if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 14 ?

Explanation: @ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 14 . then 4 n < 14 and n < 3.5 . the largest possible integer is n = 3 . the answer is c .

<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">14 / 4</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">floor(7/2)</gadget>
<output>3</output>
<result>3</result>


if 9 workers can build 9 cars in 9 days , then how many days would it take 7 workers to build 7 cars ?

Explanation: "9 workers can build 1 car per day on average . 1 worker can build 1 / 9 of a car per day . 7 workers can build 7 / 9 car per day . the time required to build 7 cars is 7 / ( 7 / 9 ) = 9 days the answer is d ."

multiply(divide(multiply(9, 9), 9), divide(7, 7))

<gadget id="calculator">9 * 9</gadget>
<output>81</output>
<gadget id="calculator">81 / 9</gadget>
<output>9</output>
<gadget id="calculator">7 / 7</gadget>
<output>1</output>
<gadget id="calculator">9 * 1</gadget>
<output>9</output>
<result>9</result>


the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.20 . the probability that neither a nor b occur is _________

Explanation: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 20 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : c"

subtract(const_1, subtract(add(0.25, 0.40), 0.20))

<gadget id="calculator">0.25 + 0.4</gadget>
<output>0.65</output>
<gadget id="calculator">0.65 - 0.2</gadget>
<output>0.45</output>
<gadget id="calculator">1 - 0.45</gadget>
<output>0.55</output>
<result>0.55</result>


the length of a rectangular floor is more than its breadth by 200 % . if rs . 300 is required to paint the floor at the rate of rs . 5 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 = 300 / 5 = 60 sq m l b = 60 i . e . , l * l / 3 = 60 l 2 = 180 = > l = 13.42 answer : b"

multiply(sqrt(divide(divide(300, 5), const_3)), const_3)

<gadget id="calculator">300 / 5</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 ** (1/2)</gadget>
<output>2*sqrt(5) = around 4.472136</output>
<gadget id="calculator">(2*sqrt(5)) * 3</gadget>
<output>6*sqrt(5) = around 13.416408</output>
<result>6*sqrt(5) = around 13.416408</result>


the s . i . on a certain sum of money for 5 years at 10 % per annum is half the c . i . on rs . 5000 for 2 years at 12 % per annum . the sum placed on s . i . is ?

Explanation: c . i . = [ 5000 * ( 1 + 12 / 100 ) 2 - 5000 ] = ( 5000 * 28 / 25 * 28 / 25 - 5000 ) = rs . 1272 . sum = ( 636 * 100 ) / ( 5 * 10 ) = rs . 1272 answer : e

divide(divide(subtract(multiply(5000, power(add(const_1, divide(12, const_100)), 2)), 5000), 2), multiply(5, divide(10, const_100)))

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">1 + (3/25)</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">(28/25) ** 2</gadget>
<output>784/625 = around 1.2544</output>
<gadget id="calculator">5_000 * (784/625)</gadget>
<output>6_272</output>
<gadget id="calculator">6_272 - 5_000</gadget>
<output>1_272</output>
<gadget id="calculator">1_272 / 2</gadget>
<output>636</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">5 * (1/10)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">636 / (1/2)</gadget>
<output>1_272</output>
<result>1_272</result>


dropbox charges $ 3.10 for first 1 / 5 of a month for 500 gb storage , plus $ 0.40 for each additional 1 / 5 of a month . what would dropbox charge for a data storage of 500 gb for 8 months ?

Explanation: first 1 / 5 month charge = $ 3.10 rest of the months = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the months = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 answer is d .

add(subtract(divide(multiply(500, 0.4), 8), 8), 1)

<gadget id="calculator">500 * 0.4</gadget>
<output>200</output>
<gadget id="calculator">200 / 8</gadget>
<output>25</output>
<gadget id="calculator">25 - 8</gadget>
<output>17</output>
<gadget id="calculator">17 + 1</gadget>
<output>18</output>
<result>18</result>


find the simple interest on rs . 72,000 at 16 2 / 3 % per year for 9 months .

Explanation: "p = rs . 72000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 72,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9000 answer is c ."

multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>
<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">48 + 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>8_625</result>


if it would take one machine 20 minutes to fill a large production order and another machine 30 minutes to fill the same order , how many minutes would it take both machines working together , at their respective rates , to fill the order ?

Explanation: this question can be solved using the work formula : work = ( a ) ( b ) / ( a + b ) where a and b are the individual completion rates of the respective entities ( for the same job ) . we ' re told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job . plugging in those values gets us . . . ( 20 ) ( 30 ) / ( 20 + 30 ) = 600 / 50 = 12 minutes answer is b

inverse(add(divide(const_1, 20), divide(const_1, 30)))

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/20) + (1/30)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


how many digits are required to number a book containing 220 pages ?

Explanation: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 220 - ( 90 + 9 ) = 121 pages will require 121 * 3 = 363 digits . the total number of digits is 9 + 180 + 363 = 552 . the answer is c ."

add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(220, const_100), const_1), const_3))

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 2</gadget>
<output>180</output>
<gadget id="calculator">9 + 180</gadget>
<output>189</output>
<gadget id="calculator">220 - 100</gadget>
<output>120</output>
<gadget id="calculator">120 + 1</gadget>
<output>121</output>
<gadget id="calculator">121 * 3</gadget>
<output>363</output>
<gadget id="calculator">189 + 363</gadget>
<output>552</output>
<result>552</result>


a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent w of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?

Explanation: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is w = . 25 / 1 * 100 = 25 % d is the answer ."

subtract(const_100, multiply(divide(9, 12), const_100))

<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<result>25</result>


the ratio between the number of sheep and the number of horses at the stewart farm is 5 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?

Explanation: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 5 x = 5 * 8 = 40 . hence c ."

multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 5)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">8 * 100</gadget>
<output>800</output>
<gadget id="calculator">80 + 800</gadget>
<output>880</output>
<gadget id="calculator">12 * 1_000</gadget>
<output>12_000</output>
<gadget id="calculator">880 + 12_000</gadget>
<output>12_880</output>
<gadget id="calculator">12_880 / 230</gadget>
<output>56</output>
<gadget id="calculator">56 / 7</gadget>
<output>8</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>40</result>


calculate the amount that an investor needs to be invest to earn $ 1005 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 11 % compounded semi - annually ?

Explanation: "the approach is substitution , our interest requirement is $ 1005 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 8900 yielded $ 1005 using the formula a = p ( 1 + r / n ) nt hence answer is c"


a reduction of 42 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?

Explanation: "explanation : 40 * ( 42 / 100 ) = 16.8 - - - 64 ? - - - 12 = > rs . 3.15 answer : d"

multiply(const_12, divide(multiply(42, divide(42, const_100)), 64))

<gadget id="calculator">42 / 100</gadget>
<output>21/50 = around 0.42</output>
<gadget id="calculator">42 * (21/50)</gadget>
<output>441/25 = around 17.64</output>
<gadget id="calculator">(441/25) / 64</gadget>
<output>441/1_600 = around 0.275625</output>
<gadget id="calculator">12 * (441/1_600)</gadget>
<output>1_323/400 = around 3.3075</output>
<result>1_323/400 = around 3.3075</result>


a train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds . what is the length of the train in metres ?

Explanation: "let length of train = l case - 1 : distance = 1500 + l ( while crossing the bridge ) time = 70 seconds i . e . speed = distance / time = ( 1500 + l ) / 70 case - 2 : distance = l ( while passing the lamp post ) time = 20 seconds i . e . speed = distance / time = ( l ) / 20 but since speed has to be same in both cases so ( 1500 + l ) / 70 = ( l ) / 20 i . e . 1500 + l = 3.5 l i . e . 2.5 l = 1500 i . e . l = 600 answer : option d"

multiply(divide(1500, subtract(70, 20)), 20)

<gadget id="calculator">70 - 20</gadget>
<output>50</output>
<gadget id="calculator">1_500 / 50</gadget>
<output>30</output>
<gadget id="calculator">30 * 20</gadget>
<output>600</output>
<result>600</result>


what will be the cost of building a fence around a square plot with area equal to 289 square feet , if the price per foot of building the fence is rs . 58 ?

