if the area of a circle decreases by 30 % , then the radius of a circle decreases by

Explanation: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 30 ) % = ( 100 − 10 √ 70 ) % = 100 - 84 = 16 % answer b"

multiply(subtract(const_1, sqrt(divide(subtract(const_100, 30), const_100))), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) ** (1/2)</gadget>
<output>sqrt(70)/10 = around 0.83666</output>
<gadget id="calculator">1 - (sqrt(70)/10)</gadget>
<output>1 - sqrt(70)/10 = around 0.16334</output>
<gadget id="calculator">(1 - sqrt(70)/10) * 100</gadget>
<output>100 - 10*sqrt(70) = around 16.333997</output>
<result>100 - 10*sqrt(70) = around 16.333997</result>


the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 25 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?

Explanation: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 25 = 2 r a = 12 / 5 r and r = 75 a = 180 required total cost = 4 * 180 + 3 * 75 + 5 * 25 = 720 + 225 + 125 = $ 1070 c"

add(add(multiply(4, multiply(divide(24, 10), divide(multiply(25, 6), 2))), multiply(3, divide(multiply(25, 6), 2))), multiply(5, 25))

<gadget id="calculator">24 / 10</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">25 * 6</gadget>
<output>150</output>
<gadget id="calculator">150 / 2</gadget>
<output>75</output>
<gadget id="calculator">(12/5) * 75</gadget>
<output>180</output>
<gadget id="calculator">4 * 180</gadget>
<output>720</output>
<gadget id="calculator">3 * 75</gadget>
<output>225</output>
<gadget id="calculator">720 + 225</gadget>
<output>945</output>
<gadget id="calculator">5 * 25</gadget>
<output>125</output>
<gadget id="calculator">945 + 125</gadget>
<output>1_070</output>
<result>1_070</result>


in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?

Explanation: "percent of students who are 25 years old or older is 0.4 * 48 + 0.2 * 52 = ~ 30 , so percent of people who are less than 25 years old is 100 - 30 = 70 . answer : b ."

subtract(const_1, multiply(divide(40, const_100), divide(subtract(const_100, 20), const_100)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</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">(2/5) * (4/5)</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">1 - (8/25)</gadget>
<output>17/25 = around 0.68</output>
<result>17/25 = around 0.68</result>


a train 300 m long , running with a speed of 54 km / hr will pass a tree in ?

Explanation: "speed = 54 * 5 / 18 = 15 m / sec time taken = 300 * 1 / 15 = 20 sec answer : c"

multiply(divide(300, multiply(54, const_1000)), const_3600)

<gadget id="calculator">54 * 1_000</gadget>
<output>54_000</output>
<gadget id="calculator">300 / 54_000</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(1/180) * 3_600</gadget>
<output>20</output>
<result>20</result>


a student got twice as many sums wrong as he got right . if he attempted 27 sums in all , how many did he solve correctly ?

Explanation: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 27 3 x = 27 x = 9 . answer : d"

<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<result>9</result>


the compound interest on a sum for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound and simple interest for 3 years will be

Explanation: explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 × si / pt = ( 100 × 32 ) / ( 400 × 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 × 8 × 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b

add(subtract(832, 800), multiply(832, divide(subtract(832, 800), divide(800, 2))))

<gadget id="calculator">832 - 800</gadget>
<output>32</output>
<gadget id="calculator">800 / 2</gadget>
<output>400</output>
<gadget id="calculator">32 / 400</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">832 * (2/25)</gadget>
<output>1_664/25 = around 66.56</output>
<gadget id="calculator">32 + (1_664/25)</gadget>
<output>2_464/25 = around 98.56</output>
<result>2_464/25 = around 98.56</result>


the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8463 for a computer table , then what was the cost price of the computer table ?

Explanation: ": cp = sp * ( 100 / ( 100 + profit % ) ) = 8463 ( 100 / 124 ) = rs . 6825 . answer : b"

divide(8463, add(const_1, divide(24, const_100)))

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 + (6/25)</gadget>
<output>31/25 = around 1.24</output>
<gadget id="calculator">8_463 / (31/25)</gadget>
<output>6_825</output>
<result>6_825</result>


15 beavers , working together in a constant pace , can build a dam in 4 hours . how many hours will it take 20 beavers that work at the same pace , to build the same dam ?

Explanation: "total work = 15 * 4 = 60 beaver hours 20 beaver * x = 60 beaver hours x = 60 / 20 = 3 answer : e"

<gadget id="calculator">4 * 15</gadget>
<output>60</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>3</result>


the sum q of prime numbers that are greater than 60 but less than 70 is

Explanation: a prime number is a number that has only two factors : 1 and itself . therefore , a prime number is divisible by two numbers only . let ' s list the numbers from 61 to 69 . 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 immediately we can eliminate the even numbers because they are divisible by 2 and thus are not prime . we are now left with : 61 , 63 , 65 , 67 , 69 we can next eliminate 65 because 65 is a multiple of 5 . we are now left with 61 , 63 , 67 , 69 . to eliminate any remaining values , we would look at those that are multiples of 3 . if you don ’ t know an easy way to do this , just start with a number that is an obvious multiple of 3 , such as 60 , and then keep adding 3 . we see that 60 , 63 , 66 , 69 are all multiples of 3 and therefore are not prime . thus , we can eliminate 63 and 69 from the list because they are not prime . finally , we are left with 61 and 67 , and we must determine whether they are divisible by 7 . they are not , and therefore they must be both prime . thus , the sum q of 61 and 67 is 128 . answer b .

add(add(60, const_1), subtract(70, const_3))

<gadget id="calculator">60 + 1</gadget>
<output>61</output>
<gadget id="calculator">70 - 3</gadget>
<output>67</output>
<gadget id="calculator">61 + 67</gadget>
<output>128</output>
<result>128</result>


the probability that a man will be alive for 10 more yrs is 1 / 2 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is

Explanation: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 3 ans . ( c )"

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

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/2) * (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to

Explanation: 3 * 5 + 5 * 3 = ( 2 x 3 - 3 x 5 + 3 x 5 ) + ( 2 x 5 - 3 x 3 + 5 x 3 ) = 22 answer a 22

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">6 + 15</gadget>
<output>21</output>
<result>21</result>


if 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x , then what is the value of x ?

