
<output>1_602</output>
<gadget id="calculator">1_602 + 30</gadget>
<output>1_632</output>
<result>1_632</result>


a rectangle with width 8 and diagonal 30 . find the area ?

Explanation: then the area is : 8 ' ' x 30 ' ' = 240 square inches , or 240 square units hence a

rectangle_area(sqrt(subtract(power(30, const_2), power(8, const_2))), 8)

<gadget id="calculator">30 ** 2</gadget>
<output>900</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">900 - 64</gadget>
<output>836</output>
<gadget id="calculator">836 ** (1/2)</gadget>
<output>2*sqrt(209) = around 28.913665</output>
<gadget id="calculator">(2*sqrt(209)) * 8</gadget>
<output>16*sqrt(209) = around 231.309317</output>
<result>16*sqrt(209) = around 231.309317</result>


train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 35 miles per hour . how many miles from the station was train a overtaken by train b ?

Explanation: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 5 miles per hour . the time to catch up is 60 / 5 = 12 hours . in 12 hours , train a travels another 30 * 12 = 360 miles for a total of 420 miles . the answer is a ."

multiply(divide(multiply(30, const_2), subtract(35, 30)), 35)

<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">35 - 30</gadget>
<output>5</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<gadget id="calculator">12 * 35</gadget>
<output>420</output>
<result>420</result>


a box contains 25 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 ) = 21 c 2 / 25 c 2 = 7 / 10 p ( at least one is defective ) = ( 1 - 7 / 10 ) = 3 / 10 . answer a"

subtract(const_1, divide(choose(subtract(25, 4), const_2), choose(25, const_2)))

<gadget id="calculator">25 - 4</gadget>
<output>21</output>
<gadget id="calculator">binomial(21, 2)</gadget>
<output>210</output>
<gadget id="calculator">binomial(25, 2)</gadget>
<output>300</output>
<gadget id="calculator">210 / 300</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>


how many prime numbers are between 28 / 3 and 86 / 6 ?

Explanation: "28 / 3 = 9 . xxx 86 / 6 = 14 . xxx so we need to find prime numbers between 9 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"

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


in a school of 800 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?

Explanation: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 800 * 18 / 100 = 144 the answer is c ."

subtract(800, add(add(multiply(divide(44, const_100), 800), multiply(divide(28, const_100), 800)), multiply(divide(10, const_100), 800)))

<gadget id="calculator">44 / 100</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 800</gadget>
<output>352</output>
<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) * 800</gadget>
<output>224</output>
<gadget id="calculator">352 + 224</gadget>
<output>576</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 800</gadget>
<output>80</output>
<gadget id="calculator">576 + 80</gadget>
<output>656</output>
<gadget id="calculator">800 - 656</gadget>
<output>144</output>
<result>144</result>


in what ratio must rice of rs . 25 per kg be mixed with rice of rs . 12 per kg so that cost of mixture is rs . 20 per kg ?

Explanation: "( 20 - 12 ) / ( 25 - 20 = 8 / 5 = 8 : 5 answer : a"

divide(divide(subtract(20, 12), subtract(25, 12)), subtract(const_1, divide(subtract(20, 12), subtract(25, 12))))

<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">25 - 12</gadget>
<output>13</output>
<gadget id="calculator">8 / 13</gadget>
<output>8/13 = around 0.615385</output>
<gadget id="calculator">1 - (8/13)</gadget>
<output>5/13 = around 0.384615</output>
<gadget id="calculator">(8/13) / (5/13)</gadget>
<output>8/5 = around 1.6</output>
<result>8/5 = around 1.6</result>


10 men and 15 women together can complete a work in 4 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?

Explanation: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 4 15 women ' s 1 day work = ( 1 / 4 - 10 / 100 ) = 3 / 20 1 woman ' s 1 day work = 1 / 100 1 woman alone can complete the work in 100 days . answer : a"

multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 4))), multiply(15, 4))

<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">100 / 60</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">15 * 4</gadget>
<output>60</output>
<gadget id="calculator">(5/3) * 60</gadget>
<output>100</output>
<result>100</result>


if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 4 other contributions made before john ' s , what is the size of his donation ?

Explanation: cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 4 people . so $ 100 . but , he also has to put in the average for himself ( the fiveth person ) , so add $ 75 . so $ 175 is your answer . answer b

add(subtract(multiply(add(4, const_1), 75), multiply(add(4, const_1), 50)), 50)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 75</gadget>
<output>375</output>
<gadget id="calculator">5 * 50</gadget>
<output>250</output>
<gadget id="calculator">375 - 250</gadget>
<output>125</output>
<gadget id="calculator">125 + 50</gadget>
<output>175</output>
<result>175</result>


if 0.5 : x : : 5 : 8 , then x is equal to :

Explanation: "( x * 5 ) = ( 0.5 * 8 ) x = 4 / 5 x = 0.8 answer = e"

<gadget id="calculator">0.5 * 8</gadget>
<output>4</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what is the weight of the new person ?

Explanation: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 75 + 20 ) kg = 95 kg the answer is c ."

<gadget id="calculator">2.5 * 8</gadget>
<output>20</output>
<gadget id="calculator">20 + 75</gadget>
<output>95</output>
<result>95</result>


the radius of a wheel is 12.6 cm . what is the distance covered by the wheel in making 200 resolutions ?

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 12.6 = 15825.6 cm = 158.256 m answer : d"

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 12.6), const_2), 200), 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) * 12.6</gadget>
<output>39.6</output>
<gadget id="calculator">39.6 * 2</gadget>
<output>79.2</output>
<gadget id="calculator">79.2 * 200</gadget>
<output>15_840</output>
<gadget id="calculator">15_840 / 100</gadget>
<output>792/5 = around 158.4</output>
<result>792/5 = around 158.4</result>


on my sister ' s birthday , she was 143 cm in height , having grown 10 % since the year before . how tall was she the previous year ?

