the length of a rectangular floor is more than its breadth by 200 % . if rs . 324 is required to paint the floor at the rate of rs . 3 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 = 324 / 3 = 108 sq m l b = 108 i . e . , l * l / 3 = 108 l 2 = 324 = > l = 18 . answer : c"

multiply(sqrt(divide(divide(324, 3), const_3)), const_3)

<gadget id="calculator">324 / 3</gadget>
<output>108</output>
<gadget id="calculator">108 / 3</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>


a watch was sold at a loss of 10 % . if it was sold for rs . 182 more , there would have been a gain of 4 % . what is the cost price ?

Explanation: "90 % 104 % - - - - - - - - 14 % - - - - 182 100 % - - - - ? = > rs : 1300 answer : d"

divide(multiply(182, const_100), subtract(add(const_100, 4), subtract(const_100, 10)))

<gadget id="calculator">182 * 100</gadget>
<output>18_200</output>
<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">104 - 90</gadget>
<output>14</output>
<gadget id="calculator">18_200 / 14</gadget>
<output>1_300</output>
<result>1_300</result>


a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 10 - sided polygon have ?

Explanation: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 10 . plugging it in , we get 35 diagonals ! answer ( b ) ."

divide(multiply(subtract(10, const_3), 10), const_2)

<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>


a and b start walking towards each other at 5 am at speed of 4 kmph and 8 kmph . they were initially 36 km apart . at what time do they meet ?

Explanation: time of meeting = distance / relative speed = 36 / 8 + 4 = 36 / 12 = 3 hrs after 5 am = 8 am answer is a

<gadget id="calculator">4 + 8</gadget>
<output>12</output>
<gadget id="calculator">36 / 12</gadget>
<output>3</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<result>8</result>


a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over . what is the sum of the two smallest possible values of n ?

Explanation: n = 4 k + 1 = 7 j + 3 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 3 . 1 , 5 , 9 , 13 , 17 = 7 ( 2 ) + 3 the next such number is 17 + 4 * 7 = 45 . 17 + 45 = 62 the answer is c .

add(add(multiply(7, const_2), 3), add(multiply(7, multiply(const_2, const_3)), 3))

<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">14 + 3</gadget>
<output>17</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">7 * 6</gadget>
<output>42</output>
<gadget id="calculator">42 + 3</gadget>
<output>45</output>
<gadget id="calculator">17 + 45</gadget>
<output>62</output>
<result>62</result>


a train 150 m long running at 72 kmph crosses a platform in 28 sec . what is the length of the platform ?

Explanation: "a 410 a = ( 72 * 5 / 18 ) * 28 - 150 = 410"

subtract(multiply(28, multiply(72, const_0_2778)), 150)

<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">28 * 20</gadget>
<output>560</output>
<gadget id="calculator">560 - 150</gadget>
<output>410</output>
<result>410</result>


the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs , find his highest score .

Explanation: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 170 x + ( x - 170 ) = 208 2 x = 378 x = 189 runs answer : c"

divide(add(170, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

<gadget id="calculator">60 * 46</gadget>
<output>2_760</output>
<gadget id="calculator">46 - 2</gadget>
<output>44</output>
<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>
<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>
<gadget id="calculator">170 + 208</gadget>
<output>378</output>
<gadget id="calculator">378 / 2</gadget>
<output>189</output>
<result>189</result>


the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 1000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?

Explanation: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 1000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 1000 ) * t = = = > 3 d = ts + 1000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 1000 t - 2 d = - 2 st + 1000 t 2 d = 2 st - 1000 t d = st - 500 t x 13 : d = s * t st - 500 t = s * t s - 500 = s - 250 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 1000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 1000 2 = 500 d = s * t d = 500 * ( 1 / 2 ) d = 250 answer : a"

multiply(divide(1000, 2), divide(const_1, 2))

<gadget id="calculator">1_000 / 2</gadget>
<output>500</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">500 * (1/2)</gadget>
<output>250</output>
<result>250</result>


in town x , 64 percent of the population are employed , and 35 percent of the population are employed males . what percent of the employed people in town x are females ?

Explanation: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 35 are employed males , hence 29 % are employed females . ( employed females ) / ( total employed people ) = 29 / 64 = 45 % answer : d ."

multiply(divide(subtract(64, 35), 64), const_100)

<gadget id="calculator">64 - 35</gadget>
<output>29</output>
<gadget id="calculator">29 / 64</gadget>
<output>29/64 = around 0.453125</output>
<gadget id="calculator">(29/64) * 100</gadget>
<output>725/16 = around 45.3125</output>
<result>725/16 = around 45.3125</result>


Explanation: "( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d"

<gadget id="calculator">220 / 900</gadget>
<output>11/45 = around 0.244444</output>
<gadget id="calculator">(11/45) + 950</gadget>
<output>42_761/45 = around 950.244444</output>
<gadget id="calculator">(42_761/45) * 900</gadget>
<output>855_220</output>
<result>855_220</result>


__ 2 a x __ b ____ cc in the multiplication problem above , a , b , and c represent distinct digits . if the sum of a and b is equal to 4.6 , what is the value of c ?

Explanation: if a + b = 4.6 assuming a and b are positive then a * b < 10 ( they could be either 1,2 , 3,4 ) therefore a * b = c 2 * b = c a + b = 4.6 three simple equations - divide the 1 st / 2 nd - - > a = 2 plug it the 3 rd - - > b = 2.6 - - > c = 5.2 ( answer b )

divide(multiply(subtract(4.6, 2), const_10), add(const_4, const_1))

<gadget id="calculator">4.6 - 2</gadget>
<output>2.6</output>
<gadget id="calculator">2.6 * 10</gadget>
<output>26</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">26 / 5</gadget>
<output>26/5 = around 5.2</output>
<result>26/5 = around 5.2</result>


country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18,000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?

Explanation: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b

divide(subtract(1950, multiply(multiply(multiply(const_3, multiply(const_2, const_3)), const_1000), divide(9, const_100))), subtract(divide(12, const_100), divide(9, const_100)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">3 * 6</gadget>
<output>18</output>
<gadget id="calculator">18 * 1_000</gadget>
<output>18_000</output>
<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">18_000 * (9/100)</gadget>
<output>1_620</output>
<gadget id="calculator">1_950 - 1_620</gadget>
<output>330</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) - (9/100)</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">330 / (3/100)</gadget>
<output>11_000</output>
<result>11_000</result>


a scuba diver descends at a rate of 40 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3000 feet below the sea level . . how long will he take to reach the ship ?

Explanation: "time taken to reach = 3000 / 40 = 75 minutes answer : c"

<gadget id="calculator">3_000 / 40</gadget>
<output>75</output>
<result>75</result>


a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 18 days , how long will a woman take to complete the work ?

Explanation: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the woman alone can finish the work in 9 days . answer : option a"

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/6) + (1/18)</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(1/3) - (2/9)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>


running at the same constant rate , 6 identical machines can produce a total of 270 pens per minute . at this rate , how many pens could 10 such machines produce in 4 minutes ?

Explanation: "explanation : let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 | | : : 270 : x time 1 : 4 | = > 6 * 1 * x = 10 * 4 * 270 = > x = ( 10 * 4 * 270 ) / 6 = > x = 1800 answer : d"

multiply(multiply(divide(270, 6), 4), 10)

<gadget id="calculator">270 / 6</gadget>
<output>45</output>
<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">180 * 10</gadget>
<output>1_800</output>
<result>1_800</result>


from the sale of sleeping bags , a retailer made a gross profit of 13 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?

Explanation: "cost price * 1.13 = selling price - - > cost price * 1.13 = $ 28 - - > cost price = $ 24.78 . answer : c ."

divide(multiply(28, const_100), add(const_100, 13))

<gadget id="calculator">28 * 100</gadget>
<output>2_800</output>
<gadget id="calculator">100 + 13</gadget>
<output>113</output>
<gadget id="calculator">2_800 / 113</gadget>
<output>2_800/113 = around 24.778761</output>
<result>2_800/113 = around 24.778761</result>


a light has a rating of 86 watts , it is replaced with a new light that has 18 % higher wattage . how many watts does the new light have ?