Explanation: 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 × 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3

divide(subtract(multiply(const_2, 5), 1), const_3)

<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<result>3</result>


a lady starts from p towards q and realizes that at a point r , if he walks 50 km further he will be at a point s , which is as far away from r as it is from q . what is the distance between p and q if the distance between p and r is half the distance from r to q ? ( assume that p , q , r and s are all on the same straight line )

Explanation: p ___ 50 _____ r ___ 50 _____ s ____ 50 ___ q the above figure gives the locations of p , r , s & q in relation to each other . answer : a

add(multiply(50, const_2), divide(multiply(50, const_2), const_2))

<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<result>150</result>


in kaya ' s teacher ' s desk there are 24 pink highlighters , 28 yellow highlighters , and 25 blue highlighters . how many highlighters are there in all ?

Explanation: "add the numbers of highlighters . 24 + 28 + 25 = 77 . answer is c ."

<gadget id="calculator">24 + 28</gadget>
<output>52</output>
<gadget id="calculator">52 + 25</gadget>
<output>77</output>
<result>77</result>


a train speeds past a pole in 10 seconds and a platform 50 m long in 20 seconds . its length is :

Explanation: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 50 / 20 = x / 10 x = 50 m . answer : option d"

<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">50 * 1</gadget>
<output>50</output>
<result>50</result>


the denominator of a fraction is 6 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 4 â  „ 5 . what is the value of the original fraction ?

Explanation: "let the numerator be x . then the denominator is x + 6 . x + 1 / x + 7 = 4 / 5 . 5 x + 5 = 4 x + 28 . x = 23 . the original fraction is 23 / 29 . the answer is b ."

divide(divide(subtract(multiply(4, add(1, 6)), 5), subtract(5, 4)), add(divide(subtract(multiply(4, add(1, 6)), 5), subtract(5, 4)), 6))

<gadget id="calculator">1 + 6</gadget>
<output>7</output>
<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<gadget id="calculator">28 - 5</gadget>
<output>23</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">23 / 1</gadget>
<output>23</output>
<gadget id="calculator">23 + 6</gadget>
<output>29</output>
<gadget id="calculator">23 / 29</gadget>
<output>23/29 = around 0.793103</output>
<result>23/29 = around 0.793103</result>


consider the sets tn = { n , n + 1 , n + 2 , n + 3 , n + 4 ) , where n = 1 , 2 , 3 , … , 96 . how many of these sets contain 6 or any integral multiple thereof ( i . e . , any one of the numbers 6 , 12 , 18 , … ) ?

Explanation: explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of “ 6 members ” ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a

multiply(divide(add(const_2, const_3), 6), 96)

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(5/6) * 96</gadget>
<output>80</output>
<result>80</result>


car z travels 55 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

Explanation: the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 55 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 44 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 44 miles / gallon * 10 gallons = 440 miles . answer e .

multiply(multiply(subtract(const_1, divide(20, const_100)), 55), 10)

<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">(4/5) * 55</gadget>
<output>44</output>
<gadget id="calculator">44 * 10</gadget>
<output>440</output>
<result>440</result>


a clock shows the time as 9 a . m . if the minute hand gains 6 minutes every hour , how many minutes will the clock gain by 6 p . m . ?

Explanation: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 6 = 54 minutes . answer : e"

<gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<result>54</result>


20 people went to a hotel for combine dinner party 12 of them spent rs . 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20 . what was the total money spent by them .

Explanation: "solution : let average expenditure of 20 people be x . then , 20 x = 12 * 70 + 8 * ( x + 4 ) ; or , 20 x = 12 * 70 + 8 x + 32 ; or , x = 72.667 ; so , total money spent = 72.67 * 20 = rs . 1453.4 . answer : option c"

multiply(divide(add(multiply(12, 70), multiply(subtract(20, 12), 4)), subtract(20, subtract(20, 12))), 20)

<gadget id="calculator">12 * 70</gadget>
<output>840</output>
<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">840 + 32</gadget>
<output>872</output>
<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">872 / 12</gadget>
<output>218/3 = around 72.666667</output>
<gadget id="calculator">(218/3) * 20</gadget>
<output>4_360/3 = around 1_453.333333</output>
<result>4_360/3 = around 1_453.333333</result>


what annual payment will discharge a debt of rs . 1060 due in 2 years at the rate of 5 % compound interest ?

Explanation: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1060 820 x + 1060 * 441 x = 570.07 so , value of each installment = rs . 570.07 answer : option c"

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1060), 2)

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">(441/400) * 1_060</gadget>
<output>23_373/20 = around 1_168.65</output>
<gadget id="calculator">(23_373/20) / 2</gadget>
<output>23_373/40 = around 584.325</output>
<result>23_373/40 = around 584.325</result>


50 % of the population of a village is 23040 . the total population of the village is ?

Explanation: "answer ∵ 50 % of p = 23040 ∴ p = ( 23040 x 100 ) / 50 = 46080 correct option : d"

<gadget id="calculator">100 / 50</gadget>
<output>2</output>
<gadget id="calculator">2 * 23_040</gadget>
<output>46_080</output>
<result>46_080</result>


if the perimeter of a rectangular house is 1400 m , its length when its breadth is 300 m is ?

Explanation: 2 ( l + 300 ) = 1400 = > l = 400 m answer : b

<gadget id="calculator">1_400 / 2</gadget>
<output>700</output>
<gadget id="calculator">700 - 300</gadget>
<output>400</output>
<result>400</result>


if a # b = ab – b + b ^ 2 , then 3 # 4 =

Explanation: "solution - simply substitute 3 and 4 in equation in the place of a and b respectively . 3 # 4 = 3 * 4 - 4 + 4 ^ 2 = 12 - 4 + 16 = 24 . ans d"

add(subtract(multiply(3, 4), 4), power(4, 2))

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">8 + 16</gadget>
<output>24</output>
<result>24</result>


what number has a 4 : 1 ratio to the number 100 ?

Explanation: "4 : 1 = x : 100 x = 4 * 100 x = 400 answer : c"

<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<result>400</result>


after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5535 . what was the number of original inhabitants ?