Explanation: "let the side of the square plot be a foot a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 foot cost of building the fence = 68 * 58 = rs . 3944 . answer : a"

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<gadget id="calculator">4 * 17</gadget>
<output>68</output>
<gadget id="calculator">68 * 58</gadget>
<output>3_944</output>
<result>3_944</result>


points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ?

Explanation: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives d = 1 / 9 . a"

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

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">144 / 2</gadget>
<output>72</output>
<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>


the dimensions of a field are 20 m by 10 m . a pit 8 m long , 5 m wide and 2 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?

Explanation: the volume of the earth removed is 8 * 5 * 2 = 80 m ^ 3 . the remaining area of the field is 20 * 10 - 8 * 5 = 160 m ^ 2 . 80 m ^ 3 of the earth evenly spread over the area of 160 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 80 / 160 = 0.5 m . answer : c

divide(multiply(10, 8), subtract(rectangle_area(20, 10), rectangle_area(5, 8)))

<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">200 - 40</gadget>
<output>160</output>
<gadget id="calculator">80 / 160</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


the grade point average of the entire class is 90 . if the average of one third of the class is 96 , what is the average of the rest ?

Explanation: "let us take number of students on the class as ' x ' . avg grade point = sum of all grade points / x sum of all grade points = avg grade point * x = 90 x average of one third of the class = 96 = sum of one third grade points of the class / ( x / 3 ) sum of one third grade points of the class = 96 * ( x / 3 ) = 32 x sum of rest two third grade points of the class = sum of all grade points - sum of one third grade points of the class sum of rest two third grade points of the class = 90 x - 32 x = 58 x avg of two third of the class = sum of rest two third grade points of the class / ( x * 2 / 3 ) = 58 x / ( 2 x / 3 ) = 29 * 3 = 87 . hence , answer is d"

divide(subtract(multiply(90, const_4), 96), subtract(const_4, const_1))

<gadget id="calculator">90 * 4</gadget>
<output>360</output>
<gadget id="calculator">360 - 96</gadget>
<output>264</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">264 / 3</gadget>
<output>88</output>
<result>88</result>


last year department store x had a sales total for december that was 6 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?

Explanation: "let avg for 11 mos . = 10 therefore , dec = 60 year total = 11 * 10 + 60 = 170 answer = 60 / 170 = 6 / 17 = a"

divide(6, add(subtract(const_12, const_1), 6))

<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 + 6</gadget>
<output>17</output>
<gadget id="calculator">6 / 17</gadget>
<output>6/17 = around 0.352941</output>
<result>6/17 = around 0.352941</result>


points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?

Explanation: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a


if x is the median of the set { 9 / 2 , 11 / 3 , x , 28 / 9 , 21 / 5 } , x could be

Explanation: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( e )"

add(add(divide(add(add(add(divide(9, 2), divide(11, 3)), divide(28, 9)), divide(21, 5)), const_4), divide(const_10, const_100)), divide(const_10, const_100))

<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">11 / 3</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">(9/2) + (11/3)</gadget>
<output>49/6 = around 8.166667</output>
<gadget id="calculator">28 / 9</gadget>
<output>28/9 = around 3.111111</output>
<gadget id="calculator">(49/6) + (28/9)</gadget>
<output>203/18 = around 11.277778</output>
<gadget id="calculator">21 / 5</gadget>
<output>21/5 = around 4.2</output>
<gadget id="calculator">(203/18) + (21/5)</gadget>
<output>1_393/90 = around 15.477778</output>
<gadget id="calculator">(1_393/90) / 4</gadget>
<output>1_393/360 = around 3.869444</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1_393/360) + (1/10)</gadget>
<output>1_429/360 = around 3.969444</output>
<gadget id="calculator">(1_429/360) + (1/10)</gadget>
<output>293/72 = around 4.069444</output>
<result>293/72 = around 4.069444</result>


a can do a piece of work in 4 days . b can do it in 7 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?

Explanation: "c = 1 / 2 - 1 / 4 - 1 / 7 = 3 / 28 = > 28 / 3 days answer : b"

divide(multiply(4, 7), divide(subtract(multiply(4, 7), multiply(add(divide(multiply(4, 7), 4), divide(multiply(4, 7), 7)), 2)), 2))

<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<gadget id="calculator">28 / 4</gadget>
<output>7</output>
<gadget id="calculator">28 / 7</gadget>
<output>4</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">28 - 22</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">28 / 3</gadget>
<output>28/3 = around 9.333333</output>
<result>28/3 = around 9.333333</result>


what least no . must be subtracted from 101054 so that remaining no . is divisible by 10 ?

Explanation: "explanation : on dividing 101054 by 10 we get the remainder 4 , so 4 should be subtracted option b"

subtract(101054, multiply(floor(divide(101054, 10)), 10))

<gadget id="calculator">101_054 / 10</gadget>
<output>50_527/5 = around 10_105.4</output>
<gadget id="calculator">floor(50_527/5)</gadget>
<output>10_105</output>
<gadget id="calculator">10_105 * 10</gadget>
<output>101_050</output>
<gadget id="calculator">101_054 - 101_050</gadget>
<output>4</output>
<result>4</result>


at what rate percent on simple interest will rs . 750 amount to rs . 900 in 8 years ?

Explanation: 150 = ( 750 * 8 * r ) / 100 r = 2.5 % answer : b

multiply(divide(divide(subtract(900, 750), 750), 8), const_100)

<gadget id="calculator">900 - 750</gadget>
<output>150</output>
<gadget id="calculator">150 / 750</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) / 8</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">(1/40) * 100</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


machine – x produces 50 % of the total output and machine - y produces 75 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - x and two unit of 500 units produced by machine - x prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?

Explanation: suppose machine x produce 1000 units total defective = 9 machine y then produces = 1500 units total defective = 6 probability = 15 / 2500 = 0.006 answer : d

divide(add(9, divide(divide(9, divide(75, const_100)), const_2)), add(add(1000, multiply(1000, divide(50, const_100))), 1000))

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">9 / (3/4)</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">9 + 6</gadget>
<output>15</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1_000 * (1/2)</gadget>
<output>500</output>
<gadget id="calculator">1_000 + 500</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 + 1_000</gadget>
<output>2_500</output>
<gadget id="calculator">15 / 2_500</gadget>
<output>3/500 = around 0.006</output>
<result>3/500 = around 0.006</result>


find the cost of fencing around a circular field of diameter 22 m at the rate of rs . 2.50 a meter ?

Explanation: "2 * 22 / 7 * 11 = 69 69 * 2 1 / 2 = rs . 172 answer : b"

<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<gadget id="calculator">2 * pi * 11</gadget>
<output>22*pi = around 69.115038</output>
<gadget id="calculator">(22*pi) * 2.5</gadget>
<output>55.0*pi = around 172.787596</output>
<result>55.0*pi = around 172.787596</result>


two cycles are standing side - by - side . one cycle , which is 2.5 feets tall , casts a shadow that is 5 feets long . the other cycle is 2 feets tall . compute , in feets , the length of the shadow that the shorter cycle casts .

Explanation: the ratio of shadow to height is constant , so if x is the length of the shadow , then 2.5 / 5 = 2 / x and x = 4 . correct answer b

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 2.5</gadget>
<output>4</output>
<result>4</result>


stacy has a 12 page history paper due in 12 days . how many pages per day would she have to write to finish on time ?

Explanation: "12 / 12 = 1 answer : d"

<gadget id="calculator">12 / 12</gadget>
<output>1</output>
<result>1</result>


on a two - dimensional coordinate plane , the line a = x ^ 2 - x ^ 3 touches the x - axis in how many places ?

Explanation: "apparently it ' s a = x ^ 2 - x ^ 3 instead of a = x ^ 2 - a ^ 3 . in this case : the x - intercept is the value ( s ) of x for a = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."

<gadget id="calculator">max(3, 2)</gadget>
<output>3</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<result>2</result>


if the wages of 6 men for 15 days be rs . 2100 , then find the wages of for 12 days .