Explanation: final number = initial number + 18 % ( original number ) = 86 + 18 % ( 86 ) = 86 + 15 = 101 . answer e

multiply(86, add(const_1, divide(18, const_100)))

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">1 + (9/50)</gadget>
<output>59/50 = around 1.18</output>
<gadget id="calculator">86 * (59/50)</gadget>
<output>2_537/25 = around 101.48</output>
<result>2_537/25 = around 101.48</result>


a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?

Explanation: let the man ' s rate upstream be x kmph and that downstream be y kmph . then , distance covered upstream in 8 hrs 48 min = distance covered downstream in 4 hrs . 44 * x / 5 = 4 * y y = 11 / 5 * x required ratio = ( y + x ) / 2 : ( y - x ) / 2 = 8 / 5 : 3 / 5 = 8 / 3 ans - b

divide(divide(add(divide(add(divide(48, const_60), 8), 4), const_1), const_2), divide(subtract(divide(add(divide(48, const_60), 8), 4), const_1), const_2))

<gadget id="calculator">48 / 60</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) + 8</gadget>
<output>44/5 = around 8.8</output>
<gadget id="calculator">(44/5) / 4</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">(11/5) + 1</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(16/5) / 2</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(11/5) - 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) / 2</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(8/5) / (3/5)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>


a worker makes a toy in every 1 h . if he works for 100 h , then how many toys will he make ?

Explanation: "no . of toys = 100 / 1 = 100 answer : e"

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


there are 3000 students in a school and among them 20 % of them attends chess class . 40 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

Explanation: "20 % of 3000 gives 600 . so 600 attends chess and 40 % of 600 gives 240 so 240 enrolled for swimming answer : a"

divide(multiply(divide(multiply(20, 3000), const_100), 40), const_100)

<gadget id="calculator">20 * 3_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 100</gadget>
<output>600</output>
<gadget id="calculator">600 * 40</gadget>
<output>24_000</output>
<gadget id="calculator">24_000 / 100</gadget>
<output>240</output>
<result>240</result>


the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ?

Explanation: "p = 280 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 280 * ( 1 + 10 / 100 ) = 280 * ( 11 / 10 ) = 308 answer is e"

add(280, divide(multiply(280, 10), const_100))

<gadget id="calculator">280 * 10</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>
<gadget id="calculator">280 + 28</gadget>
<output>308</output>
<result>308</result>


mary sold boxes of butter cookies . ann sold 5 times as much as she did . 18 boxes of cookies were sold that day , how many boxes did mary sell ?

Explanation: # of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a

<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">18 / 6</gadget>
<output>3</output>
<result>3</result>


a batsman in his 9 th inning makes a score of 75 and their by increasing his average by 7 . what is his average after the 9 th inning ?

Explanation: 8 x + 75 = 9 ( x + 7 ) x = 12 + 7 = 19 answer : b

<gadget id="calculator">7 * 9</gadget>
<output>63</output>
<gadget id="calculator">75 - 63</gadget>
<output>12</output>
<gadget id="calculator">12 + 7</gadget>
<output>19</output>
<result>19</result>


a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?

Explanation: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the requited distance be x km total time taken = 1 hour = > x / 6 + x / 4 = 1 = > 2 x + 3 x = 12 = > 5 x = 12 = > x = 2.4 km . answer : option c"

divide(multiply(subtract(5, 1), const_3), 5)

<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>


working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 4 x boxes ?

Explanation: rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 4 x / 5 x * 10 = 8 min ans : e

divide(multiply(4, 10), add(speed(10, 10), speed(multiply(2, 10), 5)))

<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<result>8</result>


in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 4 rows in all and a total of 134 bricks in the wall , how many bricks does the bottom row contain ?

Explanation: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 = 134 4 x - 6 = 134 4 x = 128 x = 32 answer : c"

divide(subtract(subtract(subtract(subtract(134, const_1), const_2), const_3), const_4), 4)

<gadget id="calculator">134 - 1</gadget>
<output>133</output>
<gadget id="calculator">133 - 2</gadget>
<output>131</output>
<gadget id="calculator">131 - 3</gadget>
<output>128</output>
<gadget id="calculator">128 - 4</gadget>
<output>124</output>
<gadget id="calculator">124 / 4</gadget>
<output>31</output>
<result>31</result>


if paint costs $ 3.10 per quart , and a quart covers 20 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?

Explanation: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 20 = 30 cost will be 30 * 3.1 = $ 93 ans : c"

<gadget id="calculator">3.1 / 20</gadget>
<output>0.155</output>
<gadget id="calculator">6 * (10 ** 2)</gadget>
<output>600</output>
<gadget id="calculator">0.155 * 600</gadget>
<output>93</output>
<result>93</result>


a man engaged a servant on the condition that he would pay him rs . 1000 and a uniform after one year service . he served only for 9 months and received uniform and rs . 550 , find the price of the uniform ?

Explanation: "9 / 12 = 3 / 4 * 1000 = 750 550 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : d"

multiply(divide(subtract(multiply(9, 1000), multiply(multiply(const_3, const_4), 550)), multiply(multiply(const_3, const_4), const_1)), const_4)

<gadget id="calculator">9 * 1_000</gadget>
<output>9_000</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 550</gadget>
<output>6_600</output>
<gadget id="calculator">9_000 - 6_600</gadget>
<output>2_400</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">2_400 / 12</gadget>
<output>200</output>
<gadget id="calculator">200 * 4</gadget>
<output>800</output>
<result>800</result>


a glass was filled with 24 ounces of water , and 0.06 ounce of the water evaporated each day during a 12 - day period . what percent of the original amount of water evaporated during this period ?

Explanation: "in 12 days 12 * 0.06 = 0.72 ounces of water evaporated , which is 0.72 / 24 â ˆ — 100 = 3 of the original amount of water . answer : c ."

multiply(divide(multiply(0.06, 12), 24), const_100)

<gadget id="calculator">0.06 * 12</gadget>
<output>0.72</output>
<gadget id="calculator">0.72 / 24</gadget>
<output>0.03</output>
<gadget id="calculator">0.03 * 100</gadget>
<output>3</output>
<result>3</result>


i chose a number and divide it by 4 . then i subtracted 18 from the result and got 7 . what was the number i chose ?

Explanation: solution : let x be the number i chose , then x / 4 â ˆ ’ 18 = 7 x / 4 = 25 x = 100 answer b

<gadget id="calculator">18 + 7</gadget>
<output>25</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<result>100</result>


there are 76 persons . 54 can read hindu , 43 can read times , 37 can read deccan and 15 can read all . if 24 can read hindu and deccan and 27 can read deccan and times then what is the number of persons who read only times and hindu .

Explanation: let ' a ' can be read hindu , let ' b ' can be read times , let ' c ' can be read deccan , from the given data : n ( aubuc ) = 76 , n ( a ) = 54 , n ( b ) = 43 , n ( c ) = 37 , n ( anbnc ) = 15 , n ( anc ) = 24 , n ( bnc ) = 27 , n ( anb ) = ? n ( aubuc ) = n ( a ) + n ( b ) + n ( c ) - n ( anb ) - n ( bnc ) - n ( anc ) + n ( anbnc ) = = > 76 = 54 + 43 + 37 - n ( anb ) - 24 - 27 + 15 = = > n ( anb ) = 54 + 43 + 37 + 15 - 24 - 27 - 76 = = > n ( anb ) = 149 - 127 = = > n ( anb ) = 22 answer : b

<gadget id="calculator">24 - 15</gadget>
<output>9</output>
<gadget id="calculator">27 - 15</gadget>
<output>12</output>
<gadget id="calculator">9 + 12</gadget>
<output>21</output>
<result>21</result>


the original price of a suit is $ 100 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?