Explanation: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5535 ( 27 / 40 ) * x = 5535 x = 5535 * 40 / 27 = 8200 the answer is b ."

divide(5535, subtract(subtract(const_1, divide(10, const_100)), multiply(subtract(const_1, divide(10, const_100)), divide(25, const_100))))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(9/10) * (1/4)</gadget>
<output>9/40 = around 0.225</output>
<gadget id="calculator">(9/10) - (9/40)</gadget>
<output>27/40 = around 0.675</output>
<gadget id="calculator">5_535 / (27/40)</gadget>
<output>8_200</output>
<result>8_200</result>


is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , then how old is b ?

Explanation: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 5 x = 40 = > x = 8 hence , b ' s age = 2 x = 16 years . answer : a"

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

<gadget id="calculator">42 - 2</gadget>
<output>40</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>16</result>


last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ?

Explanation: let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b

multiply(20000, add(const_1, divide(10, const_100)))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">20_000 * (11/10)</gadget>
<output>22_000</output>
<result>22_000</result>


the list price of an article is rs . 65 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

Explanation: "explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 4 % answer : option b"

multiply(divide(subtract(subtract(65, multiply(65, divide(10, const_100))), 56.16), subtract(65, multiply(65, divide(10, const_100)))), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">65 * (1/10)</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">65 - (13/2)</gadget>
<output>117/2 = around 58.5</output>
<gadget id="calculator">(117/2) - 56.16</gadget>
<output>2.34</output>
<gadget id="calculator">2.34 / (117/2)</gadget>
<output>0.04</output>
<gadget id="calculator">0.04 * 100</gadget>
<output>4</output>
<result>4</result>


a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 3 liters of water cost ?

Explanation: c . 50 cents yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 50 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 25 cents . fraction of spirit is 1 / 2 . 25 = k * ( 1 / 2 ) k = 50 cost per liter = 50 * ( 1 / 4 ) ( 1 part spirit , 3 parts water ) cost for 4 liters = 50 * ( 1 / 4 ) * 4 = 50 cents d . 50 cents

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

<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">50 * (1/4)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 4</gadget>
<output>50</output>
<result>50</result>


a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1004 in total compensation , how many total hours did he work that week ?

Explanation: "for 40 hrs = 40 * 16 = 640 excess = 1004 - 640 = 364 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 364 / 28 = 13 total hrs = 40 + 13 = 53 answer e 53"

add(40, divide(subtract(1004, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))

<gadget id="calculator">16 * 40</gadget>
<output>640</output>
<gadget id="calculator">1_004 - 640</gadget>
<output>364</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>
<gadget id="calculator">364 / 28</gadget>
<output>13</output>
<gadget id="calculator">40 + 13</gadget>
<output>53</output>
<result>53</result>


you have to send 3000 grapes 1000 kilometers from grapecity to appleland . your truck can carry 1000 grapes at a time . every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction ( towards grapecity ) . what is highest number of grapes you can get to appleland ?

Explanation: step one : first you want to make 3 trips of 1,000 grapes 333 kilometers . you will be left with 2,001 grapes and 667 kilometers to go . step two : next you want to take 2 trips of 1,000 grapes 500 kilometers . you will be left with 1,000 grapes and 167 kilometers to go ( you have to leave a grape behind ) . step three : finally , you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland . correct answer is a ) 833

subtract(1000, subtract(subtract(1000, floor(divide(1000, const_3))), divide(1000, const_2)))

<gadget id="calculator">1_000 / 3</gadget>
<output>1_000/3 = around 333.333333</output>
<gadget id="calculator">floor(1_000/3)</gadget>
<output>333</output>
<gadget id="calculator">1_000 - 333</gadget>
<output>667</output>
<gadget id="calculator">1_000 / 2</gadget>
<output>500</output>
<gadget id="calculator">667 - 500</gadget>
<output>167</output>
<gadget id="calculator">1_000 - 167</gadget>
<output>833</output>
<result>833</result>


the contents of a certain box consist of 14 apples and 25 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?

Explanation: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 25 oranges , so to get to 6 oranges , we should remove 25 - 6 = 19 oranges . answer d"

subtract(add(14, 25), divide(14, divide(70, const_100)))

<gadget id="calculator">14 + 25</gadget>
<output>39</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">14 / (7/10)</gadget>
<output>20</output>
<gadget id="calculator">39 - 20</gadget>
<output>19</output>
<result>19</result>


jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 7 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

Explanation: u / i = 7 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 35 : 21 : 2 i . e . u : b = 35 : 2 answer : option e

<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">35 / 2</gadget>
<output>35/2 = around 17.5</output>
<result>35/2 = around 17.5</result>


how many prime numbers are between 13 / 3 and 83 / 6 ?

Explanation: "13 / 3 = 4 . xxx 83 / 6 = 13 . xxx so we need to find prime numbers between 4 ( exclusive ) - 12 ( inclusive ) there are 2 prime numbers 7 11 hence answer will be ( b ) 2 b"

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


john makes $ 60 a week from his job . he earns a raise andnow makes $ 80 a week . what is the % increase ?

Explanation: "increase = ( 20 / 60 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b"

multiply(divide(subtract(80, 60), 60), const_100)

<gadget id="calculator">80 - 60</gadget>
<output>20</output>
<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c which is at midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?

Explanation: "explanation : speed in downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed in upstream = ( 14 â € “ 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 â ‡ ” x / 18 + x / 20 = 19 â ‡ ’ x = 180 km . answer : a"

divide(19, add(divide(const_1, add(14, 4)), divide(const_1, multiply(subtract(14, 4), const_2))))

<gadget id="calculator">14 + 4</gadget>
<output>18</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/18) + (1/20)</gadget>
<output>19/180 = around 0.105556</output>
<gadget id="calculator">19 / (19/180)</gadget>
<output>180</output>
<result>180</result>


in a division sum , the quotient is 18 , the divisor 43 and the remainder 12 , find the dividend ?

Explanation: "explanation : 18 * 43 + 12 = 786 answer : d"

<gadget id="calculator">18 * 43</gadget>
<output>774</output>
<gadget id="calculator">774 + 12</gadget>
<output>786</output>
<result>786</result>


niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ?

Explanation: we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a

<gadget id="calculator">40 + 40</gadget>
<output>80</output>
<gadget id="calculator">80 + 10</gadget>
<output>90</output>
<gadget id="calculator">80 / 90</gadget>
<output>8/9 = around 0.888889</output>
<result>8/9 = around 0.888889</result>


Explanation: 2 a * 4 b = 10 * 10 = 100 8 ab = 100 i . e . 40 ab = 500 answer : option e

multiply(40, multiply(divide(10, 2), divide(10, 4)))

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">5 * (5/2)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">40 * (25/2)</gadget>
<output>500</output>
<result>500</result>


rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ?