Explanation: . let the required wages be rs . x . more men , more wages ( direct proportion ) less days , less wages ( direct proportion ) men 6 : 9 : : 2100 : x days 15 : 12 therefore ( 6 x 15 x x ) = ( 9 x 12 x 2100 )  x = ( 9 x 12 x 2100 ) / ( 6 x 15 ) = 2520 hence the required wages are rs . 2520 . answer is c

multiply(multiply(const_3, const_3), multiply(12, divide(divide(2100, 15), 6)))

<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">2_100 / 15</gadget>
<output>140</output>
<gadget id="calculator">140 / 6</gadget>
<output>70/3 = around 23.333333</output>
<gadget id="calculator">12 * (70/3)</gadget>
<output>280</output>
<gadget id="calculator">9 * 280</gadget>
<output>2_520</output>
<result>2_520</result>


a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 40 percent of the drive from the center , what percent of the round - trip has the technician completed ?

Explanation: "the complete round trip consists of driving to the service center and then back home again . so , once the technician drives to the service center he / she has already competed 50 % of the entire trip . since the technician completes a portion of the trip back home , the correct answer must be greater than 50 % so 0.5 + 0.5 * 0.4 = 0.70 answer : b"

add(divide(const_100, const_2), divide(multiply(40, divide(const_100, const_2)), const_100))

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">50 + 20</gadget>
<output>70</output>
<result>70</result>


what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 35 ?

Explanation: "number divisible by 11 : - 1000 / 11 = 90 numbers divisible by 35 : - 1000 / 35 = 28 numbers divisible by both 11 and 35 = 2 total numbers divisible by both 11 and 28 = 90 + 28 - 2 = 116 ( because we counted 2 in both 90 and 28 ) total numbers not divisible by 11 or 35 = 1000 - 116 = 884 answer : a"

subtract(1000, subtract(add(divide(1000, 11), divide(1000, 35)), divide(1000, multiply(11, 35))))


3 positive integers a , b , and c are such that their average is 20 and a ≤ b ≤ c . if the median is ( a + 13 ) , what is the least possible value of c ?

Explanation: solution : we know that the average value is 20 therefore ( a + b + c ) / 3 = 20 so a + b + c = 60 and b = a + 13 therefore a + ( a + 13 ) + c = 60 the least value of c is when c = b so take c = a + 13 hence , a + ( a + 13 ) + ( a + 13 ) = 60 i . e . , a = 34 / 3 a non integer therefore c is not equal to b so take c = b + 1 therefore c = a + 14 a + ( a + 13 ) + ( a + 14 ) = 60 i . e . , a = 33 / 3 = 11 hence , a = 11 , b = 24 , and c = 25 answer : e

add(divide(subtract(multiply(20, 3), add(13, add(13, const_1))), 3), add(13, const_1))

<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">13 + 1</gadget>
<output>14</output>
<gadget id="calculator">13 + 14</gadget>
<output>27</output>
<gadget id="calculator">60 - 27</gadget>
<output>33</output>
<gadget id="calculator">33 / 3</gadget>
<output>11</output>
<gadget id="calculator">11 + 14</gadget>
<output>25</output>
<result>25</result>


if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips ?

Explanation: "p ( hhhhtt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 the answer is d ."

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 6</gadget>
<output>1/64 = around 0.015625</output>
<result>1/64 = around 0.015625</result>


a man goes downstream at 10 kmph , and upstream 8 kmph . the speed of the stream is

Explanation: "speed of the stream = 1 / 2 ( 10 - 8 ) kmph = 1 kmph . correct option : c"

<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>1</result>


if shares of two persons in profits are rs . 600 and rs . 1000 then ratio of their capitals is

Explanation: "profit = time * capital so 600 : 1000 = 3 : 5 answer : a"

<gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


Explanation: 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 = > 4 x 2 ^ 2 n = 4 ^ 22 = 2 ^ 44 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 44 = > 2 ^ ( 2 n + 2 ) = 2 ^ 44 = > 2 n + 2 = 44 = > n = 21 so . answer will be e .

<gadget id="calculator">22 * 2</gadget>
<output>44</output>
<gadget id="calculator">44 - 2</gadget>
<output>42</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<result>21</result>


a is the average ( arithmetic mean ) of the first 7 positive multiples of 5 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?

Explanation: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 20 , which also equals b . b is the second positive multiple of n , thus n = 20 / 2 = 10 . the answer is c ."

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


length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?

Explanation: "let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 / 26.5 = 200 m . 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m b"

divide(add(divide(5300, 26.50), multiply(const_2, 10)), const_4)

<gadget id="calculator">5_300 / 26.5</gadget>
<output>200</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">200 + 20</gadget>
<output>220</output>
<gadget id="calculator">220 / 4</gadget>
<output>55</output>
<result>55</result>


2 men and 4 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )

Explanation: the list should be wmwmw . hence , from women 4 ! and men 2 ! , we get ( 4 ! ) ( 2 ! ) = 48 . therefore , the correct answer is e .

<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">2 * 24</gadget>
<output>48</output>
<result>48</result>


each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 40 minutes earlier than usual . how much time did the man spend walking ?

Explanation: "as they arrived 40 minutes earlier than usual , they saved 40 minutes on round trip from home to station ( home - station - home ) - - > 20 minutes in each direction ( home - station ) - - > wife meets husband 20 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 20 minutes = 40 minutes . answer : c"

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<result>40</result>


students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio a of men to women ?

Explanation: ( a ) a = 184 x 5 + 170 x 2 = 1260 . a

divide(subtract(180, 170), subtract(184, 180))

<gadget id="calculator">180 - 170</gadget>
<output>10</output>
<gadget id="calculator">184 - 180</gadget>
<output>4</output>
<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


Explanation: ( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) = > ( 8000 ) ( 6000 ) / 480 = 10 ^ y = > 100000 = 100 ^ y = > 10 ^ 5 = 10 ^ y since , base is same so powers will be same too . so , y = 5 answer will be a

divide(log(divide(multiply(8000, 6000), 480)), log(const_10))

<gadget id="calculator">8_000 * 6_000</gadget>
<output>48_000_000</output>
<gadget id="calculator">48_000_000 / 480</gadget>
<output>100_000</output>
<gadget id="calculator">log(100_000)</gadget>
<output>log(100000) = around 11.512925</output>
<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>
<gadget id="calculator">log(100000) / log(10)</gadget>
<output>log(100000)/log(10) = around 5</output>
<result>log(100000)/log(10) = around 5</result>


if ( 5 + k ) ( 5 - k ) = ( 5 ^ 2 ) - ( 2 ^ 3 ) , then what is the value of k ?

Explanation: obviously , it is in the formula a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) so k is 2 option d

subtract(multiply(5, 3), add(3, const_10))

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">3 + 10</gadget>
<output>13</output>
<gadget id="calculator">15 - 13</gadget>
<output>2</output>
<result>2</result>


a train consists of 48 boxcars pulled by 2 engines . the boxcars are 15 meters long and the two engines are each 20 meters long . it crosses over a highway 24 meters wide at a speed of 14 m / s . how long does it take for the entire train to cross ?

Explanation: a 56 sec d = 48 * 15 m + 2 * 20 m + 24 m = 784 m t = 784 m / 14 m / s = 56 s

divide(add(multiply(48, 15), multiply(20, 2)), 14)

<gadget id="calculator">48 * 15</gadget>
<output>720</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">720 + 40</gadget>
<output>760</output>
<gadget id="calculator">760 / 14</gadget>
<output>380/7 = around 54.285714</output>
<result>380/7 = around 54.285714</result>


a store reported total sales of $ 416 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?

Explanation: "new value – old value ) / old value x 100 we are given : february sales this year = 416 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 416 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 416 – 320 ) / 320 ] x 100 = 30 % the answer is c ."

multiply(divide(subtract(416, 320), 320), const_100)

<gadget id="calculator">416 - 320</gadget>
<output>96</output>
<gadget id="calculator">96 / 320</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>


the ratio of the radius of two circles is 2 : 5 , and then the ratio of their areas is ?

Explanation: "r 1 : r 2 = 2 : 5 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 25 answer : a"

<gadget id="calculator">pi * (2 ** 2)</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">pi * (5 ** 2)</gadget>
<output>25*pi = around 78.539816</output>
<gadget id="calculator">(4*pi) / (25*pi)</gadget>
<output>4/25 = around 0.16</output>
<result>4/25 = around 0.16</result>


of the families in city x in 2000 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2004 was 20 percent greater than it was in 1994 , and the total number of families in city x was 10 percent greater in 2004 than it was in 2000 . what percent of the families in city x owned a personal computer in 1998 ?