Explanation: "let the previous year ' s height be x . 1.1 x = 143 x = 130 the answer is c ."

subtract(143, divide(multiply(143, 10), const_100))

<gadget id="calculator">143 * 10</gadget>
<output>1_430</output>
<gadget id="calculator">1_430 / 100</gadget>
<output>143/10 = around 14.3</output>
<gadget id="calculator">143 - (143/10)</gadget>
<output>1_287/10 = around 128.7</output>
<result>1_287/10 = around 128.7</result>


the length of each side of an equilateral triangle having an area of 4 â ˆ š 3 cm 2 is ?

Explanation: explanation : â ˆ š 3 / 4 a 2 = 4 â ˆ š 3 - > a = 4 answer is d

sqrt(divide(multiply(4, sqrt(3)), multiply(multiply(divide(const_1, 2), divide(const_1, 2)), sqrt(3))))

<gadget id="calculator">3 ** (1/2)</gadget>
<output>sqrt(3) = around 1.732051</output>
<gadget id="calculator">4 * (sqrt(3))</gadget>
<output>4*sqrt(3) = around 6.928203</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * (sqrt(3))</gadget>
<output>sqrt(3)/4 = around 0.433013</output>
<gadget id="calculator">(4*sqrt(3)) / (sqrt(3)/4)</gadget>
<output>16</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<result>4</result>


if the sides of a rectangle are increased by 25 % , what is the percentage increase in the area ?

Explanation: "if sides are a and b , after increase sides would be 1.25 a and 1.25 b . percentage increase in area = ( 1.25 a * 1.25 b - ab ) * 100 / ab = 56.25 % answer : b"

multiply(subtract(power(add(divide(25, const_100), const_1), const_2), const_1), const_100)

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) ** 2</gadget>
<output>25/16 = around 1.5625</output>
<gadget id="calculator">(25/16) - 1</gadget>
<output>9/16 = around 0.5625</output>
<gadget id="calculator">(9/16) * 100</gadget>
<output>225/4 = around 56.25</output>
<result>225/4 = around 56.25</result>


the charge for a single room at hotel p is 30 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?

Explanation: "let rate in r = 100 x then p = 70 x g = 100 y p = 90 y thus 70 x = 90 y or x = 1.28 y ans r = 128 y so increase = 28 % answer : a"

multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 30), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 30), subtract(const_100, 10)), const_100)), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">70 / 90</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">(7/9) * 100</gadget>
<output>700/9 = around 77.777778</output>
<gadget id="calculator">100 - (700/9)</gadget>
<output>200/9 = around 22.222222</output>
<gadget id="calculator">(200/9) / (700/9)</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>


a trader marked the selling price of an article at 11 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :

Explanation: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 111 * 100 ] % = 9.9 % answer c"

multiply(const_100, divide(add(multiply(add(const_2, const_3), const_2), 1), add(const_100, 11)))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">100 + 11</gadget>
<output>111</output>
<gadget id="calculator">11 / 111</gadget>
<output>11/111 = around 0.099099</output>
<gadget id="calculator">100 * (11/111)</gadget>
<output>1_100/111 = around 9.90991</output>
<result>1_100/111 = around 9.90991</result>


bottle r contains 250 capsules and costs $ 5.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?

Explanation: cost per capsule in r is 5.25 / 250 = 0.525 / 25 = 0.021 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.002 the answer is e

<gadget id="calculator">2.99 / 130</gadget>
<output>0.023</output>
<gadget id="calculator">5.25 / 250</gadget>
<output>0.021</output>
<gadget id="calculator">0.023 - 0.021</gadget>
<output>0.002</output>
<result>0.002</result>


area of four walls of a room is 99 m 2 . the length and breadth of the room are 7.5 m and 3.5 m respectively . the height of the room is :

Explanation: 2 ( 7.5 + 3.5 ) × h = 99 2 ( 11 ) h = 99 22 h = 99 h = 99 / 22 = 9 / 2 = 4.5 m answer is d .

divide(99, add(multiply(7.5, const_2), multiply(3.5, const_2)))

<gadget id="calculator">7.5 * 2</gadget>
<output>15</output>
<gadget id="calculator">3.5 * 2</gadget>
<output>7</output>
<gadget id="calculator">15 + 7</gadget>
<output>22</output>
<gadget id="calculator">99 / 22</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>


x is a positive integer less than 300 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?

Explanation: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 300 n = 22.13 or n = 22 answer : - b"

subtract(add(multiply(reminder(7, 300), 3), reminder(3, 300)), reminder(1, 300))

<gadget id="calculator">7 % 300</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">3 % 300</gadget>
<output>3</output>
<gadget id="calculator">21 + 3</gadget>
<output>24</output>
<gadget id="calculator">1 % 300</gadget>
<output>1</output>
<gadget id="calculator">24 - 1</gadget>
<output>23</output>
<result>23</result>


how many different ways can 2 students be seated in a row of 4 desks , so that there is always at least one empty desk between the students ?

Explanation: "total cases : 12 ( student one has 4 options and student two has three options , 4 x 3 = 12 ) non - favourable cases : 6 ( when two students sit together . students in desk 1 and desk 2 , in desk 2 and desk 3 , in desk 3 and desk 4 ) for each of these cases there are two possibilities because the positions can be interchanged . hence 2 x 3 = 6 . so favourable cases : 12 - 6 = 6 . answer : d"

<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">factorial(3) / factorial(3 - 2)</gadget>
<output>6</output>
<result>6</result>


a dishonest dealer professes to sell goods at the cost price but uses a weight of 720 grams per kg , what is his percent ?

Explanation: "explanation : 720 - - - 280 100 - - - ? = > 38.9 % answer : c"

subtract(multiply(divide(const_100, 720), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

<gadget id="calculator">100 / 720</gadget>
<output>5/36 = around 0.138889</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">(5/36) * 1_000</gadget>
<output>1_250/9 = around 138.888889</output>
<gadget id="calculator">(1_250/9) - 100</gadget>
<output>350/9 = around 38.888889</output>
<result>350/9 = around 38.888889</result>


machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 80 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 20 minutes ?