Explanation: "average price per book = ( 1200 + 480 ) / ( 52 + 32 ) = 1680 / 84 = rs . 20 answer : d"

<gadget id="calculator">1_200 + 480</gadget>
<output>1_680</output>
<gadget id="calculator">52 + 32</gadget>
<output>84</output>
<gadget id="calculator">1_680 / 84</gadget>
<output>20</output>
<result>20</result>


if 2 ^ 5 , 4 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

Explanation: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 4 * 4 = 208 smash d"

multiply(multiply(multiply(power(2, 2), 4), divide(13, 2)), 2)

<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">16 * (13/2)</gadget>
<output>104</output>
<gadget id="calculator">104 * 2</gadget>
<output>208</output>
<result>208</result>


if 3 < x < 6 < y < 11 , then what is the greatest possible positive integer difference of x and y ?

Explanation: "3 < x < 6 < y < 11 ; 3 < x y < 11 3 + y < x + 11 y - x < 8 . positive integer difference is 7 ( for example y = 10.5 and x = 3.5 ) answer : e ."

<gadget id="calculator">11 - 3</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<result>7</result>


chris age after 20 years will be 5 times his age 5 years back . what is the present age of chris ?

Explanation: chris present age = x after 20 years = x + 20 5 years back = x - 5 x + 20 = 5 ( x - 5 ) x = 5 answer is e

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

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 + 20</gadget>
<output>45</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">45 / 4</gadget>
<output>45/4 = around 11.25</output>
<gadget id="calculator">(45/4) - 5</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(45/4) - (25/4)</gadget>
<output>5</output>
<result>5</result>


the weight of a glass of jar is 30 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?

Explanation: let weight of jar filled with beans = 100 g weight of jar = 30 g weight of coffee beans = 70 g weight of jar and remaining beans = 60 g weight of remaining beans = 30 g fraction remaining = 30 / 70 = 3 / 7 answer is e .

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

<gadget id="calculator">60 - 30</gadget>
<output>30</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">30 / 70</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>


a number increased by 15 % gives 1150 . the number is

Explanation: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 15 % = 115 % 115 % - - - - - - - > 1150 ( 115 × 100 = 1150 ) 100 % - - - - - - - > 1000 ( 100 × 100 = 1000 ) b )"

divide(1150, add(const_1, divide(15, const_100)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">1_150 / (23/20)</gadget>
<output>1_000</output>
<result>1_000</result>


a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 390 m long platform ?

Explanation: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 390 ) / 36 * 5 / 18 = 51 min . answer : c"

divide(add(390, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 36</gadget>
<output>10</output>
<gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">390 + 120</gadget>
<output>510</output>
<gadget id="calculator">510 / 10</gadget>
<output>51</output>
<result>51</result>


the average of 7 numbers is 23 . if each number be multiplied by 5 . find the average of new set of numbers ?

Explanation: "explanation : average of new numbers = 23 * 5 = 115 answer : option d"

<gadget id="calculator">23 * 5</gadget>
<output>115</output>
<result>115</result>


if 8 men or 12 women can do a piece of work in 35 days , in how many days can the same work be done by 6 men and 11 women ?

Explanation: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 35 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 35 = 1 / 420 so , 20 women work = 20 / 420 = 1 / 21 ans : 21 days answer : e"

inverse(add(divide(6, multiply(8, 35)), divide(11, multiply(12, 35))))

<gadget id="calculator">8 * 35</gadget>
<output>280</output>
<gadget id="calculator">6 / 280</gadget>
<output>3/140 = around 0.021429</output>
<gadget id="calculator">12 * 35</gadget>
<output>420</output>
<gadget id="calculator">11 / 420</gadget>
<output>11/420 = around 0.02619</output>
<gadget id="calculator">(3/140) + (11/420)</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">1 / (1/21)</gadget>
<output>21</output>
<result>21</result>


the total age of a and b is 18 years more than the total age of b and c . c is how many year younger than

Explanation: "given that a + b = 182 + b + c = > a â € “ c = 18 + b â € “ b = 18 = > c is younger than a by 18 years answer : e"

<gadget id="calculator">18 * 1</gadget>
<output>18</output>
<result>18</result>


the greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively , is :

Explanation: "explanation : required number = h . c . f . of ( 1657 - 9 ) and ( 2037 - 5 ) = h . c . f . of 1648 and 2032 = 16 . answer : a"

gcd(subtract(2037, 5), subtract(1657, 9))

<gadget id="calculator">2_037 - 5</gadget>
<output>2_032</output>
<gadget id="calculator">1_657 - 9</gadget>
<output>1_648</output>
<gadget id="calculator">gcd(2_032, 1_648)</gadget>
<output>16</output>
<result>16</result>


a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?

Explanation: "l * 30 = 1200 l = 40 40 + 30 + 50 = 120 120 * 10 = 1200 e"

<gadget id="calculator">1_200 / 30</gadget>
<output>40</output>
<gadget id="calculator">30 + 40</gadget>
<output>70</output>
<gadget id="calculator">30 ** 2</gadget>
<output>900</output>
<gadget id="calculator">40 ** 2</gadget>
<output>1_600</output>
<gadget id="calculator">900 + 1_600</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>
<gadget id="calculator">70 + 50</gadget>
<output>120</output>
<gadget id="calculator">120 * 10</gadget>
<output>1_200</output>
<result>1_200</result>


the length of a rectangle is 2 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?

Explanation: "if the width is 4 in and the length is 2 times the width , then the length is 2 * 4 = 8 in the area is given by 4 * 8 = 32 square inches correct answer e"

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<result>32</result>


the ratio between the sale price and the cost price of an article is 7 : 4 . what is the ratio between the profit and the cost price of that article ?

Explanation: "c . p . = rs . 4 x and s . p . = rs . 7 x . then , gain = rs . 3 x required ratio = 3 x : 4 x = 3 : 4 a"

<gadget id="calculator">7 - 4</gadget>
<output>3</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>


barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?