Explanation: "0.8 * ( 1.2 * 100 ) = $ 96 the answer is b ."

subtract(add(100, divide(multiply(100, 20), const_100)), divide(multiply(add(100, divide(multiply(100, 20), const_100)), 20), const_100))

<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 * 20</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 100</gadget>
<output>24</output>
<gadget id="calculator">120 - 24</gadget>
<output>96</output>
<result>96</result>


the average runs scored by a batsman in 20 matches is 40 . in the next 30 matches the batsman scored an average of 20 runs . find his average in all the 50 matches ?

Explanation: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 30 matches = 600 . total score of the batsman in the 50 matches = 1400 . average score of the batsman = 1400 / 50 = 28 . answer : c"

divide(add(multiply(40, 20), multiply(20, 30)), add(20, 30))

<gadget id="calculator">40 * 20</gadget>
<output>800</output>
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
<gadget id="calculator">800 + 600</gadget>
<output>1_400</output>
<gadget id="calculator">20 + 30</gadget>
<output>50</output>
<gadget id="calculator">1_400 / 50</gadget>
<output>28</output>
<result>28</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 5000 , the number of valid votes that the other candidate got , was :

Explanation: "a number of valid votes = 80 % of 5000 = 4000 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 x 4000 ) = 1800 ."

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 5000)

<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) * 5_000</gadget>
<output>1_800</output>
<result>1_800</result>


for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?

Explanation: index for females = ( 20 - 8 ) / 20 = 3 / 5 = 0.6 index for males = ( 20 - 12 / 20 = 2 / 5 = 0.4 index for females exceeds males by 0.6 - 0.4 = 0.2 answer : c

subtract(divide(subtract(20, 8), 20), divide(8, 20))

<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">12 / 20</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


chocolate bars are sold in packages of 4 or 9 only . if mark bought 97 chocolate bars exactly , what could be the number of large packs mark bought ?

Explanation: let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">97 - 16</gadget>
<output>81</output>
<gadget id="calculator">81 / 9</gadget>
<output>9</output>
<result>9</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 20 % 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 . = 120 % of rs . 1600 = 120 / 100 * 1600 = rs . 1920 . answer : d"

multiply(divide(add(const_100, 20), const_100), divide(add(1920, 1280), const_2))

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</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">(6/5) * 1_600</gadget>
<output>1_920</output>
<result>1_920</result>


find the least number must be subtracted from 531742 so that remaining no . is divisible by 3 ?

Explanation: "on dividing 531742 by 3 we get the remainder 1 , so 1 should be subtracted c"

subtract(531742, multiply(floor(divide(531742, 3)), 3))

<gadget id="calculator">531_742 / 3</gadget>
<output>531_742/3 = around 177_247.333333</output>
<gadget id="calculator">floor(531_742/3)</gadget>
<output>177_247</output>
<gadget id="calculator">177_247 * 3</gadget>
<output>531_741</output>
<gadget id="calculator">531_742 - 531_741</gadget>
<output>1</output>
<result>1</result>


10 men can cut 10 trees in 2 hours . if 2 men leave the job , how many trees will be cut in 3 hours ?

Explanation: 10 men - working 2 hrs - cut 10 trees 1 men - working 1 hr - cuts = 10 / 10 * 2 thus 8 men - working 3 hrs - cut = 10 * 8 * 3 / 10 * 2 = 12 trees answer is a

multiply(multiply(subtract(10, 2), divide(divide(10, 2), 10)), 3)

<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">8 * (1/2)</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>12</result>


if x and y are integers such that x ^ 2 = 2 y and xy = 32 , then x – y = ?

Explanation: "here x and y are integers . x ^ 2 = 2 y , xy = 32 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 32 * 2 = > x ^ 3 = 64 . here x 3 is positive , x is also positive . x = 4 then y = 8 . x - y = - 4 so option d is correct"

subtract(power(multiply(32, 2), const_0_33), divide(32, power(multiply(32, 2), const_0_33)))

<gadget id="calculator">32 * 2</gadget>
<output>64</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>
<gadget id="calculator">32 / 4</gadget>
<output>8</output>
<gadget id="calculator">4 - 8</gadget>
<output>-4</output>
<result>-4</result>


a shopkeeper loses 15 % , if an article is sold for $ 102 . what should be the selling price of the article to gain 20 % ?

Explanation: "c $ 144 given that sp = $ 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = $ 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = $ 144"

add(divide(102, subtract(const_1, divide(15, const_100))), multiply(divide(102, subtract(const_1, divide(15, const_100))), divide(20, const_100)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">102 / (17/20)</gadget>
<output>120</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">120 * (1/5)</gadget>
<output>24</output>
<gadget id="calculator">120 + 24</gadget>
<output>144</output>
<result>144</result>


after decreasing 24 % in the price of an article costs rs . 912 . find the actual cost of an article ?

Explanation: "cp * ( 76 / 100 ) = 912 cp = 12 * 100 = > cp = 1200 answer : c"

divide(912, subtract(const_1, divide(24, const_100)))

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">912 / (19/25)</gadget>
<output>1_200</output>
<result>1_200</result>


a man sells an article at 10 % gain . had be sold at for rs . 60 / - more he could have gained 20 % what is cost price of article

Explanation: first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '

multiply(divide(60, subtract(20, 10)), const_100)

<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<result>600</result>


if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 7 ¤ √ 7 =

Explanation: "x = √ 7 and y also = √ 7 applying the function ( √ 7 + √ 7 ) ^ 2 - ( √ 7 - √ 7 ) ^ 2 = ( 2 √ 7 ) ^ 2 - 0 = 4 x 7 = 28 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 7 and y = √ 7 you get the answer 28 . answer e"

<gadget id="calculator">7 ** (1/2)</gadget>
<output>sqrt(7) = around 2.645751</output>
<gadget id="calculator">(sqrt(7)) + (sqrt(7))</gadget>
<output>2*sqrt(7) = around 5.291503</output>
<gadget id="calculator">(2*sqrt(7)) ** 2</gadget>
<output>28</output>
<result>28</result>


6 people can do work in 80 days how much people they required to complete the work in 16 days ?

Explanation: man and days concept . . . 6 m * 80 d = m * 16 d solve it , total no of people required is 30 ; answer : c

<gadget id="calculator">6 * 80</gadget>
<output>480</output>
<gadget id="calculator">480 / 16</gadget>
<output>30</output>
<result>30</result>


the average of 10 consecutive integers is 15 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?

Explanation: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is b ."

divide(subtract(multiply(10, 15), multiply(add(const_4, const_1), 9)), 10)

<gadget id="calculator">10 * 15</gadget>
<output>150</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 9</gadget>
<output>45</output>
<gadget id="calculator">150 - 45</gadget>
<output>105</output>
<gadget id="calculator">105 / 10</gadget>
<output>21/2 = around 10.5</output>
<result>21/2 = around 10.5</result>


on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 140 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?

Explanation: "explanation : since 312 inch = 140 km so 1 inch = 140 / 312 km so 34 inch = ( 140 ã — 34 ) / 312 = 15.25 km answer : d"

<gadget id="calculator">34 * 140</gadget>
<output>4_760</output>
<gadget id="calculator">4_760 / 312</gadget>
<output>595/39 = around 15.25641</output>
<result>595/39 = around 15.25641</result>


a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 8 % dividend at the end of the year , then how much does he get ?

Explanation: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 8 / 100 x 12000 ) = rs . 960 . answer c"

multiply(multiply(100, divide(add(add(multiply(const_10, const_1000), multiply(const_4, const_1000)), multiply(const_4, 100)), add(100, multiply(100, divide(20, 100))))), divide(8, 100))

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">10_000 + 4_000</gadget>
<output>14_000</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">14_000 + 400</gadget>
<output>14_400</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">100 * (1/5)</gadget>
<output>20</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">14_400 / 120</gadget>
<output>120</output>
<gadget id="calculator">100 * 120</gadget>
<output>12_000</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">12_000 * (2/25)</gadget>
<output>960</output>
<result>960</result>


a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 1500 interest only for the period . the principal amount borrowed by him was ?