Explanation: machine b produces 100 part in 80 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 80 / 2 = 40 minutes . now , machine a produces 100 parts in 40 minutes which is 100 / 40 = 10 / 4 parts / minute . 10 / 4 parts x a total of 20 minutes = 10 / 4 * 20 = 50 e

multiply(multiply(divide(100, 80), const_2), 20)

<gadget id="calculator">100 / 80</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) * 20</gadget>
<output>50</output>
<result>50</result>


a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 66 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?

Explanation: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 66 % is one st . dev , then on either side of m we have 66 / 2 = 33 % . so , 33 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 33 = 83 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 83 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c"

subtract(const_100, divide(subtract(const_100, 66), const_2))

<gadget id="calculator">100 - 66</gadget>
<output>34</output>
<gadget id="calculator">34 / 2</gadget>
<output>17</output>
<gadget id="calculator">100 - 17</gadget>
<output>83</output>
<result>83</result>


in a class of 54 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?

Explanation: "total = english + german - both + neither - - > 54 = english + 22 - 12 + 0 - - > english = 44 - - > only english = english - both = 44 - 12 = 32 . answer : e ."

<gadget id="calculator">54 + 12</gadget>
<output>66</output>
<gadget id="calculator">66 - 22</gadget>
<output>44</output>
<gadget id="calculator">44 - 12</gadget>
<output>32</output>
<result>32</result>


usc invited each south carolina high school to send up to 39 students to watch a football game . a section which has 199 seats in each row is reserved for those students . what is the least number of rows needed to guarantee that if 2006 students show up , then all students from the same high school can be seated in the same row ?

Explanation: the answer is 12 rows . if 59 schools send 34 students each , then we can sit at most 5 groups of students in the same row , so we will need 12 rows . next , 12 rows are sufficient . assume that this is not the case . suppose the groups of students are seated like this : first the largest group , then the second largest group , then the third largest group , etc . suppose we run out of space - there are not enough seats in any row to seat together the next group . suppose the first group that can not be seated together is the kth group and it consists of n students . then k 61 since any row fits at least 5 groups . also , n 2006 / k 2006 / 61 < 33 ( all groups already seated are no smaller than the kth group ) . so , n 32 . since there is not enough space in any of the 12 rows to seat the kth group , then there must be at least 168 students seated in each of the 12 rows . now , 12 × 168 = 2016 > 2006 a contradiction . so , 12 rows are sufficient . correct answer b


a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 64 ) square inches . what is the perimeter of the photograph , in inches ?

Explanation: let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 6 ) ( y + 6 ) = m and so ( 2 ) xy + 6 x + 6 y + 36 = m + 64 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 x + 4 y + 32 = 64 2 x + 2 y = 16 , which is the perimeter of the photograph . the answer is a .

divide(subtract(64, subtract(power(multiply(3, const_2), const_2), power(multiply(1, const_2), const_2))), const_2)

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">36 - 4</gadget>
<output>32</output>
<gadget id="calculator">64 - 32</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>


the unit digit in the product 4556 * 3432 * 4581 * 2784 is ?

Explanation: unit digit in the given product = unit digit in 6 * 2 * 1 * 4 = 8 answer is a

subtract(multiply(multiply(multiply(4556, 3432), 4581), 2784), subtract(multiply(multiply(multiply(4556, 3432), 4581), 2784), add(const_4, const_4)))


a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds . the length of the train ( in metres ) is :

Explanation: "explanation : let the length of train be l m . acc . to question ( 276 + l ) / 20 = l / 8 2208 + 8 l = 20 l l = 2208 / 12 = 184 m answer a"

multiply(divide(276, subtract(20, 8)), 8)

<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">276 / 12</gadget>
<output>23</output>
<gadget id="calculator">23 * 8</gadget>
<output>184</output>
<result>184</result>


to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 760 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?

Explanation: "total movies submitted are 760 . as per question we need to take 1 / 4 of 760 to be considered for top 10 movies = 190 approximate the value we 190 . imo option b is the correct answer . . ."

<gadget id="calculator">760 / 4</gadget>
<output>190</output>
<result>190</result>


each child has 4 crayons and 14 apples . if there are 9 children , how many crayons are there in total ?

Explanation: 4 * 9 = 36 . answer is d .

<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<result>36</result>


a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :

Explanation: perimeter = distance covered in 8 min = ( 12000 / 60 * 8 ) m = 1600 m let , length = 3 x meters and breadth = 2 x meters then , 2 ( 3 x + 2 x ) = 1600 or x = 160 therefore , length = 480 m and breadth = 320 m therefore , area = ( 480 * 320 ) m 2 = 153600 m 2 answer : c

multiply(multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 2), multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 3))

<gadget id="calculator">12 * 1_000</gadget>
<output>12_000</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">12_000 / 60</gadget>
<output>200</output>
<gadget id="calculator">8 * 200</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 / 10</gadget>
<output>160</output>
<gadget id="calculator">160 * 2</gadget>
<output>320</output>
<gadget id="calculator">160 * 3</gadget>
<output>480</output>
<gadget id="calculator">320 * 480</gadget>
<output>153_600</output>
<result>153_600</result>


Explanation: "12519 x 9999 = 12519 x ( 10000 - 1 ) = 12519 x 10000 - 12519 x 1 = 125190000 - 12519 = 125177481 a"

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>
<gadget id="calculator">9_995 * 12_519</gadget>
<output>125_127_405</output>
<result>125_127_405</result>


a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in .