Explanation: "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.02 = 1200 ans : ` ` a ' '"

divide(subtract(multiply(divide(6, const_100), 2400), multiply(2400, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100)))

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 2_400</gadget>
<output>144</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">2_400 * (1/20)</gadget>
<output>120</output>
<gadget id="calculator">144 - 120</gadget>
<output>24</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) - (3/50)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">24 / (1/50)</gadget>
<output>1_200</output>
<result>1_200</result>


difference between a two - digit number and the number obtained by interchanging the two digits is 36 , what is the difference between two numbers

Explanation: explanation : let the ten digit be x , unit digit is y . then ( 10 x + y ) - ( 10 y + x ) = 36 = > 9 x - 9 y = 36 = > x - y = 4 . option b

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">36 / 9</gadget>
<output>4</output>
<result>4</result>


the average score of a cricketer in 6 matches is 27 and in other 4 matches is 32 . then find the average score in all the 10 matches ?

Explanation: "average in 10 matches = ( 6 * 27 + 4 * 32 ) / 6 + 4 = 162 + 128 / 10 = 290 / 10 = 29 answer is d"

divide(add(multiply(6, 27), multiply(4, 32)), 10)

<gadget id="calculator">6 * 27</gadget>
<output>162</output>
<gadget id="calculator">4 * 32</gadget>
<output>128</output>
<gadget id="calculator">162 + 128</gadget>
<output>290</output>
<gadget id="calculator">290 / 10</gadget>
<output>29</output>
<result>29</result>


rs . 900 amounts to rs . 920 in 3 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?

Explanation: "( 900 * 3 * 3 ) / 100 = 81 920 + 81 = 1001 answer : b"

multiply(power(add(const_1, divide(3, const_100)), 3), 900)


a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 136 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?

Explanation: let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 136 = > . 1 x + 3 / 4 x = 136 = > x = 160 160 - 136 = pure gala = 24 . a

subtract(divide(136, add(divide(10, const_100), divide(3, 4))), 136)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/10) + (3/4)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">136 / (17/20)</gadget>
<output>160</output>
<gadget id="calculator">160 - 136</gadget>
<output>24</output>
<result>24</result>


at a monthly meeting , 1 / 3 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?

Explanation: "males who did not arrive on time are 1 / 5 * 1 / 3 = 1 / 15 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 3 = 1 / 9 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 15 + 1 / 9 = 8 / 45 the answer is e ."

add(multiply(subtract(const_1, divide(5, 6)), subtract(const_1, divide(1, 3))), multiply(subtract(const_1, divide(4, 5)), divide(1, 3)))

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/6) * (2/3)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * (1/3)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/9) + (1/15)</gadget>
<output>8/45 = around 0.177778</output>
<result>8/45 = around 0.177778</result>


a shopkeeper sold an book offering a discount of 5 % and earned a profit of 30 % . what would have been the percentage of profit earned if no discount was offered ?

Explanation: "let c . p . be $ 100 . then , s . p . = $ 130 let marked price be $ x . then , 95 / 100 x = 130 x = 13000 / 95 = $ 136.8 now , s . p . = $ 136.8 , c . p . = $ 100 profit % = 136.8 % . d"

multiply(const_100, divide(add(const_100, 30), subtract(const_100, 5)))

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">130 / 95</gadget>
<output>26/19 = around 1.368421</output>
<gadget id="calculator">100 * (26/19)</gadget>
<output>2_600/19 = around 136.842105</output>
<result>2_600/19 = around 136.842105</result>


a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 300 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?

Explanation: "the smallest amount that the company can spend is the lcm of 300 and 200 , which is 600 for each , which is total 1200 . the number of 1 st type of computers which costing $ 300 = 600 / 300 = 2 . the number of 2 nd type of computers which costing $ 200 = 600 / 200 = 3 . total = 2 + 3 = 5 answer is b ."

<gadget id="calculator">lcm(300, 200)</gadget>
<output>600</output>
<gadget id="calculator">600 / 300</gadget>
<output>2</output>
<gadget id="calculator">600 / 200</gadget>
<output>3</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<result>5</result>


if p is a prime number greater than 3 , find the remainder when p ^ 2 + 14 is divided by 12 .

Explanation: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c ."

subtract(add(14, power(add(const_1, const_4), 2)), multiply(12, 3))

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">14 + 25</gadget>
<output>39</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">39 - 36</gadget>
<output>3</output>
<result>3</result>


a man has some hens and cows . if the number of heads be 42 and the number of feet equals 124 , then the number of hens will be

Explanation: "explanation : let number of hens = h and number of cows = c number of heads = 42 = > h + c = 42 - - - ( equation 1 ) number of feet = 124 = > 2 h + 4 c = 124 = > h + 2 c = 62 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 62 - 42 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 42 = > h = 42 - 20 = 22 i . e . , number of hens = 22 answer : a"

divide(subtract(multiply(42, const_4), 124), const_2)

<gadget id="calculator">42 * 4</gadget>
<output>168</output>
<gadget id="calculator">168 - 124</gadget>
<output>44</output>
<gadget id="calculator">44 / 2</gadget>
<output>22</output>
<result>22</result>


find large number from below question the difference of two numbers is 1385 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 large number = 274 + 1385 = 1659 e"

multiply(divide(subtract(1385, 15), subtract(6, const_1)), 6)

<gadget id="calculator">1_385 - 15</gadget>
<output>1_370</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_370 / 5</gadget>
<output>274</output>
<gadget id="calculator">274 * 6</gadget>
<output>1_644</output>
<result>1_644</result>


Explanation: answer 0.30 = 30 / 100 = 3 / 10 correct option : c

divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.3), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">100 * 0.3</gadget>
<output>30</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>


a room is 30 m long and 24 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :

Explanation: let the height be h 2 ( 30 + 24 ) x h – 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d

volume_rectangular_prism(30, 24, divide(multiply(rectangle_area(30, 24), const_2), rectangle_perimeter(30, 24)))

<gadget id="calculator">30 * 24</gadget>
<output>720</output>
<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>
<gadget id="calculator">2 * (30 + 24)</gadget>
<output>108</output>
<gadget id="calculator">1_440 / 108</gadget>
<output>40/3 = around 13.333333</output>
<gadget id="calculator">30 * 24 * (40/3)</gadget>
<output>9_600</output>
<result>9_600</result>


if $ 120 invested at a certain rate of simple interest amounts to $ 180 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?