Explanation: "say a 100 families existed in 2000 then the number of families owning a computer in 2000 - 30 number of families owning computer in 2000 = 30 * 120 / 100 = 36 number of families in 2004 = 110 the percentage = 36 / 110 * 100 = 32.72 % . option : e"

multiply(const_100, divide(divide(multiply(add(20, const_100), 30), const_100), add(const_100, 10)))

<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">120 * 30</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 / 100</gadget>
<output>36</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">36 / 110</gadget>
<output>18/55 = around 0.327273</output>
<gadget id="calculator">100 * (18/55)</gadget>
<output>360/11 = around 32.727273</output>
<result>360/11 = around 32.727273</result>


raman mixed 48 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?

Explanation: "explanation : cp per kg of mixture = [ 48 ( 150 ) + 36 ( 125 ) ] / ( 48 + 36 ) = rs . 139.28 sp = cp [ ( 100 + profit % ) / 100 ] = 139.28 * [ ( 100 + 40 ) / 100 ] = rs . 195 answer : c"

add(divide(add(multiply(48, 150), multiply(36, 125)), add(36, 48)), multiply(divide(add(multiply(48, 150), multiply(36, 125)), add(36, 48)), divide(40, const_100)))

<gadget id="calculator">48 * 150</gadget>
<output>7_200</output>
<gadget id="calculator">36 * 125</gadget>
<output>4_500</output>
<gadget id="calculator">7_200 + 4_500</gadget>
<output>11_700</output>
<gadget id="calculator">36 + 48</gadget>
<output>84</output>
<gadget id="calculator">11_700 / 84</gadget>
<output>975/7 = around 139.285714</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(975/7) * (2/5)</gadget>
<output>390/7 = around 55.714286</output>
<gadget id="calculator">(975/7) + (390/7)</gadget>
<output>195</output>
<result>195</result>


a certain high school has 500 students . of these students , 30 are taking music , 10 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?

Explanation: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 10 z = 10 so , we have 30 students taking music , 10 taking art and 10 taking both music and art . 20 student taking just music 0 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 500 - 30 = 470 . e"

subtract(500, subtract(add(30, 10), 10))

<gadget id="calculator">30 + 10</gadget>
<output>40</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">500 - 30</gadget>
<output>470</output>
<result>470</result>


in what time will a train 100 metres long cross an electric pole , if its speed be 144 km / hr ?

Explanation: solution speed = ( 144 x 5 / 18 ) m / sec = 40 m / sec time taken = ( 100 / 40 ) sec = 2.5 sec . answer a

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>
<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 70 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

Explanation: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 170 , so from 2003 to 2005 it increased by ( 170 - 140 ) / 140 = 30 / 140 = ~ 21 % . answer : e ."

multiply(divide(subtract(add(const_1, divide(70, const_100)), add(const_1, divide(40, const_100))), add(const_1, divide(40, const_100))), const_100)

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 + (7/10)</gadget>
<output>17/10 = around 1.7</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(17/10) - (7/5)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) / (7/5)</gadget>
<output>3/14 = around 0.214286</output>
<gadget id="calculator">(3/14) * 100</gadget>
<output>150/7 = around 21.428571</output>
<result>150/7 = around 21.428571</result>


a start walking from a place at a uniform speed of 4 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .

Explanation: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 4 + 5 / 9 = 4.55 answer b"

add(divide(1, divide(add(const_60, 48), const_60)), 4)

<gadget id="calculator">60 + 48</gadget>
<output>108</output>
<gadget id="calculator">108 / 60</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">1 / (9/5)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">(5/9) + 4</gadget>
<output>41/9 = around 4.555556</output>
<result>41/9 = around 4.555556</result>


what is the smallest integer k for which 64 ^ k > 4 ^ 20 ?

Explanation: "64 ^ k > 4 ^ 20 4 ^ ( 3 k ) > 4 ^ 20 3 k > 20 k = 7 the answer is d ."

<gadget id="calculator">20 / 3</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">floor(20/3)</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<result>7</result>


a cistern 8 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :

Explanation: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : option a"

add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 4), multiply(add(divide(25, const_100), 1), 8))), multiply(4, 8))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 4</gadget>
<output>5</output>
<gadget id="calculator">(5/4) * 8</gadget>
<output>10</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">30 + 32</gadget>
<output>62</output>
<result>62</result>


Explanation: 29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 179 in the place of 2994 / 14.5 ] = 179 / 10 = 17.9 answer is e .

<gadget id="calculator">14.5 / 1.45</gadget>
<output>10</output>
<gadget id="calculator">179 / 10</gadget>
<output>179/10 = around 17.9</output>
<result>179/10 = around 17.9</result>


Explanation: "( √ 27 + √ 243 ) / √ 75 = ( 3 √ 3 + 9 √ 3 ) / 5 √ 3 = 12 √ 3 / 5 √ 3 = 12 / 5 . hence , the correct answer is e"

<gadget id="calculator">27 ** (1/2)</gadget>
<output>3*sqrt(3) = around 5.196152</output>
<gadget id="calculator">243 ** (1/2)</gadget>
<output>9*sqrt(3) = around 15.588457</output>
<gadget id="calculator">(3*sqrt(3)) + (9*sqrt(3))</gadget>
<output>12*sqrt(3) = around 20.78461</output>
<gadget id="calculator">75 ** (1/2)</gadget>
<output>5*sqrt(3) = around 8.660254</output>
<gadget id="calculator">(12*sqrt(3)) / (5*sqrt(3))</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>


a set s = { x , - 8 , - 7 , - 6 , 6 , 8 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?

Explanation: median of the set = ( - 6 + 6 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 23 - 21 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c

subtract(subtract(subtract(add(add(9, 8), 6), 6), 7), 8)

<gadget id="calculator">9 + 8</gadget>
<output>17</output>
<gadget id="calculator">17 + 6</gadget>
<output>23</output>
<gadget id="calculator">23 - 6</gadget>
<output>17</output>
<gadget id="calculator">17 - 7</gadget>
<output>10</output>
<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<result>2</result>


in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 8 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?

Explanation: "total fish = x percentage of second catch = ( 8 / 50 ) * 100 = 16 % so , x * 16 % = 50 x = 312 ans . e"

<gadget id="calculator">8 / 50</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">50 / (4/25)</gadget>
<output>625/2 = around 312.5</output>
<result>625/2 = around 312.5</result>


what is the sum of the digits of integer k , if k = ( 10 ^ 45 - 46 )

Explanation: "there are 46 digits in 10 ^ 45 when we subtract 46 from it , there will be 45 digits left . 10 ^ 45 can be written as 9999999 . . . . ( 45 times ) + 1 so , 10 ^ 45 - 46 = 9999999 . . . . ( 45 times ) + 1 - 46 = 9999999 . . . . ( 45 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 43 and the last two digits are 54 the sum of the digits will be ( 43 * 9 ) + 5 + 4 = 396 answer : - d"

add(multiply(subtract(10, const_1), subtract(45, const_2)), 10)

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">45 - 2</gadget>
<output>43</output>
<gadget id="calculator">9 * 43</gadget>
<output>387</output>
<gadget id="calculator">387 + 10</gadget>
<output>397</output>
<result>397</result>


if 5 a = 3125 , then the value of 5 ( a - 3 ) is :

Explanation: solution 5 a = 3125 ⇔ 5 a = 5 a ⇔ a = 5 . ∴ 5 ( a - 3 ) = 5 ( 5 - 3 ) = 52 = 25 . answer a

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


in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 130 marks , the no of questions he attempts correctly is :

Explanation: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 130 = > 5 x = 190 = > x = 38 answer : b"

<gadget id="calculator">130 + 60</gadget>
<output>190</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">190 / 5</gadget>
<output>38</output>
<result>38</result>


a is half good a work man as b and together they finish a job in 20 days . in how many days working alone b finish the job ?

Explanation: "wc = 1 : 2 2 x + x = 1 / 20 = > x = 1 / 60 2 x = 1 / 60 = > 30 days answer : b"

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">20 * (3/2)</gadget>
<output>30</output>
<result>30</result>


what is the value of n if the sum of the consecutive odd intergers y from 1 to n equals 169 ?