Explanation: principal = ( 100 * 1500 ) / ( 12 * 20 ) = rs . 625 answer : a

divide(divide(multiply(1500, const_100), 20), 12)

<gadget id="calculator">1_500 * 100</gadget>
<output>150_000</output>
<gadget id="calculator">150_000 / 20</gadget>
<output>7_500</output>
<gadget id="calculator">7_500 / 12</gadget>
<output>625</output>
<result>625</result>


david and lewis leave chennai for tirupati simultaneously at 7 a . m in the morning driving in two cars at speeds of 60 mph and 80 mph respectively . as soon as lewis reaches tirupati he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 160 miles , how far from chennai did david and lewis meet ?

Explanation: time taken by lewis to reach tirupati = 160 / 80 = 2 hours in 2 hours , david travels 60 * 2 = 120 miles so distance at which they meet should be greater than 120 miles . only b satisfies . answer is b .

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


the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ?

Explanation: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.6 x ( 120 ) i . e . 160 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 160 = 62.5 i . e . y decreases from 100 to 62.5 i . e . decrease of 37.5 % answer : option d"

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

<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">100 / 160</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>


linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?

Explanation: if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 400 . so 1 / 4 of her savings is $ 400 . so her original savings are 4 times $ 400 = $ 1600 correct answer b

divide(400, subtract(const_1, divide(3, 4)))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">400 / (1/4)</gadget>
<output>1_600</output>
<result>1_600</result>


city a to city b , andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph . what was the average speed for the whole trip ?

Explanation: the total distance is 1 × 50 + 3 × 60 = 2301 × 50 + 3 × 60 = 230 . and the total time is 4 hours . hence , average speed = ( total distancetotal time ) = 2304 = 57.5 b

divide(add(multiply(50, 1), multiply(60, 3)), add(3, 1))

<gadget id="calculator">50 * 1</gadget>
<output>50</output>
<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">50 + 180</gadget>
<output>230</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">230 / 4</gadget>
<output>115/2 = around 57.5</output>
<result>115/2 = around 57.5</result>


laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 15 kmph and prasanna moves southward at a speed of 45 kmph . how far will be prasanna from laxmi after 60 minutes ?

Explanation: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 15 kmph x 1 hr = 15 km total southward prasanna ' s distance = 45 kmph x 1 hr = 45 km total distance between prasanna and laxmi is = 15 + 45 = 60 km . answer : e"

<gadget id="calculator">15 + 45</gadget>
<output>60</output>
<result>60</result>


car x began traveling at an average speed of 35 miles per hour . after 84 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

Explanation: in 84 minutes , car x travels 49 miles . car y gains 7 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d .

multiply(35, divide(multiply(divide(84, const_60), 35), subtract(42, 35)))

<gadget id="calculator">84 / 60</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(7/5) * 35</gadget>
<output>49</output>
<gadget id="calculator">42 - 35</gadget>
<output>7</output>
<gadget id="calculator">49 / 7</gadget>
<output>7</output>
<gadget id="calculator">35 * 7</gadget>
<output>245</output>
<result>245</result>


the cost of producing x tools by a company is given by c ( x ) = 600 x + 5500 ( in $ ) a ) what is the cost of 100 tools ?

Explanation: solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a

<gadget id="calculator">100 * 600</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 + 5_500</gadget>
<output>65_500</output>
<result>65_500</result>


how many odd numbers between 10 and 1,000 are the squares of integers ?

Explanation: the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 14 numbers . answer : c .

<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<result>14</result>


a man can row 11 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?

Explanation: "m = 11 s = 1.2 ds = 12.2 us = 9.8 x / 12.2 + x / 9.8 = 1 x = 5.43 d = 5.43 * 2 = 10.87 answer : e"

multiply(divide(multiply(add(11, 1.2), subtract(11, 1.2)), add(add(11, 1.2), subtract(11, 1.2))), const_2)

<gadget id="calculator">11 + 1.2</gadget>
<output>12.2</output>
<gadget id="calculator">11 - 1.2</gadget>
<output>9.8</output>
<gadget id="calculator">12.2 * 9.8</gadget>
<output>119.56</output>
<gadget id="calculator">12.2 + 9.8</gadget>
<output>22</output>
<gadget id="calculator">119.56 / 22</gadget>
<output>5.434545</output>
<gadget id="calculator">5.434545 * 2</gadget>
<output>10.86909</output>
<result>10.86909</result>


if the l . c . m of two numbers is 720 and their product is 38880 , find the h . c . f of the numbers .

Explanation: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 38880 / 720 = 54 . answer : d"

<gadget id="calculator">38_880 / 720</gadget>
<output>54</output>
<result>54</result>


a , b and c have rs . 400 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?

Explanation: "a + b + c = 400 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 400 - - - - - - - - - - - - - - - - c = 150 answer : a"

<gadget id="calculator">200 + 350</gadget>
<output>550</output>
<gadget id="calculator">550 - 400</gadget>
<output>150</output>
<result>150</result>


an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth

Explanation: explanation : let the total sale be rs . x . then , 2.5 % . of x = 12.50 < = > ( 25 / 100 * 1 / 100 * x ) = 125 / 10 < = > x = 500 . answer : b ) 500

<gadget id="calculator">2.5 / 100</gadget>
<output>0.025</output>
<gadget id="calculator">12.5 / 0.025</gadget>
<output>500</output>
<result>500</result>


an empty wooden vessel weighs 20 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .

Explanation: an empty wooden vessel weighs 20 % of its total weight when filled with paint : vessel = 0.2 ( vessel + paint ) ; 20 v = v + p ( so the weight of completely filled vessel is 10 v ) p = 19 v ( so the weight of the paint when the vessels is completely filled is 19 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 20 v ; p ' = 9 v ( so the weight of the paint when the vessels is partially filled is 9 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 9 v / 19 v = 9 / 19 . answer : d .

divide(subtract(divide(20, const_2), const_1), subtract(20, const_1))

<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">9 / 19</gadget>
<output>9/19 = around 0.473684</output>
<result>9/19 = around 0.473684</result>


a cycle is bought for rs . 900 and sold for rs . 990 , find the gain percent ?

Explanation: "900 - - - - 90 100 - - - - ? = > 10 % answer : e"

multiply(divide(subtract(990, 900), 900), const_100)

<gadget id="calculator">990 - 900</gadget>
<output>90</output>
<gadget id="calculator">90 / 900</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>


Explanation: "( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) = 0.0060 * 360 / 4 * ( 0.1 ) ( 0.006 ) = 0.066 * 90 / 1 * 0.006 = 66 * 90 / 6 = 11 * 90 = 990 answer : a"

<gadget id="calculator">0.0066 * 3.6</gadget>
<output>0.02376</output>
<gadget id="calculator">0.04 * 0.1</gadget>
<output>0.004</output>
<gadget id="calculator">0.004 * 0.006</gadget>
<output>0.000024</output>
<gadget id="calculator">0.02376 / 0.000024</gadget>
<output>990</output>
<result>990</result>


in the manufacture of a certain product , 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

Explanation: "0.09 * 0.05 = 0.0045 = 0.45 % the answer is b ."

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">9 * (1/20)</gadget>
<output>9/20 = around 0.45</output>
<result>9/20 = around 0.45</result>


if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9600 ?

Explanation: required difference = [ 3 ½ % of rs . 9600 ] – [ 3 1 / 3 % of rs . 9600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9600 = 1 / 6 % of rs . 9600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9600 ] = rs . 16 . answer is e .

divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 9600), const_100)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 3</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) + 3</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">(7/2) - (10/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 9_600</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 / 100</gadget>
<output>16</output>
<result>16</result>


a 6 % stock yields 8 % . the market value of the stock is :

Explanation: for an income of rs . 8 , investment = rs . 100 . for an income of rs . 6 , investment = rs . 100 x 6 = rs . 75 . 8 market value of rs . 100 stock = rs . 75 . answer : b

<gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 6</gadget>
<output>75</output>
<result>75</result>


john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 16 , what was the price before the first discount ?