Explanation: "120 amounts to 180 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 180 120 + 120 * ( r / 100 ) * ( 3 ) = 140 = > r = 50 / 3 150 in 6 years = principal + interest = 300 answer is e ."

add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(180, 120), 120), 120), 3)), 120))

<gadget id="calculator">150 * 6</gadget>
<output>900</output>
<gadget id="calculator">180 - 120</gadget>
<output>60</output>
<gadget id="calculator">60 * 120</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 120</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">900 * 20</gadget>
<output>18_000</output>
<gadget id="calculator">18_000 / 120</gadget>
<output>150</output>
<gadget id="calculator">150 + 150</gadget>
<output>300</output>
<result>300</result>


the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ?

Explanation: the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a .

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 1.2</gadget>
<output>1.8</output>
<result>1.8</result>


a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , the how old is b ?

Explanation: explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 ⇒ 5 x = 35 ⇒ x = 7 . hence , b ' s age = 2 x = 14 years . answer : d

divide(multiply(subtract(37, const_2), const_2), add(const_4, const_1))

<gadget id="calculator">37 - 2</gadget>
<output>35</output>
<gadget id="calculator">35 * 2</gadget>
<output>70</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">70 / 5</gadget>
<output>14</output>
<result>14</result>


if c and t are positive integers , ct + c + t can not be

Explanation: let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b

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


the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 2 ) = rs . 2972 . answer : option a"

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 2)


a man swims downstream 30 km and upstream 12 km taking 3 hours each time , what is the speed of the man in still water ?

Explanation: "30 - - - 3 ds = 10 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 10 + 4 ) / 2 = 7 answer : b"

divide(add(divide(12, 3), divide(30, 3)), const_2)

<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<gadget id="calculator">4 + 10</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>7</result>


a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 7 x km .

Explanation: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 7 x / ( x / 8 ) = 56 kmph answer : a"

divide(multiply(40, 7), add(divide(40, 40), divide(multiply(2, 40), 20)))

<gadget id="calculator">40 * 7</gadget>
<output>280</output>
<gadget id="calculator">40 / 40</gadget>
<output>1</output>
<gadget id="calculator">2 * 40</gadget>
<output>80</output>
<gadget id="calculator">80 / 20</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">280 / 5</gadget>
<output>56</output>
<result>56</result>


if the average of 6 digits is 16 and the average of 4 of them is 10 , calculate the average of the remaining 2 numbers ?

Explanation: "explanation : total of the 6 digits - 6 * 16 = 96 total of the 4 digits - 4 * 10 = 40 total of the remaining 2 digits - 96 - 40 = 56 average of the remaining 2 numbers = 56 / 2 = 28 answer : c"

divide(subtract(multiply(6, 16), multiply(4, 10)), 2)

<gadget id="calculator">6 * 16</gadget>
<output>96</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">96 - 40</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>


a company pays 20.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?

Explanation: "explanation : dividend on 1 share = ( 20.5 * 50 ) / 100 = rs . 10.25 rs . 25 is income on an investment of rs . 100 rs . 10.25 is income on an investment of rs . ( 10.25 * 100 ) / 25 = rs . 41 answer : e"

divide(multiply(divide(multiply(20.5, 50), const_100), const_100), 25)

<gadget id="calculator">20.5 * 50</gadget>
<output>1_025</output>
<gadget id="calculator">1_025 / 100</gadget>
<output>41/4 = around 10.25</output>
<gadget id="calculator">(41/4) * 100</gadget>
<output>1_025</output>
<gadget id="calculator">1_025 / 25</gadget>
<output>41</output>
<result>41</result>


how many diagonals does a 59 - sided convex polygon have ?

Explanation: a 59 - sided convex polygon has 59 vertices . if we examine a single vertex , we can see that we can connect it with 56 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be ( 59 ) ( 56 ) = 3304 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3304 by 2 to get 1652 . the answer is b .

divide(factorial(59), multiply(factorial(subtract(59, const_2)), factorial(const_2)))


a shopkeeper sold an book offering a discount of 5 % and earned a profit of 33 % . what would have been the percentage of profit earned if no discount was offered ?

Explanation: "let c . p . be $ 100 . then , s . p . = $ 133 let marked price be $ x . then , 95 / 100 x = 133 x = 13300 / 95 = $ 140 now , s . p . = $ 140 , c . p . = $ 100 profit % = 40 % . a"

multiply(const_100, divide(add(const_100, 33), subtract(const_100, 5)))

<gadget id="calculator">100 + 33</gadget>
<output>133</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">133 / 95</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 * (7/5)</gadget>
<output>140</output>
<result>140</result>


calculate how long it will take a swimmer to swim a distance of 10 km against the current of a river which flows at 3 km / hr , given that he can swim in still water at 5 km / h

Explanation: "swim in still water at = 5 speed of river = 3 us = 5 - 3 = 2 distance = 10 t = 10 / 2 = 5 answer : c"

<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was :

Explanation: explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665

<gadget id="calculator">84 * 8</gadget>
<output>672</output>
<gadget id="calculator">672 + 85</gadget>
<output>757</output>
<gadget id="calculator">757 - 92</gadget>
<output>665</output>
<result>665</result>


at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 20 seconds . how long does it tick at 12 ′ o clock

Explanation: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 20 / 5 = 4 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 4 = 44 secs . answer : c"

multiply(divide(20, subtract(6, const_1)), subtract(12, const_1))

<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">4 * 11</gadget>
<output>44</output>
<result>44</result>


the price of a t . v . set worth rs . 30000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?

Explanation: "money paid in cash = rs . 1000 balance payment = ( 30000 - 1000 ) = rs . 29000 answer : c"

<gadget id="calculator">30_000 - 1_000</gadget>
<output>29_000</output>
<result>29_000</result>


55 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :

Explanation: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 55 ⇔ = [ 55 * 20 * 20 * 7 / 22 ] = 7000 cm = 70 m . answer d"

divide(55, multiply(power(divide(1, const_2), const_2), const_pi))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * pi</gadget>
<output>pi/4 = around 0.785398</output>
<gadget id="calculator">55 / (pi/4)</gadget>
<output>220/pi = around 70.028175</output>
<result>220/pi = around 70.028175</result>


a metallic sheet is of rectangular shape with dimensions 48 m x 34 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 = ( 48 - 16 ) m = 32 m , b = ( 34 - 16 ) m = 18 m , h = 8 m . volume of the box = ( 32 x 18 x 8 ) m 3 = 4608 m 3 . answer : option c"

volume_rectangular_prism(subtract(48, multiply(8, const_2)), subtract(34, multiply(8, const_2)), 8)

<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">48 - 16</gadget>
<output>32</output>
<gadget id="calculator">34 - 16</gadget>
<output>18</output>
<gadget id="calculator">32 * 18 * 8</gadget>
<output>4_608</output>
<result>4_608</result>


a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?