Explanation: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."

add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1)

<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<gadget id="calculator">13 * 2</gadget>
<output>26</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>25</result>


if log 4 x + log 4 ( 1 / 6 ) = 1 / 2 then the value of x is ?

Explanation: log 4 x + log 4 ( 1 / 6 ) = 1 / 2 = > log 4 [ x x 1 / 6 ] = 1 / 2 = > log 4 [ x / 6 ] = 1 / 2 = > 41 / 2 = x / 6 = > 2 = x / 6 therefore , x = 12 answer : d

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<result>12</result>


what quantity of water should taken out to concentrate 27 liters of 40 % acidic liquid to 60 % acidic liquid ?

Explanation: "required answer is = 27 ( 60 - 40 ) / 60 = 9 liters answer is d"

subtract(27, divide(multiply(27, 40), 60))

<gadget id="calculator">27 * 40</gadget>
<output>1_080</output>
<gadget id="calculator">1_080 / 60</gadget>
<output>18</output>
<gadget id="calculator">27 - 18</gadget>
<output>9</output>
<result>9</result>


marts income is 30 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income

Explanation: "m = ( 130 / 100 ) t t = ( 60 / 100 ) j = > m = ( 78 / 100 ) j answer c ."

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

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">100 / 60</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 100</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">130 / (500/3)</gadget>
<output>39/50 = around 0.78</output>
<gadget id="calculator">(39/50) * 100</gadget>
<output>78</output>
<result>78</result>


there is a 5 - digit number . the fifth digit is one fourth of the third digit and one half of the fourth digit . third digit is one half of the first digit . second digit is 5 more than the fifth digit . what is that 5 - digit number ?

Explanation: we can prove it as follows suppose number is pqrst , now t = ( 1 / 4 ) r = ( 1 / 2 ) s . . . . . . ( 1 ) , r = ( 1 / 2 ) p . . . . . ( 2 ) , q = t + 5 . . . . ( 3 ) now from ( 1 ) 4 t = r = 2 s = k ( suppose ) . . . . ( 4 ) from ( 2 ) 2 r = p . . . ( 5 ) now ( 4 ) * 2 then we get 8 t = 2 r = 4 s = k ( again some integer ) . . . . ( 6 ) from ( 5 ) and ( 6 ) 8 t = 2 r = 4 s = p = k . . . . . . . . . ( 7 ) now we have to choose the value of k 1 ) if choose k = 0 then it is worthless number will be 00000 ( not a answer ) 2 ) for k = 1 to 7 and for k = 9 digits will be in fractions 3 ) for k = 8 we get p = 8 , s = 2 , r = 4 , t = 1 and q = 6 and number is pqrst = 86421 answer : a

add(add(add(add(multiply(multiply(const_4, const_2), multiply(const_1000, const_10)), multiply(5, const_1000)), multiply(const_4, const_100)), multiply(const_2, const_10)), const_1)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">1_000 * 10</gadget>
<output>10_000</output>
<gadget id="calculator">8 * 10_000</gadget>
<output>80_000</output>
<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">80_000 + 5_000</gadget>
<output>85_000</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">85_000 + 400</gadget>
<output>85_400</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">85_400 + 20</gadget>
<output>85_420</output>
<gadget id="calculator">85_420 + 1</gadget>
<output>85_421</output>
<result>85_421</result>


a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?

Explanation: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 36 x / 100 - 24 x / 100 = 840 = > 12 x / 100 = 840 = > x = 7000 . answer : a"

divide(840, divide(multiply(subtract(18, 12), const_2), const_100))

<gadget id="calculator">18 - 12</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">840 / (3/25)</gadget>
<output>7_000</output>
<result>7_000</result>


for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.15 – 6.15 * ?

Explanation: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.15 * = 6 ( the greatest positive even integer less than or equal to 6.15 is 6 ) . hence , 6.15 – 6.15 * = 6.15 - 6 = 0.15 answer : b ."

<gadget id="calculator">floor(6.15)</gadget>
<output>6</output>
<gadget id="calculator">6.15 - 6</gadget>
<output>0.15</output>
<result>0.15</result>


when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.15 , what is the value of y ?

Explanation: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.15 and remainder is 9 so . 15 x y = 9 hence y = 60 ans b"

<gadget id="calculator">floor(96.15)</gadget>
<output>96</output>
<gadget id="calculator">96.15 - 96</gadget>
<output>0.15</output>
<gadget id="calculator">9 / 0.15</gadget>
<output>60</output>
<result>60</result>


the cost of the paint is rs . 40.00 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 10 feet each side

Explanation: "explanation : surface area of a cube = 6 x 10 ^ 2 = 600 s q . ft quantity of paint required = ( 600 / 20 ) = 30 kg cost of painting = 40 x 30 = rs . 1200 answer : a"

<gadget id="calculator">6 * (10 ** 2)</gadget>
<output>600</output>
<gadget id="calculator">600 / 20</gadget>
<output>30</output>
<gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<result>1_200</result>


what is the perimeter of a rectangular field whose diagonal is 10 m and length is 3 m ?

Explanation: sol : breadth of the rectangular plot is = 10 ^ 2 - 3 ^ 2 = 1 m therefore , perimeter of the rectangular plot = 2 ( 3 + 1 ) = 8 m d ) 8 m

divide(add(add(sqrt(subtract(power(10, const_2), power(3, const_2))), 3), add(sqrt(subtract(power(10, const_2), power(3, const_2))), 3)), const_3)

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">100 - 9</gadget>
<output>91</output>
<gadget id="calculator">91 ** (1/2)</gadget>
<output>sqrt(91) = around 9.539392</output>
<gadget id="calculator">(sqrt(91)) + 3</gadget>
<output>3 + sqrt(91) = around 12.539392</output>
<gadget id="calculator">(3 + sqrt(91)) + (3 + sqrt(91))</gadget>
<output>6 + 2*sqrt(91) = around 25.078784</output>
<gadget id="calculator">(6 + 2*sqrt(91)) / 3</gadget>
<output>2 + 2*sqrt(91)/3 = around 8.359595</output>
<result>2 + 2*sqrt(91)/3 = around 8.359595</result>


cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 3 % sugar , what should be the ratio of cereal a to cereal b , by weight ?

Explanation: 2 % is 1 % - point below 3 % and 10 % is 7 % - points above 3 % . the ratio of a : b should be 1 : 7 . the answer is c .

<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>


a 120.00001 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?

Explanation: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 120 / 9 = 500 / 9 = > x + 120 = 500 = > x = 380 so the length of the train is 380 meters option c"

<gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">(500/9) * 9</gadget>
<output>500</output>
<gadget id="calculator">500 - 120.00001</gadget>
<output>379.99999</output>
<result>379.99999</result>


the ratio between the length and the breadth of a rectangular plot is 7 : 5 . if the perimeter of the plot is 288 metres , what is its area ?

Explanation: let the length and breadth be 7 x and 5 x respectively . then , p = 2 ( 7 x + 5 x ) = 288 â ‡ ’ x = 12 area = 7 ã — 12 ã — 5 ã — 12 = 5040 sq . m . answer d

rectangle_area(divide(multiply(7, divide(288, multiply(const_2, add(const_1, divide(7, 5))))), 5), divide(288, multiply(const_2, add(const_1, divide(7, 5)))))

<gadget id="calculator">7 / 5</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">1 + (7/5)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">2 * (12/5)</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">288 / (24/5)</gadget>
<output>60</output>
<gadget id="calculator">7 * 60</gadget>
<output>420</output>
<gadget id="calculator">420 / 5</gadget>
<output>84</output>
<gadget id="calculator">84 * 60</gadget>
<output>5_040</output>
<result>5_040</result>


during the first two weeks of january , the total rainfall in springdale was 20 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?

Explanation: "total rainfall in 2 weeks = 20 inches . assume the rainfall in second week = 1.5 x rainfall in first week = x total rainfall = 2.5 x = 20 inches x = 8 and 1.5 x = 12 rainfall during second week = 12 inches option e"

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

<gadget id="calculator">1 + 1.5</gadget>
<output>2.5</output>
<gadget id="calculator">1.5 / 2.5</gadget>
<output>0.6</output>
<gadget id="calculator">20 * 0.6</gadget>
<output>12</output>
<result>12</result>


the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 3 or 4 as its largest number ?