Explanation: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : e"

multiply(divide(multiply(9, add(const_2, const_1)), const_2), const_2)

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">27 / 2</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">(27/2) * 2</gadget>
<output>27</output>
<result>27</result>


find the value of ( 875 233 / 899 ) × 899

Explanation: "( 875 233 / 899 ) × 899 ( 786625 + 233 ) / 899 × 899 786858 / 899 × 899 786858 c"


the length of a rectangular floor is more than its breadth by 200 % . if rs . 150 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 150 / 2 = 75 sq m l b = 75 i . e . , l * l / 3 = 75 l 2 = 225 = > l = 15 answer : b"

multiply(sqrt(divide(divide(150, 2), const_3)), const_3)

<gadget id="calculator">150 / 2</gadget>
<output>75</output>
<gadget id="calculator">75 / 3</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<result>15</result>


a car traveled from san diego to san francisco at an average speed of 66 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?

Explanation: "let the time taken be = x one way distance = 66 x total distance traveled = 2 * 66 x = 132 x total time taken = x + 2 x = 3 x average speed = 132 x / 3 x = 44 answer : e"

<gadget id="calculator">1 / 66</gadget>
<output>1/66 = around 0.015152</output>
<gadget id="calculator">(1/66) / 2</gadget>
<output>1/132 = around 0.007576</output>
<gadget id="calculator">(1/66) + (1/132)</gadget>
<output>1/44 = around 0.022727</output>
<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>


rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 2 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?

Explanation: "for 100 - 40 - 10 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 40 pages the cost is : first time 5 $ + 2 $ of the first revision - 40 * ( 5 + 2 ) = 280 $ ; for 10 pages the cost is : first time 5 $ + 2 $ of the first revision + 2 $ of the second revision - 10 ( 5 + 2 + 2 ) = 90 $ ; total : 250 + 280 + 90 = 620 $ . answer : b ."

add(add(multiply(100, 5), multiply(40, 2)), multiply(multiply(10, 2), const_2))

<gadget id="calculator">100 * 5</gadget>
<output>500</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">500 + 80</gadget>
<output>580</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">580 + 40</gadget>
<output>620</output>
<result>620</result>


some persons can do a piece of work in 32 days . two times the number of these people will do half of that work in ?

Explanation: 32 / ( 2 * 2 ) = 8 days answer : e

multiply(multiply(32, divide(const_1, const_2)), divide(const_1, const_2))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">32 * (1/2)</gadget>
<output>16</output>
<gadget id="calculator">16 * (1/2)</gadget>
<output>8</output>
<result>8</result>


a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?

Explanation: they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .

add(add(multiply(multiply(6, 5), 4), multiply(6, 5)), multiply(6, 5))

<gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 4</gadget>
<output>120</output>
<gadget id="calculator">120 + 30</gadget>
<output>150</output>
<gadget id="calculator">150 + 30</gadget>
<output>180</output>
<result>180</result>


forks , spoons , and knives in drawer are in the ratio of 4 : 4 : 3 . if there are 16 forks , the number of knives in the drawer is :

Explanation: explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c

<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>12</result>


in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6000 , the number of valid votes that the other candidate got , was :

Explanation: "c number of valid votes = 80 % of 6000 = 4800 . valid votes polled by other candidate = 45 % of 4800 = ( 45 / 100 x 4800 ) = 2160 ."

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 6000)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 6_000</gadget>
<output>2_160</output>
<result>2_160</result>


Explanation: "10 * 6 = 4 * x x = 15 answer : b"

<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">6 * (5/2)</gadget>
<output>15</output>
<result>15</result>


a train passes a platform in 36 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: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 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 = 36 = > 300 + l = 15 × 36 = 540 = > l = 540 - 300 = 240 meter answer is a ."

multiply(multiply(const_0_2778, 54), subtract(36, 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">36 - 20</gadget>
<output>16</output>
<gadget id="calculator">15 * 16</gadget>
<output>240</output>
<result>240</result>


if two dice are thrown together , the probability of getting a doublet on the dice is

Explanation: "the number of exhaustive outcomes is 36 . let e be the event of getting doublet on the dies is 6 / 36 = 1 / 6 p ( e ) = 1 / 6 . a )"

<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">6 / 36</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


a 6 % stock yields 9 % . the market value of the stock is :

Explanation: "explanation : for an income of rs . 9 , investment = rs . 100 . for an income of rs 6 , investment = rs . 100 / 9 x 6 = rs 66.66 market value of rs . 100 stock = rs . 66.66 answer is e"

<gadget id="calculator">100 / 9</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">(100/9) * 6</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>


jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 36 , what is the probability that the next one she draws will be pink ?

Explanation: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 36 = ( 5 / 6 ) * ( 5 / 6 ) therefore probability that the next one she draws is pink = 1 / 6 option ( a )"

<gadget id="calculator">25 / 36</gadget>
<output>25/36 = around 0.694444</output>
<gadget id="calculator">(25/36) ** (1/2)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 253 games will be played during the tournament . what is the number of participants ?

Explanation: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 253 n * ( n - 1 ) = 506 = 23 * 22 ( trial and error ) the answer is c ."

divide(add(sqrt(add(multiply(multiply(253, const_2), const_4), const_1)), const_1), const_2)

<gadget id="calculator">253 * 2</gadget>
<output>506</output>
<gadget id="calculator">506 * 4</gadget>
<output>2_024</output>
<gadget id="calculator">2_024 + 1</gadget>
<output>2_025</output>
<gadget id="calculator">2_025 ** (1/2)</gadget>
<output>45</output>
<gadget id="calculator">45 + 1</gadget>
<output>46</output>
<gadget id="calculator">46 / 2</gadget>
<output>23</output>
<result>23</result>


it takes 10 days for digging a trench of 100 m long , 50 m broad and 10 m deep . what length of trench , 25 m broad and 15 m deep can be dug in 30 days ?