Explanation: some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c

add(divide(subtract(6.3, multiply(0.7, const_4)), 0.5), const_4)

<gadget id="calculator">0.7 * 4</gadget>
<output>2.8</output>
<gadget id="calculator">6.3 - 2.8</gadget>
<output>3.5</output>
<gadget id="calculator">3.5 / 0.5</gadget>
<output>7</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<result>11</result>


if 25 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?

Explanation: "we know 25 % people study biology , therefore the no of people not studying = 100 - 25 = 75 % > therefore the people not studying biology out of a total 880 people are = 75 % of 880 > ( 75 / 100 ) * 880 = 660 people e"

multiply(divide(880, const_100), subtract(const_100, 25))

<gadget id="calculator">880 / 100</gadget>
<output>44/5 = around 8.8</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">(44/5) * 75</gadget>
<output>660</output>
<result>660</result>


find large number from below question the difference of two numbers is 1380 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1380 ) . x + 1380 = 6 x + 15 5 x = 1365 x = 273 large number = 273 + 1380 = 1653 e"

multiply(divide(subtract(1380, 15), subtract(6, const_1)), 6)

<gadget id="calculator">1_380 - 15</gadget>
<output>1_365</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_365 / 5</gadget>
<output>273</output>
<gadget id="calculator">273 * 6</gadget>
<output>1_638</output>
<result>1_638</result>


tough and tricky questions : word problems . operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 8 , when a # b = 100 ?

Explanation: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d

<gadget id="calculator">100 / 4</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">5 + 8</gadget>
<output>13</output>
<result>13</result>


according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 240 6 ounces servings of orange juice ?

Explanation: "its e . total juice rquired = 240 * 6 = 1440 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1440 / 48 = 30 . answer e"

divide(divide(multiply(240, 6), 12), const_4)

<gadget id="calculator">240 * 6</gadget>
<output>1_440</output>
<gadget id="calculator">1_440 / 12</gadget>
<output>120</output>
<gadget id="calculator">120 / 4</gadget>
<output>30</output>
<result>30</result>


mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 38400 , how much amount per month would he have spent on clothes and transport ?

Explanation: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 38400 ⁄ 12 = 3200 answer c"

multiply(divide(divide(38400, divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)), multiply(const_3, const_4)), divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100))

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">38_400 / (1/5)</gadget>
<output>192_000</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">192_000 / 12</gadget>
<output>16_000</output>
<gadget id="calculator">16_000 * (1/5)</gadget>
<output>3_200</output>
<result>3_200</result>


daniel went to a shop and bought things worth rs . 50 , out of which 90 paise went on sales tax on taxable purchases . if the tax rate was 15 % , then what was the cost of the tax free items ?

Explanation: total cost of the items he purchased = rs . 50 given that out of this rs . 50 , 90 paise is given as tax = > total tax incurred = 90 paise = rs . 90 / 100 let the cost of the tax free items = x given that tax rate = 15 % ∴ ( 50 − 90 / 100 − x ) 15 / 100 = 90 / 100 ⇒ 15 ( 50 − 0.9 − x ) = 90 ⇒ ( 50 − 0.9 − x ) = 6 ⇒ x = 50 − 0.9 − 6 = 43.1 c

subtract(subtract(50, divide(90, const_100)), divide(90, 15))

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">50 - (9/10)</gadget>
<output>491/10 = around 49.1</output>
<gadget id="calculator">90 / 15</gadget>
<output>6</output>
<gadget id="calculator">(491/10) - 6</gadget>
<output>431/10 = around 43.1</output>
<result>431/10 = around 43.1</result>


if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3410 , r will receive

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3410 * ( 6 / 31 ) = 110 * 6 = 660 . answer : option a"

multiply(3410, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 10</gadget>
<output>25</output>
<gadget id="calculator">25 + 6</gadget>
<output>31</output>
<gadget id="calculator">6 / 31</gadget>
<output>6/31 = around 0.193548</output>
<gadget id="calculator">3_410 * (6/31)</gadget>
<output>660</output>
<result>660</result>


running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets ?

Explanation: let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 1 * 6 = 6 days to produce 1 w widgets . answer : b

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

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">24 - 12</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>6</result>


a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 175 , how many coins of each type are there ?

Explanation: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 175 ⇒ 1.75 x = 175 ⇒ x = 100 coins answer d"

divide(175, add(add(inverse(const_4), inverse(const_2)), const_1))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">175 / (7/4)</gadget>
<output>100</output>
<result>100</result>


x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5000 . the amount invested by y is

Explanation: solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d

<gadget id="calculator">5_000 * 6</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 2</gadget>
<output>15_000</output>
<result>15_000</result>


little john had $ 16.10 . he spent $ 3.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?

Explanation: john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 16.10 - 7.65 = $ 8.45 answer : e

<gadget id="calculator">2.2 + 2.2</gadget>
<output>4.4</output>
<gadget id="calculator">3.25 + 4.4</gadget>
<output>7.65</output>
<gadget id="calculator">16.1 - 7.65</gadget>
<output>8.45</output>
<result>8.45</result>


3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 10 pumps work to empty the tank in 1 day ?

Explanation: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 10 pumps then 48 / 10 = 4.8 hrs . answer : a"

<gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">48 / 10</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>


the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?

Explanation: given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !

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

<gadget id="calculator">4 * pi</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">3 / pi</gadget>
<output>3/pi = around 0.95493</output>
<gadget id="calculator">(4*pi) * (3/pi)</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">pi * (3/pi)</gadget>
<output>3</output>
<gadget id="calculator">6 + 3</gadget>
<output>9</output>
<result>9</result>


if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n .