Explanation: the set s has 2 ^ 5 = 32 subsets . the number 5 is in half of these subsets . of the remaining 16 subsets , 4 is an element in 8 of them . thus 4 is the largest number in 8 subsets of s . of the remaining 8 subsets , 3 is an element in 4 of them . thus 3 is the largest number in 4 subsets of s . the probability that 3 or 4 is the largest number is 12 / 32 = 3 / 8 . the answer is c .

divide(multiply(4, 3), power(const_2, 5))

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">2 ** 5</gadget>
<output>32</output>
<gadget id="calculator">12 / 32</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>


in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 4 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?

Explanation: "the probability of survival for each of the first 3 months of life is 1 - 1 / 4 = 3 / 4 , so of 200 newborn 200 * 3 / 4 * 3 / 4 * 3 / 4 = ~ 85 is expected to survive . answer : e ."

multiply(multiply(multiply(200, subtract(1, divide(1, 4))), subtract(1, divide(1, 4))), subtract(1, divide(1, 4)))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">200 * (3/4)</gadget>
<output>150</output>
<gadget id="calculator">150 * (3/4)</gadget>
<output>225/2 = around 112.5</output>
<gadget id="calculator">(225/2) * (3/4)</gadget>
<output>675/8 = around 84.375</output>
<result>675/8 = around 84.375</result>


a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 390 kilograms of pears that day , how many kilograms did he sell in the afternoon ?

Explanation: "3 x = 390 x = 130 therefore , the salesman sold 130 kg in the morning and 2 ⋅ 130 = 260 kg in the afternoon . so answer is c ."

<gadget id="calculator">390 / 3</gadget>
<output>130</output>
<gadget id="calculator">130 * 2</gadget>
<output>260</output>
<result>260</result>


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

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

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


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

Explanation: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 20 y = 20 z = 10 so , we have 20 students taking music , 20 taking art and 10 taking both music and art . that 10 person has been counted twice though ( once in the music ' group ' and once in the art ' group ' ) , so what we really have is . . . 10 student taking just music 10 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 5000 - 30 = 470 . e"

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

<gadget id="calculator">20 + 20</gadget>
<output>40</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">500 - 30</gadget>
<output>470</output>
<result>470</result>


a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.15 ?

Explanation: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.15 - $ 0.65 = $ 1.50 the charge for the next 1400 grams is $ 1.40 which leaves a charge of $ 0.10 the weight is somewhere between 1650 and 1750 . the answer is e ."

divide(add(subtract(2.15, divide(65, 100)), multiply(divide(divide(10, 100), 100), 250)), divide(divide(10, 100), 100))

<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">2.15 - (13/20)</gadget>
<output>1.5</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) / 100</gadget>
<output>1/1_000 = around 0.001</output>
<gadget id="calculator">(1/1_000) * 250</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1.5 + (1/4)</gadget>
<output>1.75</output>
<gadget id="calculator">1.75 / (1/1_000)</gadget>
<output>1_750</output>
<result>1_750</result>


if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 1 year the amount to be paid is ?

Explanation: "a = 7500 ( 26 / 25 ) ^ 1 = 7800 answer : d"

multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100)))

<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">104 / 100</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) * (26/25)</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">7_500 * (676/625)</gadget>
<output>8_112</output>
<result>8_112</result>


a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?

Explanation: "originally , the distance the car could go on a full tank was 12 * 24 = 288 miles . after it has been modified , the car can go 24 / 0.75 = 32 miles per gallon . on a full tank , the car can go 32 * 12 = 384 miles , thus 96 miles more . the answer is a ."

subtract(multiply(multiply(divide(24, 75), const_100), 12), multiply(24, 12))

<gadget id="calculator">24 / 75</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<gadget id="calculator">32 * 12</gadget>
<output>384</output>
<gadget id="calculator">24 * 12</gadget>
<output>288</output>
<gadget id="calculator">384 - 288</gadget>
<output>96</output>
<result>96</result>


the h . c . f . of two numbers is 15 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :

Explanation: "the numbers are ( 15 x 11 ) and ( 15 x 15 ) . larger number = ( 15 x 15 ) = 225 . answer : a"

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<result>225</result>


a metallic sheet is of rectangular shape with dimensions 46 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :

Explanation: "l = ( 46 - 16 ) m = 30 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 30 x 20 x 8 ) m 3 = 4800 m 3 . answer : option d"

volume_rectangular_prism(subtract(46, multiply(8, const_2)), subtract(36, multiply(8, const_2)), 8)

<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">46 - 16</gadget>
<output>30</output>
<gadget id="calculator">36 - 16</gadget>
<output>20</output>
<gadget id="calculator">30 * 20 * 8</gadget>
<output>4_800</output>
<result>4_800</result>


in an election between two candidates , one got 60 % of the total valid votes , 30 % of the votes were invalid . if the total number of votes was 9000 , the number of valid votes that the other candidate got , was :

Explanation: "explanation : number of valid votes = 70 % of 9000 = 6300 . valid votes polled by other candidates = 40 % of 6300 ( 40 / 1006300 ) = 2520 . harsh mishra a year ago 0 upvotes answer : b"

multiply(multiply(subtract(const_1, divide(30, const_100)), subtract(const_1, divide(60, const_100))), 9000)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(7/10) * (2/5)</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) * 9_000</gadget>
<output>2_520</output>
<result>2_520</result>


on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?

Explanation: suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = x / 10 or y / x = 1 / 8 or y / x * 100 = 1 / 8 * 100 = 12.5 % answer : b

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

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">10 / 80</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 30 km / hr . his average speed during the whole journey in km / hr . is :

Explanation: "solution : average speed = 2 xy / x + y = 2 * 60 * 30 / 60 + 30 = 40 answer : c"

divide(add(add(subtract(60, const_10), const_100), add(subtract(60, const_10), const_100)), add(divide(add(subtract(60, const_10), const_100), 60), divide(add(subtract(60, const_10), const_100), 30)))

<gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">50 + 100</gadget>
<output>150</output>
<gadget id="calculator">150 + 150</gadget>
<output>300</output>
<gadget id="calculator">150 / 60</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">150 / 30</gadget>
<output>5</output>
<gadget id="calculator">(5/2) + 5</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">300 / (15/2)</gadget>
<output>40</output>
<result>40</result>


a drink vendor has 20 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?

Explanation: "the number of liters in each can = hcf of 20 , 144 and 368 = 4 liters . number of cans of maaza = 20 / 4 = 5 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 5 + 36 + 92 = 133 cans . answer : e"

<gadget id="calculator">gcd(20, 144)</gadget>
<output>4</output>
<gadget id="calculator">gcd(4, 368)</gadget>
<output>4</output>
<gadget id="calculator">368 / 4</gadget>
<output>92</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">144 / 4</gadget>
<output>36</output>
<gadget id="calculator">5 + 36</gadget>
<output>41</output>
<gadget id="calculator">92 + 41</gadget>
<output>133</output>
<result>133</result>


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

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

<gadget id="calculator">40 / 24</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">40 / 40</gadget>
<output>1</output>
<gadget id="calculator">40 / 30</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">1 + (4/3)</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">(5/3) + (7/3)</gadget>
<output>4</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<result>10</result>


find the least number must be subtracted from 62575 so that remaining number is divisible by 99 .

Explanation: on dividing 62571 by 99 we get the remainder 7 , so 7 should be subtracted . answer is b

subtract(62575, multiply(floor(divide(62575, 99)), 99))

<gadget id="calculator">62_575 / 99</gadget>
<output>62_575/99 = around 632.070707</output>
<gadget id="calculator">floor(62_575/99)</gadget>
<output>632</output>
<gadget id="calculator">632 * 99</gadget>
<output>62_568</output>
<gadget id="calculator">62_575 - 62_568</gadget>
<output>7</output>
<result>7</result>


a man is 12 years older than his brother . in two years , his age will be twice the age of his brother . the present age of his brother is :

Explanation: let the brother ' s present age be x years . then , man ' s present age = ( x + 12 ) years . ( x + 12 ) + 2 = 2 ( x + 2 ) x + 14 = 2 x + 4 x = 10 . answer : a

subtract(add(12, const_2), multiply(const_2, const_2))

<gadget id="calculator">12 + 2</gadget>
<output>14</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<result>10</result>


a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 280 pounds of the mixture ?