Explanation: more days , more length ( direct ) less breadth , more length ( indirect ) more depth , less length ( indirect days 10 : 30 ; breadth 25 : 50 ; : : 100 : x depth 15 : 10 ; : . 10 * 25 * 15 * x = 30 * 50 * 10 * 100 x = ( 30 * 50 * 10 * 100 ) / 10 * 25 * 15 = 400 so the required length = 400 m answer : a

divide(multiply(multiply(multiply(30, 50), 10), 100), multiply(15, multiply(10, 25)))

<gadget id="calculator">30 * 50</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 * 10</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 * 100</gadget>
<output>1_500_000</output>
<gadget id="calculator">10 * 25</gadget>
<output>250</output>
<gadget id="calculator">15 * 250</gadget>
<output>3_750</output>
<gadget id="calculator">1_500_000 / 3_750</gadget>
<output>400</output>
<result>400</result>


if 20 men can build a water fountain 56 metres long in 3 days , what length of a similar water fountain can be built by 35 men in 3 days ?

Explanation: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 3 : 3 : : 56 : x therefore ( 20 x 3 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 60 = 98 hence , the required length is 98 m . answer : e"

multiply(divide(56, multiply(20, 3)), multiply(35, 3))

<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">56 / 60</gadget>
<output>14/15 = around 0.933333</output>
<gadget id="calculator">35 * 3</gadget>
<output>105</output>
<gadget id="calculator">(14/15) * 105</gadget>
<output>98</output>
<result>98</result>


p has $ 63 more than what q and r together would have had if both b and c had 1 / 9 of what p has . how much does p have ?

Explanation: p = ( 2 / 9 ) * p + 63 ( 7 / 9 ) * p = 63 p = 81 the answer is e .

divide(63, subtract(const_1, multiply(divide(1, 9), const_2)))

<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/9) * 2</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">1 - (2/9)</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">63 / (7/9)</gadget>
<output>81</output>
<result>81</result>


a train running at the speed of 110 km / hr crosses a pole in 9 sec . what is the length of the train ?

Explanation: "speed = 110 * 5 / 18 = 275 / 9 m / sec length of the train = speed * time = 275 / 9 * 9 = 275 m answer : b"

multiply(divide(multiply(110, const_1000), const_3600), 9)

<gadget id="calculator">110 * 1_000</gadget>
<output>110_000</output>
<gadget id="calculator">110_000 / 3_600</gadget>
<output>275/9 = around 30.555556</output>
<gadget id="calculator">(275/9) * 9</gadget>
<output>275</output>
<result>275</result>


if 2 ^ y = 4 ^ ( 5 x + 3 ) and 3 ^ ( x - 7 ) = 9 ^ y , what is the value of x + y ?

Explanation: 2 ^ y = 4 ^ ( 5 x + 3 ) 2 ^ y = 2 ^ 2 ( 5 x + 3 ) y = 10 x + 6 . . . . . . . . . . . 1 3 ^ ( x - 7 ) = 9 ^ y 3 ^ ( x - 7 ) = 3 ^ 2 y x - 7 = 2 y . . . . . . . . . . . . . 2 put value of y = 10 x + 6 in eq 2 x - 7 = 2 ( 10 x + 6 ) x - 7 = 20 x + 12 19 x = - 19 x = - 1 therefore , y = - 10 + 6 y = - 4 x + y = - 1 - 4 = - 5 answer : b

add(divide(add(divide(add(negate(7), negate(multiply(multiply(2, 3), 2))), subtract(multiply(2, const_10), const_1)), negate(7)), 2), divide(add(negate(7), negate(multiply(multiply(2, 3), 2))), subtract(multiply(2, const_10), const_1)))

<gadget id="calculator">-7</gadget>
<output>-7</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">-12</gadget>
<output>-12</output>
<gadget id="calculator">(-7) + (-12)</gadget>
<output>-19</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">(-19) / 19</gadget>
<output>-1</output>
<gadget id="calculator">(-1) + (-7)</gadget>
<output>-8</output>
<gadget id="calculator">(-8) / 2</gadget>
<output>-4</output>
<gadget id="calculator">(-4) + (-1)</gadget>
<output>-5</output>
<result>-5</result>


a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 140 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 = 240 + 140 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"

divide(add(240, 140), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

<gadget id="calculator">240 + 140</gadget>
<output>380</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">380 / 10</gadget>
<output>38</output>
<result>38</result>


of the 75 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?

Explanation: "neither car nor garage = total - garage - ( swim - common ) = 75 - 50 - ( 40 - 35 ) = 75 - 55 = 20 answer c"

subtract(75, add(add(subtract(50, 35), subtract(40, 35)), 35))

<gadget id="calculator">50 - 35</gadget>
<output>15</output>
<gadget id="calculator">40 - 35</gadget>
<output>5</output>
<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">20 + 35</gadget>
<output>55</output>
<gadget id="calculator">75 - 55</gadget>
<output>20</output>
<result>20</result>


if the price of a certain computer increased 30 percent from a dollars to 351 dollars , then 2 a =

Explanation: "before price increase price = a after 30 % price increase price = a + ( 30 / 100 ) * a = 1.3 a = 351 ( given ) i . e . a = 351 / 1.3 = $ 270 i . e . 2 a = 2 * 270 = 540 answer : option a"

multiply(divide(351, divide(add(const_100, 30), const_100)), 2)

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">351 / (13/10)</gadget>
<output>270</output>
<gadget id="calculator">270 * 2</gadget>
<output>540</output>
<result>540</result>


in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability w this college graduate has a graduate degree ?

Explanation: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d"

divide(divide(divide(1, 8), divide(2, 3)), add(divide(divide(1, 8), divide(2, 3)), 1))

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/8) / (2/3)</gadget>
<output>3/16 = around 0.1875</output>
<gadget id="calculator">(3/16) + 1</gadget>
<output>19/16 = around 1.1875</output>
<gadget id="calculator">(3/16) / (19/16)</gadget>
<output>3/19 = around 0.157895</output>
<result>3/19 = around 0.157895</result>


what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 25 % ?