Explanation: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 16 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 16 solve for x x = $ 28.44 correct answer b"

divide(multiply(multiply(const_100, const_100), 16), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25)))

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 16</gadget>
<output>160_000</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>
<gadget id="calculator">75 * 25</gadget>
<output>1_875</output>
<gadget id="calculator">7_500 - 1_875</gadget>
<output>5_625</output>
<gadget id="calculator">160_000 / 5_625</gadget>
<output>256/9 = around 28.444444</output>
<result>256/9 = around 28.444444</result>


in an election between the two candidates , the candidates who gets 60 % of votes polled is winned by 280 votes majority . what is the total number of votes polled ?

Explanation: "note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a )"

divide(multiply(const_100, 280), subtract(60, subtract(const_100, 60)))

<gadget id="calculator">100 * 280</gadget>
<output>28_000</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">28_000 / 20</gadget>
<output>1_400</output>
<result>1_400</result>


the height of a cylinder is 60 cm and the diameter of its base is 5 cm . the total surface area of the cylinder is

Explanation: given h = 60 cm and r = 5 / 2 cm total surface area = 2 π rh + 2 & pir ( power 2 ) = 2 π r ( h + r ) = [ 2 × 22 / 7 × 5 / 2 × ( 60 + 5 / 2 ) ] cm ( power 2 ) = [ 44 / 7 × 5 / 2 × ( ( 120 + 5 ) / 2 ) ] cm ( power 2 ) = 22 / 7 × 5 × 125 / 2 cm ( power 2 ) = ( 55 × 125 ) / 7 cm ( power 2 ) = 6875 / 7 cm ( power 2 ) = 982.14 cm ( power 2 ) answer is c .

<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">2 * pi * (5/2) * ((5/2) + 60)</gadget>
<output>625*pi/2 = around 981.747704</output>
<result>625*pi/2 = around 981.747704</result>


a tank is filled by 3 pipes a , b , c in 7 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?

Explanation: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 7 7 / x = 1 / 7 x = 49 hours answer is d"

multiply(add(add(multiply(const_2, const_2), const_2), const_1), 7)

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<result>49</result>


a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 70 surveys involving the use of her cellphone , how much did she get that week ?

Explanation: amount earned using her cell phone = 70 * 22 = 1540 earned for remaining surveys = 30 * 20 = 600 total earning = 2140 answer : a

add(multiply(20, 100), multiply(70, multiply(20, divide(10, const_100))))

<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">20 * (1/10)</gadget>
<output>2</output>
<gadget id="calculator">70 * 2</gadget>
<output>140</output>
<gadget id="calculator">2_000 + 140</gadget>
<output>2_140</output>
<result>2_140</result>


if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 38 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?

Explanation: "0.1 x = 0.08 ( 2000 - x ) + 38 0.18 x = 198 x = 1100 then the amount invested at 8 % is $ 2000 - $ 1100 = $ 900 the answer is c ."

subtract(multiply(multiply(const_100, 10), const_2), divide(add(multiply(multiply(10, 8), const_2), 38), add(divide(10, const_100), divide(8, const_100))))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 2</gadget>
<output>2_000</output>
<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<gadget id="calculator">80 * 2</gadget>
<output>160</output>
<gadget id="calculator">160 + 38</gadget>
<output>198</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(1/10) + (2/25)</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">198 / (9/50)</gadget>
<output>1_100</output>
<gadget id="calculator">2_000 - 1_100</gadget>
<output>900</output>
<result>900</result>


the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 42 kmph , find the speed of the stream ?

Explanation: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 42 / 3 = 14 kmph . answer : c"

subtract(42, divide(multiply(42, const_2), const_3))

<gadget id="calculator">42 * 2</gadget>
<output>84</output>
<gadget id="calculator">84 / 3</gadget>
<output>28</output>
<gadget id="calculator">42 - 28</gadget>
<output>14</output>
<result>14</result>


by selling an article at rs . 300 , a profit of 25 % is made . find its cost price ?

Explanation: "sp = 300 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 300 * [ 100 / ( 100 + 25 ) ] = 300 * [ 100 / 125 ] = rs . 240 answer : c"

divide(multiply(300, const_100), add(const_100, 25))

<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">30_000 / 125</gadget>
<output>240</output>
<result>240</result>


a batsman scores 26 runs and increases his average from 14 to 15 . find the runs to be made if he wants top increasing the average to 19 in the same match ?

Explanation: number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d

subtract(multiply(19, add(subtract(26, 15), const_1)), multiply(14, subtract(26, 15)))

<gadget id="calculator">26 - 15</gadget>
<output>11</output>
<gadget id="calculator">11 + 1</gadget>
<output>12</output>
<gadget id="calculator">19 * 12</gadget>
<output>228</output>
<gadget id="calculator">14 * 11</gadget>
<output>154</output>
<gadget id="calculator">228 - 154</gadget>
<output>74</output>
<result>74</result>


a total of 520 players participated in a single tennis knock out tournament . what is the total number of matches played in the tournament ? ( knockout means if a player loses , he is out of the tournament ) . no match ends in a tie .

Explanation: there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b

add(add(add(add(add(add(add(divide(divide(divide(520, const_2), const_2), const_2), add(divide(520, const_2), divide(divide(520, const_2), const_2))), divide(divide(divide(divide(520, const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2))

<gadget id="calculator">520 / 2</gadget>
<output>260</output>
<gadget id="calculator">260 / 2</gadget>
<output>130</output>
<gadget id="calculator">130 / 2</gadget>
<output>65</output>
<gadget id="calculator">260 + 130</gadget>
<output>390</output>
<gadget id="calculator">65 + 390</gadget>
<output>455</output>
<gadget id="calculator">65 / 2</gadget>
<output>65/2 = around 32.5</output>
<gadget id="calculator">455 + (65/2)</gadget>
<output>975/2 = around 487.5</output>
<gadget id="calculator">(65/2) / 2</gadget>
<output>65/4 = around 16.25</output>
<gadget id="calculator">(975/2) + (65/4)</gadget>
<output>2_015/4 = around 503.75</output>
<gadget id="calculator">(65/4) / 2</gadget>
<output>65/8 = around 8.125</output>
<gadget id="calculator">(2_015/4) + (65/8)</gadget>
<output>4_095/8 = around 511.875</output>
<gadget id="calculator">(65/8) / 2</gadget>
<output>65/16 = around 4.0625</output>
<gadget id="calculator">(4_095/8) + (65/16)</gadget>
<output>8_255/16 = around 515.9375</output>
<gadget id="calculator">(65/16) / 2</gadget>
<output>65/32 = around 2.03125</output>
<gadget id="calculator">(8_255/16) + (65/32)</gadget>
<output>16_575/32 = around 517.96875</output>
<gadget id="calculator">(65/32) / 2</gadget>
<output>65/64 = around 1.015625</output>
<gadget id="calculator">(16_575/32) + (65/64)</gadget>
<output>33_215/64 = around 518.984375</output>
<result>33_215/64 = around 518.984375</result>


solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22

Explanation: ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c

divide(subtract(multiply(multiply(2, 6), 22), add(multiply(8, 6), multiply(2, 6))), add(multiply(9, 6), multiply(7, const_2)))

<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">12 * 22</gadget>
<output>264</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">48 + 12</gadget>
<output>60</output>
<gadget id="calculator">264 - 60</gadget>
<output>204</output>
<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">54 + 14</gadget>
<output>68</output>
<gadget id="calculator">204 / 68</gadget>
<output>3</output>
<result>3</result>


two good train each 750 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .

Explanation: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 750 + 750 ) m = 1500 m . required time = ( 1500 x 6 / 125 ) sec = 72 sec . answer d"

multiply(multiply(750, inverse(multiply(add(45, 30), const_0_2778))), const_2)

<gadget id="calculator">45 + 30</gadget>
<output>75</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">75 * (5/18)</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">1 / (125/6)</gadget>
<output>6/125 = around 0.048</output>
<gadget id="calculator">750 * (6/125)</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<result>72</result>


the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4800 sq cm . what is the ratio of the width and the area of the rectangle ?

Explanation: let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4800 12 x ^ 2 = 4800 x ^ 2 = 400 x = 20 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 80 the answer is c .

divide(divide(sqrt(multiply(const_3, 4800)), const_2), 4800)

<gadget id="calculator">3 * 4_800</gadget>
<output>14_400</output>
<gadget id="calculator">14_400 ** (1/2)</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 / 4_800</gadget>
<output>1/80 = around 0.0125</output>
<result>1/80 = around 0.0125</result>


a work which could be finished in 7 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?