Explanation: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 280 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 280 = 200 pounds answer ( a )"

<gadget id="calculator">5 * 280</gadget>
<output>1_400</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">1_400 / 7</gadget>
<output>200</output>
<result>200</result>


how many 4 - digit numbers that do not contain the digits 2 , 3 , 4 , 5 , 6 , or 7 are there ?

Explanation: the 1 st digit can be filled up by the numbers : { 1 , 8,9 } = 3 ways the 2 nd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 3 rd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 4 th digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the total number of such four - digit numbers is 3 * 4 * 4 * 4 = 192 the answer is d .

multiply(multiply(multiply(3, 4), 4), 4)

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">48 * 4</gadget>
<output>192</output>
<result>192</result>


how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?

Explanation: "solution number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 / 25 x 11.25 x 6 ) = 6400 . answer c"

divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))

<gadget id="calculator">8 * 100</gadget>
<output>800</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">800 * 600</gadget>
<output>480_000</output>
<gadget id="calculator">480_000 * 22.5</gadget>
<output>10_800_000</output>
<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>
<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>
<gadget id="calculator">10_800_000 / 1_687.5</gadget>
<output>6_400</output>
<result>6_400</result>


the average weight of 6 person ' s increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg . what might be the weight of the new person ?

Explanation: "total weight increased = ( 6 x 1.8 ) kg = 10.8 kg . weight of new person = ( 69 + 10.8 ) kg = 79.8 kg . answer : option b"

<gadget id="calculator">6 * 1.8</gadget>
<output>10.8</output>
<gadget id="calculator">10.8 + 69</gadget>
<output>79.8</output>
<result>79.8</result>


a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 7200 interest . the principal amount borrowed by him was .

Explanation: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 7200 â ˆ — 100 / 12 â ˆ — 3 = rs 20000 option d"

divide(multiply(7200, const_100), multiply(12, 3))

<gadget id="calculator">7_200 * 100</gadget>
<output>720_000</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">720_000 / 36</gadget>
<output>20_000</output>
<result>20_000</result>


a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1986 on her 30 nd birthday first be eligible to retire under this provision ?

Explanation: "she must gain at least 70 points , now she has 30 and every year gives her two more points : one for age and one for additional year of employment , so 30 + 2 * ( # of years ) = 70 - - > ( # of years ) = 20 - - > 1986 + 20 = 2006 . answer : d ."

add(1986, divide(subtract(70, 30), const_2))

<gadget id="calculator">70 - 30</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">1_986 + 20</gadget>
<output>2_006</output>
<result>2_006</result>


i had rs . 10000 with me . out of this , money i lent some money to a for 2 years at 15 % simple interest . i lent the remaining money to b for an equal number of years at 18 % simple interest . after 2 years , i found that a had given me rs . 360 more as interest as compared to ( b ) the amount of money which i had lent to b must have been

Explanation: explanation : total amount = rs . 10000 let money lent a = rs . x and money lent to b = rs . ( 10000 x ) x = rs . 6000 . so the amount of money lent to b = rs . 4000 answer : c

divide(subtract(multiply(10000, divide(multiply(2, 15), const_100)), 360), add(divide(multiply(2, 15), const_100), divide(multiply(2, 18), const_100)))

<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">10_000 * (3/10)</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 - 360</gadget>
<output>2_640</output>
<gadget id="calculator">2 * 18</gadget>
<output>36</output>
<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(3/10) + (9/25)</gadget>
<output>33/50 = around 0.66</output>
<gadget id="calculator">2_640 / (33/50)</gadget>
<output>4_000</output>
<result>4_000</result>


to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 785 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?

Explanation: "total movies submitted are 785 . as per question we need to take 1 / 4 of 785 to be considered for top 10 movies = 196.25 approximate the value we 197 . imo option b is the correct answer . . ."

<gadget id="calculator">785 / 4</gadget>
<output>785/4 = around 196.25</output>
<result>785/4 = around 196.25</result>


the number 0.5 is how much greater than 1 / 3 ?

Explanation: "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 6 ans a"

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">0.5 - (1/3)</gadget>
<output>0.166667</output>
<result>0.166667</result>


the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution .

Explanation: quantity of spirit in new solution = ( 4 * 45 / 100 ) + ( 5 * 30 / 100 ) + ( 6 * 10 / 100 ) = 1.8 + 1.5 + 0.6 = 3.9 liters so % concentration of spirit = 100 * 3.9 / ( 4 + 5 + 6 ) = 26 % answer : a

divide(multiply(add(add(divide(multiply(4, 45), const_100), divide(multiply(30, 5), const_100)), divide(multiply(10, 6), const_100)), const_100), add(10, 5))

<gadget id="calculator">4 * 45</gadget>
<output>180</output>
<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">30 * 5</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(9/5) + (3/2)</gadget>
<output>33/10 = around 3.3</output>
<gadget id="calculator">10 * 6</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(33/10) + (3/5)</gadget>
<output>39/10 = around 3.9</output>
<gadget id="calculator">(39/10) * 100</gadget>
<output>390</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">390 / 15</gadget>
<output>26</output>
<result>26</result>


there are 2 sections a and b in a class , consisting of 50 and 70 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?

Explanation: "total weight of 50 + 70 students = 50 * 50 + 70 * 70 = 7400 average weight of the class is = 7400 / 120 = 61.67 kg answer is c"

divide(add(multiply(50, 50), multiply(70, 70)), add(50, 70))

<gadget id="calculator">50 * 50</gadget>
<output>2_500</output>
<gadget id="calculator">70 * 70</gadget>
<output>4_900</output>
<gadget id="calculator">2_500 + 4_900</gadget>
<output>7_400</output>
<gadget id="calculator">50 + 70</gadget>
<output>120</output>
<gadget id="calculator">7_400 / 120</gadget>
<output>185/3 = around 61.666667</output>
<result>185/3 = around 61.666667</result>


if x ^ 2 – 3 x = 18 , then one possible value of x – 4 =

Explanation: x ^ 2 – 3 x = 18 i . e . x ^ 2 – 3 x - 18 = 0 i . e . x ^ 2 – 6 x + 3 x - 18 = 0 i . e . ( x - 6 ) ( x + 3 ) = 0 i . e . x = 6 or - 3 i . e . x - 4 = 6 - 4 or - 3 - 4 i . e . x - 4 = 2 or - 7 answer : option e

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


if 4 x + y = 8 and 3 x - 4 y = 5 , then what is the value of 7 x - 3 y ?

Explanation: 4 x + y = 8 . . . equation 1 3 x - 4 y = 5 . . . equation 2 adding both the equations 7 x - 3 y = 23 correct answer option a

<gadget id="calculator">8 + 5</gadget>
<output>13</output>
<gadget id="calculator">13 + 10</gadget>
<output>23</output>
<result>23</result>


working alone , a can complete a certain kind of job in 3 hours . a and d , working together at their respective rates , can complete one of these jobs in 2 hours . in how many hours can d , working alone , complete one of these jobs ?

Explanation: let total time taken by d to complete the job = d total time taken by a to complete the job = 3 work done by a in an hour 1 / a = 1 / 3 working together a and d can complete the job in 2 hours 1 / a + 1 / d = 1 / 2 = > 1 / d = 1 / 2 - 1 / a = 1 / 2 - 1 / 3 = 1 / 6 = > d = 6 hours answer c

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) - (1/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / (1/6)</gadget>
<output>6</output>
<result>6</result>


a class of boys stands in a single line , one boy is 19 th in order from both the ends , how many boys are there in the class ?

Explanation: explanation : number of boys in the class = ( 18 + 1 + 18 ) = 37 answer : a ) 37

<gadget id="calculator">19 * 2</gadget>
<output>38</output>
<gadget id="calculator">38 - 1</gadget>
<output>37</output>
<result>37</result>


what number must be added to 6 , 16 and 8 to get an average of 13 ?