Explanation: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 75 2 / 3 sp 1 = 75 sp 1 = 112.50 100 - - - 12.5 = > 12.5 % answer : e"

subtract(divide(subtract(const_100, 25), divide(2, 3)), const_100)

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">75 / (2/3)</gadget>
<output>225/2 = around 112.5</output>
<gadget id="calculator">(225/2) - 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


how many 5 - digit numbers are there , if the two leftmost digits are even , the other digits are odd and the digit 2 can not appear more than once in the number .

Explanation: n = ( 4 * 5 - 1 ) * 5 * 5 * 5 = 2375 where 4 cases of first digit { 2,4 , 6,8 } 5 cases of second digit { 0 , 2,4 , 6,8 } 1 case of 22 for two leftmost digit 5 cases of third digit { 1 , 3,5 , 7,9 } 5 cases of fourth digit { 1 , 3,5 , 7,9 } 5 cases of fifth digit { 1 , 3,5 , 7,9 } c

multiply(add(multiply(const_3, const_4), add(const_3, const_4)), power(5, const_3))

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">12 + 7</gadget>
<output>19</output>
<gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">19 * 125</gadget>
<output>2_375</output>
<result>2_375</result>


alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1081 . find the cost of each ice - cream cup ?

Explanation: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1081 96 + 225 + 490 + 6 x = 1081 6 x = 270 = > x = 45 . answer : e"

divide(subtract(subtract(subtract(1081, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

<gadget id="calculator">16 * 6</gadget>
<output>96</output>
<gadget id="calculator">1_081 - 96</gadget>
<output>985</output>
<gadget id="calculator">5 * 45</gadget>
<output>225</output>
<gadget id="calculator">985 - 225</gadget>
<output>760</output>
<gadget id="calculator">7 * 70</gadget>
<output>490</output>
<gadget id="calculator">760 - 490</gadget>
<output>270</output>
<gadget id="calculator">270 / 6</gadget>
<output>45</output>
<result>45</result>


selling an kite for rs . 30 , a shop keeper gains 40 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?

Explanation: "explanation : marked price = rs . 30 c . p . = 100 / 140 * 30 = rs . 21.42 sale price = 90 % of rs . 30 = rs . 27 required gain % = 5.57 / 21.42 * 100 = 26 % . answer : e"

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(40, const_100))), divide(multiply(30, const_100), add(40, const_100))), const_100)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">(3/10) * 90</gadget>
<output>27</output>
<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>
<gadget id="calculator">40 + 100</gadget>
<output>140</output>
<gadget id="calculator">3_000 / 140</gadget>
<output>150/7 = around 21.428571</output>
<gadget id="calculator">27 - (150/7)</gadget>
<output>39/7 = around 5.571429</output>
<gadget id="calculator">(39/7) / (150/7)</gadget>
<output>13/50 = around 0.26</output>
<gadget id="calculator">(13/50) * 100</gadget>
<output>26</output>
<result>26</result>


at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 75 . if the restaurant serves 120 customers today , raising the average to 80 customers per day , what is the value of x ?

Explanation: "withoutusing the formula , we can see that today the restaurant served 40 customers above the average . the total amount above the average must equal total amount below the average . this additional 40 customers must offset the “ deficit ” below the average of 80 created on the x days the restaurant served only 75 customers per day . 40 / 5 = 8 days . choice ( a ) . withthe formula , we can set up the following : 80 = ( 75 x + 120 ) / ( x + 1 ) 80 x + 80 = 75 x + 120 5 x = 40 x = 8 answer choice ( d )"

subtract(divide(subtract(120, 80), subtract(80, 75)), divide(subtract(120, const_100), const_100))

<gadget id="calculator">120 - 80</gadget>
<output>40</output>
<gadget id="calculator">80 - 75</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">8 - (1/5)</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>


an inspector rejects 15 % of the meters as defective . how many will he examine to reject 15 ?

Explanation: "then , 15 % of x = 15 ( 15 / 100 ) x = 15 x = ( 15 * 100 * ) / 15 = 100 answer is a"

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


pipe a fills a tank of capacity 700 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?

Explanation: "in one cycle they fill 40 + 30 - 20 = 50 liters 700 = 50 * n = > n = 14 here n = number of cycles . total time = 14 * 3 = 42 as in one cycle there are 3 minutes . thus 42 minutes answer : a"

multiply(divide(700, subtract(add(40, 30), 20)), const_3)

<gadget id="calculator">40 + 30</gadget>
<output>70</output>
<gadget id="calculator">70 - 20</gadget>
<output>50</output>
<gadget id="calculator">700 / 50</gadget>
<output>14</output>
<gadget id="calculator">14 * 3</gadget>
<output>42</output>
<result>42</result>


the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ?

Explanation: "2 x * x = 72 = > x = 6 answer : a"

<gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>6</result>


a and b can finish a work together in 12 days , and b and c together in 16 days . if a alone works for 5 days and then b alone continues for 7 days , then remaining work is done by c in 13 days . in how many days can c alone finish the complete work ?

Explanation: here lcm of 12 and 16 is taken as total work . ( becomes easy to solve ) assume total work = 48 units then workdone by ( a + b ) in one day = 48 / 12 = 4 units similarly , by ( b + c ) in one day = 48 / 16 = 3 units now according to question , a works 5 days , b for 7 days and c for 13 days to complete total work so , 5 a + 7 b + 13 c = 48 units 5 ( a + b ) + 2 ( b + c ) + 11 c = 48 units 5 * 4 + 2 * 3 + 11 c = 48 units 11 c = 22 units c = 2 units ( c does 2 units of work daily ) therefore , 48 / 2 = 24 days c requires 24 days to complete the work alone . answer d

divide(const_1, divide(subtract(const_1, add(divide(5, 12), divide(const_2, 16))), subtract(add(5, 13), 7)))

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">2 / 16</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(5/12) + (1/8)</gadget>
<output>13/24 = around 0.541667</output>
<gadget id="calculator">1 - (13/24)</gadget>
<output>11/24 = around 0.458333</output>
<gadget id="calculator">5 + 13</gadget>
<output>18</output>
<gadget id="calculator">18 - 7</gadget>
<output>11</output>
<gadget id="calculator">(11/24) / 11</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>24</result>


the ages of two person , differ by 20 years . if 5 years ag , the elder one be 5 times as old as the younger one their present ages ( in years ) are respectively

Explanation: let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a

<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<result>30</result>


the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?