Explanation: "x - - - - - - - 7 ( x + 10 ) - - - - 6 x * 7 = ( x + 10 ) 6 x = 60 \ answer : c"

divide(multiply(multiply(3, const_2), 10), subtract(7, multiply(3, const_2)))

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">7 - 6</gadget>
<output>1</output>
<gadget id="calculator">60 / 1</gadget>
<output>60</output>
<result>60</result>


if ( 6 ) ( x ^ 2 ) has 3 different prime factors , at most how many different prime factors does x have ?

Explanation: x can have at most 3 prime factors , namely the prime factors 2 and 3 , plus one other . if x had more than this number of prime factors , then ( 6 ) ( x ^ 2 ) would have more than 3 prime factors . the answer is c .

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


a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 190 kilometers ?

Explanation: each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 180 ã · 40 = 9.5 ã — 1 gallon = 9.5 gallons correct answer is b ) 9.5 gallons

<gadget id="calculator">190 / 20</gadget>
<output>19/2 = around 9.5</output>
<result>19/2 = around 9.5</result>


the list price of an article is rs . 66 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

Explanation: "66 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 5.45 % answer : c"

multiply(divide(subtract(subtract(66, multiply(66, divide(10, const_100))), 56.16), subtract(66, multiply(66, divide(10, const_100)))), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">66 * (1/10)</gadget>
<output>33/5 = around 6.6</output>
<gadget id="calculator">66 - (33/5)</gadget>
<output>297/5 = around 59.4</output>
<gadget id="calculator">(297/5) - 56.16</gadget>
<output>3.24</output>
<gadget id="calculator">3.24 / (297/5)</gadget>
<output>0.054545</output>
<gadget id="calculator">0.054545 * 100</gadget>
<output>5.4545</output>
<result>5.4545</result>


a trader marked the selling price of an article at 60 % 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 . 160 , s . p . = rs . 99 . ∴ discount % = [ 11 / 160 * 100 ] % = 6.8 % answer c"

multiply(const_100, divide(add(multiply(add(const_2, const_3), const_2), 1), add(const_100, 60)))

<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 + 60</gadget>
<output>160</output>
<gadget id="calculator">11 / 160</gadget>
<output>11/160 = around 0.06875</output>
<gadget id="calculator">100 * (11/160)</gadget>
<output>55/8 = around 6.875</output>
<result>55/8 = around 6.875</result>


a person saved $ 10 in buying an item on sale . if he spent $ 200 for the item , approximately how much percent he saved in the transaction ?

Explanation: "actual price = 200 + 10 = $ 210 saving = 10 / 210 * 100 = 100 / 21 = 5 % approximately answer is d"

add(floor(multiply(divide(10, add(10, 200)), const_100)), const_1)

<gadget id="calculator">10 + 200</gadget>
<output>210</output>
<gadget id="calculator">10 / 210</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">(1/21) * 100</gadget>
<output>100/21 = around 4.761905</output>
<gadget id="calculator">floor(100/21)</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<result>5</result>


a is 1.5 times as fast as b . a alone can do the work in 20 days . if a and b working together , in how many days will the work be completed ?

Explanation: a can finish 1 work in 20 days b can finish 1 / 1.5 work in 20 days - since a is 1.5 faster than b this means b can finish 1 work in 20 * 1.5 days = 30 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 30 / ( 20 + 30 ) = 20 * 30 / 50 = 12 days so answer is c

divide(const_1, add(divide(const_1, 20), divide(divide(const_1, 20), 1.5)))

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) / 1.5</gadget>
<output>0.033333</output>
<gadget id="calculator">(1/20) + 0.033333</gadget>
<output>0.083333</output>
<gadget id="calculator">1 / 0.083333</gadget>
<output>12.000048</output>
<result>12.000048</result>


if a speaks the truth 65 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time

Explanation: "explanation : probability that a speaks truth is 65 / 100 = 0.65 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.65 × 0.6 = 0.39 answer : a"

multiply(divide(65, multiply(multiply(const_4, const_5), const_5)), divide(60, multiply(multiply(const_4, const_5), const_5)))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(13/20) * (3/5)</gadget>
<output>39/100 = around 0.39</output>
<result>39/100 = around 0.39</result>


if a = 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?

Explanation: if a = 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) ] = - [ 1 + 1 + 1 + 1 ] = - 4 answer = b = - 4

negate(add(add(add(power(1, 2), power(1, 3)), power(1, 4)), power(1, 5)))

<gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">1 ** 4</gadget>
<output>1</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">1 ** 5</gadget>
<output>1</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">-4</gadget>
<output>-4</output>
<result>-4</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 30 % ?

Explanation: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 70 2 / 3 sp 1 = 70 sp 1 = 105 100 - - - 105 = > 5 % answer : e"

subtract(divide(subtract(const_100, 30), divide(2, 3)), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">70 / (2/3)</gadget>
<output>105</output>
<gadget id="calculator">105 - 100</gadget>
<output>5</output>
<result>5</result>


an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?

Explanation: we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b

add(divide(subtract(49, multiply(1.5, add(const_2, const_4))), 8), add(const_2, const_4))

<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">1.5 * 6</gadget>
<output>9</output>
<gadget id="calculator">49 - 9</gadget>
<output>40</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">5 + 6</gadget>
<output>11</output>
<result>11</result>


village a ’ s population is 300 greater than village b ' s population . if village b ’ s population were reduced by 600 people , then village a ’ s population would be 4 times as large as village b ' s population . what is village b ' s current population ?

Explanation: a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a .

divide(add(multiply(600, 4), 300), subtract(4, const_1))

<gadget id="calculator">600 * 4</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 + 300</gadget>
<output>2_700</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">2_700 / 3</gadget>
<output>900</output>
<result>900</result>


a sum amounts to rs . 4851 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?

Explanation: "ci = 4851 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4851 = p [ 21 / 20 ] ^ 2 4851 [ 20 / 21 ] ^ 2 4400 answer : c"

divide(4851, power(add(divide(5, const_100), const_1), 2))

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">4_851 / (441/400)</gadget>
<output>4_400</output>
<result>4_400</result>


the average monthly salary of 10 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?

Explanation: "manager ' s monthly salary = rs . ( 1700 * 11 - 1600 * 10 ) = rs . 2700 answer : c"

subtract(multiply(add(1600, 100), add(10, const_1)), multiply(1600, 10))

<gadget id="calculator">1_600 + 100</gadget>
<output>1_700</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">1_700 * 11</gadget>
<output>18_700</output>
<gadget id="calculator">1_600 * 10</gadget>
<output>16_000</output>
<gadget id="calculator">18_700 - 16_000</gadget>
<output>2_700</output>
<result>2_700</result>


if a lends rs . 1200 to b at 10 % per annum and b lends the same sum to c at 18 % per annum then the gain of b in a period of 2 years is ?

Explanation: "( 1200 * 8 * 2 ) / 100 = > 192 answer : c"

subtract(divide(multiply(multiply(1200, 18), 2), const_100), divide(multiply(multiply(1200, 10), 2), const_100))

<gadget id="calculator">1_200 * 18</gadget>
<output>21_600</output>
<gadget id="calculator">21_600 * 2</gadget>
<output>43_200</output>
<gadget id="calculator">43_200 / 100</gadget>
<output>432</output>
<gadget id="calculator">1_200 * 10</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 * 2</gadget>
<output>24_000</output>
<gadget id="calculator">24_000 / 100</gadget>
<output>240</output>
<gadget id="calculator">432 - 240</gadget>
<output>192</output>
<result>192</result>


if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ?