Explanation: b 22

subtract(multiply(13, const_4), add(8, add(6, 16)))

<gadget id="calculator">13 * 4</gadget>
<output>52</output>
<gadget id="calculator">6 + 16</gadget>
<output>22</output>
<gadget id="calculator">8 + 22</gadget>
<output>30</output>
<gadget id="calculator">52 - 30</gadget>
<output>22</output>
<result>22</result>


the average age of 30 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .

Explanation: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 30 ) = 46 years answer : a"

subtract(add(add(multiply(30, 15), 16), 30), multiply(30, 15))

<gadget id="calculator">30 * 15</gadget>
<output>450</output>
<gadget id="calculator">450 + 16</gadget>
<output>466</output>
<gadget id="calculator">466 + 30</gadget>
<output>496</output>
<gadget id="calculator">496 - 450</gadget>
<output>46</output>
<result>46</result>


if x = the product of 7 distinct prime numbers , how many factors does x have besides 1 and itself ?

Explanation: since x has 7 distinct prime factors , x has a total of 2 ^ 7 = 128 factors . besides 1 and itself , x has 126 factors . the answer is d .

multiply(multiply(multiply(multiply(multiply(multiply(add(1, 1), add(1, 1)), add(1, 1)), add(1, 1)), add(1, 1)), add(1, 1)), add(1, 1))

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">16 * 2</gadget>
<output>32</output>
<gadget id="calculator">32 * 2</gadget>
<output>64</output>
<gadget id="calculator">64 * 2</gadget>
<output>128</output>
<result>128</result>


how many integers n are prime numbers in the range 200 < n < 220 ?

Explanation: to test a number n on whether it is a prime number , take square root ( n ) . consider as it is if it is a natural number . otherwise , increase the sq . root to the next natural no . then divide given no . by all prime numbers below the sq . root obtained . if the no . is divisible by any of the prime numbers , then it is not a prime number ; else it is . square root of 200 or 220 is less than 15 so , lets check if any number between 200 and 220 is not divisible by prime numbers 2 , 35 , 711 ( < 15 ) . that ' s it . out : 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 only 211 is a prime number in the given range correct option : a

<gadget id="calculator">200 / 200</gadget>
<output>1</output>
<result>1</result>


a sum of $ 800 amounts to $ 920 in 3 years at simple interest . if the interest rate is increased by 3 % it would amount to how much ?

Explanation: s . i = 920 - 800 = 120 p = $ 800 t = 3 years r = 100 * 120 / 800 * 3 = 5 % new rate = 5 + 3 = 8 % new s . i . = 800 * 8 * 3 / 100 = $ 192 new amount = 800 + 192 = $ 992 answer is c

add(800, multiply(multiply(800, divide(add(divide(multiply(divide(subtract(920, 800), 3), const_100), 800), 3), const_100)), 3))

<gadget id="calculator">920 - 800</gadget>
<output>120</output>
<gadget id="calculator">120 / 3</gadget>
<output>40</output>
<gadget id="calculator">40 * 100</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 800</gadget>
<output>5</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">800 * (2/25)</gadget>
<output>64</output>
<gadget id="calculator">64 * 3</gadget>
<output>192</output>
<gadget id="calculator">800 + 192</gadget>
<output>992</output>
<result>992</result>


a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 65 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?

Explanation: "together the two machines make 35 + 65 = 100 copies per minute . so , in half an hour they will make 100 * 30 = 3,000 copies . answer : a ."

divide(multiply(add(35, 65), const_60), const_2)

<gadget id="calculator">35 + 65</gadget>
<output>100</output>
<gadget id="calculator">100 * 60</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 2</gadget>
<output>3_000</output>
<result>3_000</result>


10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4554 , how much was it in the beginning ?

Explanation: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4554 x = 6325 answer : c"

floor(divide(4554, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100))))

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(9/10) * (4/5)</gadget>
<output>18/25 = around 0.72</output>
<gadget id="calculator">4_554 / (18/25)</gadget>
<output>6_325</output>
<gadget id="calculator">floor(6_325)</gadget>
<output>6_325</output>
<result>6_325</result>


cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost w is what percent of the original cost ?

Explanation: "original cost w , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"

<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<result>1_600</result>


if a car went the first third of the distance at 80 kmh , the second third at 30 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?

Explanation: assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 30 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 30 * t 2 = 8 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 16 hrs d = rt ( 240 * 3 ) = r * 16 r = 45 answer : d

divide(const_3, add(add(divide(const_1, 80), divide(const_1, 30)), divide(const_1, 48)))

<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/80) + (1/30)</gadget>
<output>11/240 = around 0.045833</output>
<gadget id="calculator">1 / 48</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(11/240) + (1/48)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">3 / (1/15)</gadget>
<output>45</output>
<result>45</result>


a cement mixture is composed of 3 elements . by weight , 1 / 2 of the mixture is sand , 1 / 5 of the mixture is water , and the remaining 15 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?

Explanation: "let the total weight be x . sand content = ( 1 / 2 ) x water content = ( 1 / 5 ) x gravel = x - ( 1 / 2 ) x - ( 1 / 5 ) x = ( 3 / 10 ) x = 15 x = 50 then answer will be c = 50"

divide(15, subtract(1, add(divide(1, 2), divide(1, 5))))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/2) + (1/5)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">15 / (3/10)</gadget>
<output>50</output>
<result>50</result>


reema took a loan of rs 900 with simple interest for as many years as the rate of interest . if she paid rs . 729 as interest at the end of the loan period , what was the rate of interest .

Explanation: "explanation : let rate = r % then time = r years . = > 900 ∗ r ∗ r / 100 = 729 = > r 2 = 81 = > r = 9 % option e"

<gadget id="calculator">900 / 100</gadget>
<output>9</output>
<gadget id="calculator">729 / 9</gadget>
<output>81</output>
<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<result>9</result>


a student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?

Explanation: "xc 1 * ( x - 1 ) c 1 = 132 x ^ 2 - x - 132 = 0 ( x - 12 ) ( x + 11 ) = 0 x = 12 , - 11 - 11 ca n ' t possible . hence 12 should be the answer e"

divide(add(const_1, sqrt(add(multiply(const_4, 132), power(negate(const_1), const_2)))), const_2)

<gadget id="calculator">4 * 132</gadget>
<output>528</output>
<gadget id="calculator">-1</gadget>
<output>-1</output>
<gadget id="calculator">(-1) ** 2</gadget>
<output>1</output>
<gadget id="calculator">528 + 1</gadget>
<output>529</output>
<gadget id="calculator">529 ** (1/2)</gadget>
<output>23</output>
<gadget id="calculator">1 + 23</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>12</result>


a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?

Explanation: the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 8 dollars - - > the loss from one mango = 1 / 5 - 1 / 8 = 3 / 40 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 4 / 30 * 40 / 3 = 16 / 9 b

divide(subtract(divide(const_1, 3), divide(const_1, 5)), subtract(divide(const_1, 5), divide(const_1, multiply(const_2, const_4))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/3) - (1/5)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/5) - (1/8)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(2/15) / (3/40)</gadget>
<output>16/9 = around 1.777778</output>
<result>16/9 = around 1.777778</result>


if an investor puts $ 800 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?

Explanation: "1.05 * 1.05 * 800 = $ 882 the answer is c ."

multiply(800, power(add(const_1, divide(divide(10, const_2), const_100)), const_2))

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</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">800 * (441/400)</gadget>
<output>882</output>
<result>882</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 7500 , what was the number of valid votes that the other candidate got ?

Explanation: "total no of votes = 7500 20 % invalid = > 80 % valid tot valid votes = 7500 * 80 / 100 = > valid for 2 nd candidate got 7500 * 80 / 100 * 45 / 100 = 2700 answer b"

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 7500)

<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) * 7_500</gadget>
<output>2_700</output>
<result>2_700</result>


indu gave bindu rs . 625 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?

Explanation: "625 = d ( 100 / 4 ) 2 d = 1 answer : a"

subtract(subtract(multiply(625, power(add(const_1, divide(4, const_100)), 2)), 625), multiply(multiply(625, divide(4, const_100)), 2))

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">625 * (676/625)</gadget>
<output>676</output>
<gadget id="calculator">676 - 625</gadget>
<output>51</output>
<gadget id="calculator">625 * (1/25)</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">51 - 50</gadget>
<output>1</output>
<result>1</result>