Explanation: ( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d

subtract(multiply(multiply(divide(add(const_100, 8), const_100), divide(subtract(const_100, 6), const_100)), const_100), const_100)

<gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">108 / 100</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">100 - 6</gadget>
<output>94</output>
<gadget id="calculator">94 / 100</gadget>
<output>47/50 = around 0.94</output>
<gadget id="calculator">(27/25) * (47/50)</gadget>
<output>1_269/1_250 = around 1.0152</output>
<gadget id="calculator">(1_269/1_250) * 100</gadget>
<output>2_538/25 = around 101.52</output>
<gadget id="calculator">(2_538/25) - 100</gadget>
<output>38/25 = around 1.52</output>
<result>38/25 = around 1.52</result>


the mass of 1 cubic meter of a substance is 400 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )

Explanation: "400 kg - 1 cubic meter ; 400,000 g - 1 cubic meter ; 400,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 400,000 = 10 / 4 = 2.5 cubic centimeters . answer : b ."

<gadget id="calculator">1_000 * 1_000</gadget>
<output>1_000_000</output>
<gadget id="calculator">400 * 1_000</gadget>
<output>400_000</output>
<gadget id="calculator">1_000_000 / 400_000</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 24 cm . what is the length of the wire ?

Explanation: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 24 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 4 cm answer : b"

divide(multiply(const_4, divide(power(12, const_3), power(24, const_2))), const_3)

<gadget id="calculator">12 ** 3</gadget>
<output>1_728</output>
<gadget id="calculator">24 ** 2</gadget>
<output>576</output>
<gadget id="calculator">1_728 / 576</gadget>
<output>3</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<result>4</result>


boys and girls in a class are writing letters . there are twice as many girls as boys in the class , and each girl writes 3 more letters than each boy . if boys write 24 of the 90 total letters written by the class , how many letters does each boy write ?

Explanation: there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d .

divide(24, divide(subtract(90, multiply(3, 24)), multiply(3, const_2)))

<gadget id="calculator">3 * 24</gadget>
<output>72</output>
<gadget id="calculator">90 - 72</gadget>
<output>18</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">18 / 6</gadget>
<output>3</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>8</result>


a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in meters ) is :

Explanation: "speed = ( 5 * 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 * 15 * 60 ) m = 1250 m . correct option : d"

multiply(divide(multiply(5, const_1000), const_60), 15)

<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 60</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">(250/3) * 15</gadget>
<output>1_250</output>
<result>1_250</result>


mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8010 / - . find out the amount that he borrowed .

Explanation: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8010 = p + ( 54 p / 100 ) 8010 = ( 100 p + 54 p ) / 100 8010 = 154 p / 100 p = ( 8010 * 100 ) / 154 = rs . 5201.298 answer : d"

divide(8010, add(const_1, divide(multiply(6, 9), const_100)))

<gadget id="calculator">6 * 9</gadget>
<output>54</output>
<gadget id="calculator">54 / 100</gadget>
<output>27/50 = around 0.54</output>
<gadget id="calculator">1 + (27/50)</gadget>
<output>77/50 = around 1.54</output>
<gadget id="calculator">8_010 / (77/50)</gadget>
<output>400_500/77 = around 5_201.298701</output>
<result>400_500/77 = around 5_201.298701</result>


in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6500 , the number of valid votes that the other candidate got , was :

Explanation: "d number of valid votes = 80 % of 6500 = 5200 . valid votes polled by other candidate = 45 % of 5200 = ( 45 / 100 x 5200 ) = 2340 ."

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 6500)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 6_500</gadget>
<output>2_340</output>
<result>2_340</result>


if 9 ! / 3 ^ x is an integer , what is the greatest possible value of x ?

Explanation: 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 4 is allowed . imo b .

add(divide(9, 3), divide(3, divide(9, 3)))

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


the average of 13 result is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?

Explanation: sum of all the 13 results = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . c

subtract(add(multiply(7, 57), multiply(7, 61)), multiply(13, 60))

<gadget id="calculator">7 * 57</gadget>
<output>399</output>
<gadget id="calculator">7 * 61</gadget>
<output>427</output>
<gadget id="calculator">399 + 427</gadget>
<output>826</output>
<gadget id="calculator">13 * 60</gadget>
<output>780</output>
<gadget id="calculator">826 - 780</gadget>
<output>46</output>
<result>46</result>


after decreasing 25 % in the price of an article costs rs . 1500 . find the actual cost of an article ?

Explanation: "cp * ( 75 / 100 ) = 1500 cp = 20 * 100 = > cp = 2000 answer : d"

divide(1500, subtract(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>3/4 = around 0.75</output>
<gadget id="calculator">1_500 / (3/4)</gadget>
<output>2_000</output>
<result>2_000</result>


if the sides of a triangle are 52 cm , 48 cm and 20 cm , what is its area ?

Explanation: "the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"

<gadget id="calculator">48 * 20</gadget>
<output>960</output>
<gadget id="calculator">960 / 2</gadget>
<output>480</output>
<result>480</result>


5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3443 , how much was it in the beginning ?

Explanation: "x * ( 95 / 100 ) * ( 85 / 100 ) = 3443 x = 4264 answer : a"

floor(divide(3443, multiply(divide(subtract(const_100, 5), const_100), divide(subtract(const_100, 15), const_100))))

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(19/20) * (17/20)</gadget>
<output>323/400 = around 0.8075</output>
<gadget id="calculator">3_443 / (323/400)</gadget>
<output>1_377_200/323 = around 4_263.77709</output>
<gadget id="calculator">floor(1_377_200/323)</gadget>
<output>4_263</output>
<result>4_263</result>


8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 6 men , 4 women and 10 children together complete the piece of work ?