Explanation: i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 6 = integer , therefore we have 48 / 96 numbers divisible by 6 o e o / 6 = not integer we can not forget multiples of 6 from 1 to 96 we have 16 numbers that are multiple of 8 therefore , 48 / 96 + 16 / 96 = 64 / 96 = 2 / 3 answer : a

divide(add(divide(96, 2), divide(96, 6)), 96)

<gadget id="calculator">96 / 2</gadget>
<output>48</output>
<gadget id="calculator">96 / 6</gadget>
<output>16</output>
<gadget id="calculator">48 + 16</gadget>
<output>64</output>
<gadget id="calculator">64 / 96</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5 ?

Explanation: "the numbers should be of the form 5 c + 3 . the minimum is 3 when c = 0 . the maximum is 48 when c = 9 . there are 10 such numbers . the answer is e ."

<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<result>10</result>


6 students wrote science exam . their average marks are 70 . 5 students got 65 , 75 , 55 , 72 and 69 marks respectively . therefore what is the marks of the sixth student ?

Explanation: explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) – 336 ] = ( 420 – 336 ) = 84 answer a

<gadget id="calculator">70 * 6</gadget>
<output>420</output>
<gadget id="calculator">65 + 75</gadget>
<output>140</output>
<gadget id="calculator">140 + 55</gadget>
<output>195</output>
<gadget id="calculator">195 + 72</gadget>
<output>267</output>
<gadget id="calculator">267 + 69</gadget>
<output>336</output>
<gadget id="calculator">420 - 336</gadget>
<output>84</output>
<result>84</result>


a bowl was filled with 10 ounces of water , and 0.010 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?

Explanation: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 010 * 100 / 2 = 1.0 / 2 = . 5 percent of the original amount of water evaporated during this period = ( . 5 / 10 ) * 100 % = 5 % answer d"

multiply(divide(multiply(50, 0.010), 10), const_100)

<gadget id="calculator">50 * 0.01</gadget>
<output>0.5</output>
<gadget id="calculator">0.5 / 10</gadget>
<output>0.05</output>
<gadget id="calculator">0.05 * 100</gadget>
<output>5</output>
<result>5</result>


the sum of 7 th and 23 rd term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0

Explanation: t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a

<gadget id="calculator">8 + 15</gadget>
<output>23</output>
<gadget id="calculator">13 + 23</gadget>
<output>36</output>
<gadget id="calculator">7 + 23</gadget>
<output>30</output>
<gadget id="calculator">36 - 30</gadget>
<output>6</output>
<result>6</result>


let c be defined as the sum of all prime numbers between 0 and 35 . what is c / 3

Explanation: prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 33 sum , c = 193 c / 3 = 64.3 answer c

add(divide(3, const_10), power(const_2, add(const_2, const_4)))

<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">2 ** 6</gadget>
<output>64</output>
<gadget id="calculator">(3/10) + 64</gadget>
<output>643/10 = around 64.3</output>
<result>643/10 = around 64.3</result>


the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :

Explanation: speed downstream = ( 22 + 5 ) = 27 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 27 = 10.8 km answer is c .

multiply(add(22, 5), divide(24, const_60))

<gadget id="calculator">22 + 5</gadget>
<output>27</output>
<gadget id="calculator">24 / 60</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">27 * (2/5)</gadget>
<output>54/5 = around 10.8</output>
<result>54/5 = around 10.8</result>


a boat having a length 3 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

Explanation: "volume of water displaced = ( 3 x 3 x 0.01 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced x density of water = ( 0.09 x 1000 ) kg = 90 kg . answer : d"

multiply(multiply(multiply(3, 3), divide(1, const_100)), const_1000)

<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">9 * (1/100)</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">(9/100) * 1_000</gadget>
<output>90</output>
<result>90</result>


by selling 12 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?

Explanation: "80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8 answer : a"

multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 20)))), 12)

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">120 * (1/80)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">1 / (3/2)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 12</gadget>
<output>8</output>
<result>8</result>


walking with 4 / 5 of my usual speed , i miss the bus by 7 minutes . what is my usual time ?

Explanation: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 7 4 - - - - - - - - - ? è 28 answer : c"

<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">7 / (5/4)</gadget>
<output>28/5 = around 5.6</output>
<gadget id="calculator">(28/5) * 5</gadget>
<output>28</output>
<result>28</result>


if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 150 then sum is

Explanation: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 150 15000 answer : a"

divide(150, multiply(divide(10, const_100), divide(10, const_100)))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * (1/10)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">150 / (1/100)</gadget>
<output>15_000</output>
<result>15_000</result>


in one hour , a boat goes 8 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :

Explanation: "solution speed in still water = 1 / 2 ( 8 + 2 ) km / hr = 5 kmph . answer b"

<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


coconuts were purchased at 150 per 100 and sold at 2 per coconut . if 2000 coconuts were sold , what was the total profit made ?

Explanation: c . p . for one coconut = 150 ⁄ 100 = 3 ⁄ 2 s . p . for one coconut = 2 profit on one coconut = 2 - 3 ⁄ 2 = 1 ⁄ 2 ∴ profit on 2000 coconut = 1 ⁄ 2 × 2000 = 1000 answer b

multiply(2000, subtract(2, divide(150, 100)))

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">2 - (3/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2_000 * (1/2)</gadget>
<output>1_000</output>
<result>1_000</result>


a train is 435 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length

Explanation: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 435 + 140 = 575 meter time = distance / speed = 575 ∗ 2 / 25 = 46 seconds option c"

divide(add(435, 140), divide(multiply(45, const_1000), const_3600))

<gadget id="calculator">435 + 140</gadget>
<output>575</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">575 / (25/2)</gadget>
<output>46</output>
<result>46</result>


if the l . c . m of two numbers is 450 and their product is 22500 , find the h . c . f of the numbers .

Explanation: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 22500 / 450 = 50 . answer : a"

<gadget id="calculator">22_500 / 450</gadget>
<output>50</output>
<result>50</result>


the area of a parallelogram is 72 cm ^ 2 and its altitude is twice the corresponding base . what is the length of the base ?

Explanation: let base = x cm height = 2 x cm area = x ã — 2 x = 2 x ^ 2 area = x ã — 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c

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


martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for $ 1.15 cents , and zachary buys a pencil and an eraser for 75 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )

Explanation: pencil + notebook = 80 notebook + eraser = 115 pencil + eraser = 75 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 270 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 270 ) = 405 the answer is e .

multiply(divide(add(add(multiply(1.15, const_100), 80), 75), const_2), 3)

<gadget id="calculator">1.15 * 100</gadget>
<output>115</output>
<gadget id="calculator">115 + 80</gadget>
<output>195</output>
<gadget id="calculator">195 + 75</gadget>
<output>270</output>
<gadget id="calculator">270 / 2</gadget>
<output>135</output>
<gadget id="calculator">135 * 3</gadget>
<output>405</output>
<result>405</result>


when 200 is divided by positive integer x , the remainder is 3 . what is the remainder when 297 is divided by x ?

Explanation: "f 200 / x leaves a reminder 3 then ( 200 - 3 ) i . e . 197 is divisible by x so ( 200 + 197 ) / x leaves a reminder rem ( 200 / x ) + rem ( 197 / x ) = > 3 + 0 = 3 answer : b"

<gadget id="calculator">297 - 200</gadget>
<output>97</output>
<gadget id="calculator">100 - 97</gadget>
<output>3</output>
<result>3</result>


if a fast song has 160 beats per minute , and a slow song has 90 beats per minute , how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1020 beats ?

Explanation: we can determine quickly that total number should range between 1020 / 160 < = n < = 1020 / 90 , so ans should be between 6 and 12 . now solving the expression 160 a + 90 b = 1020 decreasing 1020 by multiples of 160 and checking divisibility of that number by 9 , we get fast song plays for 3 minutes and slow somg plays for 6 minutes , 3 * 160 + 6 * 90 = 1020 hence total number of minutes stream of music plays is 3 + 6 = 9 minutes ans d

add(floor(multiply(divide(1020, add(160, 90)), const_2)), const_1)

<gadget id="calculator">160 + 90</gadget>
<output>250</output>
<gadget id="calculator">1_020 / 250</gadget>
<output>102/25 = around 4.08</output>
<gadget id="calculator">(102/25) * 2</gadget>
<output>204/25 = around 8.16</output>
<gadget id="calculator">floor(204/25)</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<result>9</result>


in a party every person shakes hands with every other person . if there were a total of 190 handshakes in the party then what is the number of persons present in the party ?