Explanation: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 6 men ’ s 1 day ’ s work = 1 × 6 / 96 = 1 / 16 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 6 men + 4 women + 10 children ) ’ s 1 day ’ s work = 1 / 16 + 1 / 48 + 1 / 24 = 1 / 8 the required no . of days = 8 days answer : option d"

inverse(add(multiply(10, inverse(multiply(24, 10))), add(multiply(inverse(multiply(12, 8)), 6), multiply(inverse(multiply(48, 4)), 4))))

<gadget id="calculator">24 * 10</gadget>
<output>240</output>
<gadget id="calculator">1 / 240</gadget>
<output>1/240 = around 0.004167</output>
<gadget id="calculator">10 * (1/240)</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">12 * 8</gadget>
<output>96</output>
<gadget id="calculator">1 / 96</gadget>
<output>1/96 = around 0.010417</output>
<gadget id="calculator">(1/96) * 6</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">48 * 4</gadget>
<output>192</output>
<gadget id="calculator">1 / 192</gadget>
<output>1/192 = around 0.005208</output>
<gadget id="calculator">(1/192) * 4</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(1/16) + (1/48)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/24) + (1/12)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<result>8</result>


if henry were to add 6 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?

Explanation: "7 / 8 x - 3 / 4 x = 6 galls 1 / 8 * x = 6 gallons x = 48 gallons answer b"

multiply(6, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(7/8) - (3/4)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<result>48</result>


in what time will a railway train 120 m long moving at the rate of 70 kmph pass a telegraph post on its way ?

Explanation: "t = 120 / 70 * 18 / 5 = 6 sec answer : d"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">70 * (5/18)</gadget>
<output>175/9 = around 19.444444</output>
<gadget id="calculator">120 / (175/9)</gadget>
<output>216/35 = around 6.171429</output>
<result>216/35 = around 6.171429</result>


there are 400 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?

Explanation: "there are 396 managers and 4 others . the 4 others would compose 2 % of the total number of people if there were 200 people in the room . thus 200 managers must leave . the answer is d ."

divide(subtract(multiply(400, divide(99, const_100)), multiply(400, divide(98, const_100))), subtract(const_1, divide(98, const_100)))

<gadget id="calculator">99 / 100</gadget>
<output>99/100 = around 0.99</output>
<gadget id="calculator">400 * (99/100)</gadget>
<output>396</output>
<gadget id="calculator">98 / 100</gadget>
<output>49/50 = around 0.98</output>
<gadget id="calculator">400 * (49/50)</gadget>
<output>392</output>
<gadget id="calculator">396 - 392</gadget>
<output>4</output>
<gadget id="calculator">1 - (49/50)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">4 / (1/50)</gadget>
<output>200</output>
<result>200</result>


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 97 % 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 97 % water and 3 % of non - water , so now 1 pound of non - water composes 3 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.03 = 34 pounds . answer : b ."

multiply(divide(subtract(100, 99), subtract(100, 97)), 100)

<gadget id="calculator">100 - 99</gadget>
<output>1</output>
<gadget id="calculator">100 - 97</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</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>


a light flashes every 5 seconds , how many times will it flash in ? of an hour ?

Explanation: "1 flash = 5 sec for 1 min = 12 flashes so for 1 hour = 12 * 60 = 720 flashes . answer : a"

<gadget id="calculator">3_600 / 5</gadget>
<output>720</output>
<result>720</result>


a 6 litre sol is 40 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?

Explanation: "40 % of 6 = 2.4 50 % of 6 = 3 shortage is 0.6 so we need to have 0.6 / 50 % to get 50 % alcohol content . = 1.2 b"

subtract(6, multiply(const_2, multiply(divide(40, const_100), 6)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 6</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">2 * (12/5)</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">6 - (24/5)</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>


in arun ' s opinion , his weight is greater than 63 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 66 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?

Explanation: "let arun ' s weight be x kg . according to arun , 63 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 66 . the values satisfying all the above conditions are 64 and 65 . required average = ( 64 + 65 ) / 2 = 64.5 kg answer : b"

divide(add(66, add(63, const_1)), const_2)

<gadget id="calculator">63 + 1</gadget>
<output>64</output>
<gadget id="calculator">66 + 64</gadget>
<output>130</output>
<gadget id="calculator">130 / 2</gadget>
<output>65</output>
<result>65</result>


a cat leaps 5 leaps for every 4 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?

Explanation: given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 5 / 3 * 4 = 5 : 6 . ' ' answer : 5 : 6 ;

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 5</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">(10/3) / 4</gadget>
<output>5/6 = around 0.833333</output>
<result>5/6 = around 0.833333</result>


the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 15 % profit ?

Explanation: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 115 % of rs . 1600 = 115 / 100 * 1600 = rs . 1840 . answer : c"

multiply(divide(add(const_100, 15), const_100), divide(add(1920, 1280), const_2))

<gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">115 / 100</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>
<gadget id="calculator">(23/20) * 1_600</gadget>
<output>1_840</output>
<result>1_840</result>


rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 125 . how much was lent at 5 % ?

Explanation: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 125 x = 2500 answer : e"

divide(subtract(125, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100)))

<gadget id="calculator">6 * 2_500</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<gadget id="calculator">125 - 150</gadget>
<output>-25</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(1/20) - (3/50)</gadget>
<output>-1/100 = around -0.01</output>
<gadget id="calculator">(-25) / (-1/100)</gadget>
<output>2_500</output>
<result>2_500</result>


surface area of two spheres are in the ratio 1 : 4 what is the ratio of their volumes ?

Explanation: 1 : 8 answer : b

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) ** (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 3</gadget>
<output>1/8 = around 0.125</output>
<result>1/8 = around 0.125</result>