Explanation: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 190 n ( n - 1 ) / 2 = 190 â ˆ ´ n = 20 answer : option e"

divide(add(sqrt(add(multiply(multiply(190, const_2), const_4), const_1)), const_1), const_2)

<gadget id="calculator">190 * 2</gadget>
<output>380</output>
<gadget id="calculator">380 * 4</gadget>
<output>1_520</output>
<gadget id="calculator">1_520 + 1</gadget>
<output>1_521</output>
<gadget id="calculator">1_521 ** (1/2)</gadget>
<output>39</output>
<gadget id="calculator">39 + 1</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 30 years . what is deepak present age ?

Explanation: "present age is 4 x and 3 x , = > 4 x + 6 = 30 = > x = 6 so deepak age is = 3 ( 6 ) = 18 answer : a"

<gadget id="calculator">30 - 6</gadget>
<output>24</output>
<gadget id="calculator">24 * 3</gadget>
<output>72</output>
<gadget id="calculator">72 / 4</gadget>
<output>18</output>
<result>18</result>


what is remainder of the division ( 1525 * 1527 * 1529 ) / 12 ?

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

subtract(multiply(multiply(1525, 1527), 1529), subtract(multiply(multiply(1525, 1527), 1529), const_3))


a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?

Explanation: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 5 / 20 = 1 / 4 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 5 / 20 ) x 12 = 3 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 12 = 1 we can plug 15 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 1 – 3 ) / 3 ] x 100 - 200 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 200 / 3 is just a bit less than ½ , we know that - 200 / 3 x 100 is about a 67 % decrease . answer e .

multiply(divide(subtract(multiply(divide(5, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(5, 20), const_100)), const_100)

<gadget id="calculator">5 / 20</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">25 - (25/3)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) / 25</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>


in the first 10 overs of a cricket game , the run rate was only 5.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?

Explanation: "10 overs - run rate = 5.2 runs scored in first 10 overs = 52 remaining overs 40 total runs to be scored = 282 52 runs already scored 282 - 52 = 230 230 runs to be scored in 40 overs let required runrate be x 40 * x = 230 x = 230 / 40 x = 5.75 the required runrate is 5.75 answer : d"

divide(subtract(282, multiply(10, 5.2)), 40)

<gadget id="calculator">10 * 5.2</gadget>
<output>52</output>
<gadget id="calculator">282 - 52</gadget>
<output>230</output>
<gadget id="calculator">230 / 40</gadget>
<output>23/4 = around 5.75</output>
<result>23/4 = around 5.75</result>


of the diplomats attending a summit conference , 30 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?

Explanation: "{ total } = { french } + { russian } - { both } + { neither } { total } = 30 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 20 . answer : a ."

divide(subtract(32, 30), subtract(divide(20, const_100), divide(10, const_100)))

<gadget id="calculator">32 - 30</gadget>
<output>2</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) - (1/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">2 / (1/10)</gadget>
<output>20</output>
<result>20</result>


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

Explanation: "0.2 a = 0.08 b - > a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 : . a : b = 2 : 5 answer : c"

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

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


a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is

Explanation: explanation : let distance = x km and usual rate = y kmph . then , x / y - x / ( y + 3 ) = 40 / 60 - - > 2 y ( y + 3 ) = 9 x - - - - - ( i ) also , x / ( y - 2 ) - x / y = 40 / 60 - - > y ( y - 2 ) = 3 x - - - - - - - - ( ii ) on dividing ( i ) by ( ii ) , we get : x = 40 km . answer : c

multiply(multiply(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), divide(40, const_60)), add(const_1, divide(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), 3)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">12 / 1</gadget>
<output>12</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">12 * (2/3)</gadget>
<output>8</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>40</result>


if the average of w , b , c , 14 and 15 is 12 . what is the average value of w , b , c and 29

Explanation: w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d

divide(add(subtract(subtract(multiply(add(const_1, const_4), 12), 15), 14), 29), const_4)

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">60 - 15</gadget>
<output>45</output>
<gadget id="calculator">45 - 14</gadget>
<output>31</output>
<gadget id="calculator">31 + 29</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<result>15</result>


set a of 8 positive integers may have the same element and have 40 . and set b of 8 positive integers must have different elements and have 40 . when m and n are the greatest possible differences between 40 and other elements ’ sums in set a and set b , respectively , m - n = ?

Explanation: this is maximum - minimum . hence , 40 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 40 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is a .

<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">40 - 18</gadget>
<output>22</output>
<result>22</result>


after 6 games , team b had an average of 65 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?

Explanation: "( 6 * 65 ) + 47 + x > 500 390 + 47 + x > 500 437 + x > 500 = > x > 63 option d"

<gadget id="calculator">6 * 65</gadget>
<output>390</output>
<gadget id="calculator">390 + 47</gadget>
<output>437</output>
<gadget id="calculator">500 - 437</gadget>
<output>63</output>
<result>63</result>


on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 16 more transactions than cal . how much transactions did jade handled ?

Explanation: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 16 = 82 jade handled = 82 transactions . answer : c"

add(divide(multiply(multiply(divide(90, const_100), add(10, const_100)), 2), 3), 16)

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">(9/10) * 110</gadget>
<output>99</output>
<gadget id="calculator">99 * 2</gadget>
<output>198</output>
<gadget id="calculator">198 / 3</gadget>
<output>66</output>
<gadget id="calculator">66 + 16</gadget>
<output>82</output>
<result>82</result>


a man buys an article for $ 100 . and sells it for $ 125 . find the gain percent ?

Explanation: "c . p . = $ 100 s . p . = $ 125 gain = $ 25 gain % = 25 / 100 * 100 = 25 % answer is c"

subtract(divide(125, divide(100, const_100)), const_100)

<gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">125 / 1</gadget>
<output>125</output>
<gadget id="calculator">125 - 100</gadget>
<output>25</output>
<result>25</result>


list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ?

Explanation: since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .

subtract(subtract(12, add(4, const_1)), const_1)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">12 - 5</gadget>
<output>7</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<result>6</result>


joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 2 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 2 ) * 360 = 180 gallons . remaning paint = 180 gallons paint used in the second week = ( 1 / 5 ) * 180 = 36 gallons total paint used = 216 gallons . option d"

add(multiply(divide(360, 2), 1), divide(subtract(360, multiply(divide(360, 2), 1)), 5))

<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<gadget id="calculator">180 * 1</gadget>
<output>180</output>
<gadget id="calculator">360 - 180</gadget>
<output>180</output>
<gadget id="calculator">180 / 5</gadget>
<output>36</output>
<gadget id="calculator">180 + 36</gadget>
<output>216</output>
<result>216</result>


if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 4 ?

Explanation: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 4 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 4 = not integer we can not forget multiples of 8 from 1 to 96 we have 24 numbers that are multiple of 4 therefore , 48 / 96 + 24 / 96 = 72 / 96 = 3 / 4 answer : e"

divide(add(divide(96, 2), divide(96, 4)), 96)

<gadget id="calculator">96 / 2</gadget>
<output>48</output>
<gadget id="calculator">96 / 4</gadget>
<output>24</output>
<gadget id="calculator">48 + 24</gadget>
<output>72</output>
<gadget id="calculator">72 / 96</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>


when y is divided by 288 , the remainder is 44 . what is the remainder when the same y is divided by 24 ?

Explanation: y = 288 * a + 44 = ( 24 * 12 ) * a + 24 + 20 the answer is a .

<gadget id="calculator">44 % 24</gadget>
<output>20</output>
<result>20</result>


after decreasing 24 % in the price of an article costs rs . 1140 . find the actual cost of an article ?

Explanation: "cp * ( 76 / 100 ) = 1140 cp = 15 * 100 = > cp = 1500 answer : a"

divide(1140, subtract(const_1, divide(24, const_100)))

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">1_140 / (19/25)</gadget>
<output>1_500</output>
<result>1_500</result>