Explanation: we write n ! = n * ( n - 1 ) ( n - 2 ! ) therefore n ! / ( n - 2 ) ! = n ( n - 1 ) * ( n - 2 ) ! / ( n - 2 ) ! = n ( n - 1 ) . - - > n ( n - 1 ) = 342 - - > n ^ 2 - n - 342 = 0 - - > n ^ 2 - 19 n + 18 n - 342 = 0 - - > n ( n - 19 ) + 18 ( n - 19 ) = 0 - - > ( n - 19 ) ( n + 18 ) = 0 therefore n - 19 = 0 ; n + 18 = 0 ; ( i . e ) n = 19 ; n = - 18 we want positive integer . so , n = 19 . answer : c

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">342 + (1/4)</gadget>
<output>1_369/4 = around 342.25</output>
<gadget id="calculator">(1_369/4) ** (1/2)</gadget>
<output>37/2 = around 18.5</output>
<result>37/2 = around 18.5</result>


a person has 100 $ in 10 $ and 5 $ bill . if the 5 $ bill quantity is twice that of 10 $ bill . what is quantity of 10 $ .

Explanation: let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e

<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 5 of whom are females , by how much does the index for the females exceed the index for the males in the group ?

Explanation: "index for females = ( 20 - 5 ) / 20 = 3 / 4 = 0.75 index for males = ( 20 - 15 / 20 = 1 / 4 = 0.25 index for females exceeds males by 0.75 - 0.25 = 0.5 answer : c"

subtract(divide(subtract(20, 5), 20), divide(5, 20))

<gadget id="calculator">20 - 5</gadget>
<output>15</output>
<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">5 / 20</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(3/4) - (1/4)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 12 meters , and the interior of tank b has a height of 12 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?

Explanation: "the radius of tank a is 12 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 144 / ( 4 * pi ^ 2 ) = 360 / ( pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 12 * pi * 100 / ( 4 * pi ^ 2 ) = 300 / ( pi ) tank a / tank b = 360 / 300 = 12 / 10 = 120 % the answer is e ."

multiply(multiply(power(divide(12, 10), const_2), divide(10, 12)), const_100)

<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">10 / 12</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(36/25) * (5/6)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 100</gadget>
<output>120</output>
<result>120</result>


eric throws 2 dice , and his score is the sum of the values shown . sandra throws one dice and her score is the square of the value shown . what is the probabilty that sandras score will be strictly higher than erics score ? ?

Explanation: sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a

divide(add(add(add(add(const_3, subtract(power(multiply(2, const_3), const_2), const_10)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), multiply(power(multiply(2, const_3), const_2), multiply(2, const_3)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">36 - 10</gadget>
<output>26</output>
<gadget id="calculator">3 + 26</gadget>
<output>29</output>
<gadget id="calculator">29 + 36</gadget>
<output>65</output>
<gadget id="calculator">65 + 36</gadget>
<output>101</output>
<gadget id="calculator">101 + 36</gadget>
<output>137</output>
<gadget id="calculator">36 * 6</gadget>
<output>216</output>
<gadget id="calculator">137 / 216</gadget>
<output>137/216 = around 0.634259</output>
<result>137/216 = around 0.634259</result>


if $ 910 are divided between worker a and worker b in the ratio 5 : 9 , what is the share that worker b will get ?

Explanation: worker b will get 9 / 14 = 64.29 % the answer is c .

<gadget id="calculator">5 + 9</gadget>
<output>14</output>
<gadget id="calculator">910 / 14</gadget>
<output>65</output>
<result>65</result>


someone on a skateboard is traveling 8 miles per hour . how many feet does she travel in 5 seconds ? ( 1 mile = 5280 feet )

Explanation: "per second = > 8 * 5280 ft / 60 * 60 = 11.73 ft 5 seconds = > 11.73 * 5 = 58.65 ft answer : e"

multiply(5, divide(multiply(8, 5280), const_3600))

<gadget id="calculator">8 * 5_280</gadget>
<output>42_240</output>
<gadget id="calculator">42_240 / 3_600</gadget>
<output>176/15 = around 11.733333</output>
<gadget id="calculator">5 * (176/15)</gadget>
<output>176/3 = around 58.666667</output>
<result>176/3 = around 58.666667</result>


a car traveling at a certain constant speed takes 30 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 30 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?

Explanation: "30 * t = 1 km = > t = 1 / 30 km / h v * ( t + 30 / 3600 ) = 1 v ( 1 / 30 + 30 / 3600 ) = 1 v ( 150 / 3600 ) = 1 v = 24 km / h the answer is e ."

divide(1, divide(add(multiply(const_3600, divide(1, 30)), 30), const_3600))

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">3_600 * (1/30)</gadget>
<output>120</output>
<gadget id="calculator">120 + 30</gadget>
<output>150</output>
<gadget id="calculator">150 / 3_600</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>24</result>


of the families in city x in 1998 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 20 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?

Explanation: say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30 number of families owning computer in 2002 = 30 * 120 / 100 = 36 number of families in 2002 = 108 the percentage = 36 / 108 * 100 = 33.33 % . option : d

multiply(const_100, divide(divide(multiply(add(20, const_100), 30), const_100), add(const_100, 8)))

<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 + 8</gadget>
<output>108</output>
<gadget id="calculator">36 / 108</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">100 * (1/3)</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


recently , i decided to walk down an escalator of a tube station . i did some quick calculation in my mind . i found that if i walk down 20 ` ` 6 steps , i require thirty seconds to reach the bottom . however , if i am able to step down thirty ` ` 4 stairs , i would only require eighteen seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time i step off the last step at the bottom ?

Explanation: 26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto . means he covered 8 steps ( i . e . 34 - 26 ) in 12 ( i . e 30 - 18 ) seconds the spped of the boy is 8 steps in 12 seconds after further simplyfy . . 2 steps in 3 seconds after 34 steps only 18 seconds , means 12 more steps are left total steps are 34 + 12 = 46 answer : e

add(add(multiply(const_3, const_10), 4), multiply(divide(subtract(add(multiply(const_3, const_10), 4), add(20, 6)), subtract(multiply(const_3, const_10), multiply(6, const_3))), multiply(6, const_3)))

<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">30 + 4</gadget>
<output>34</output>
<gadget id="calculator">20 + 6</gadget>
<output>26</output>
<gadget id="calculator">34 - 26</gadget>
<output>8</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">30 - 18</gadget>
<output>12</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 18</gadget>
<output>12</output>
<gadget id="calculator">34 + 12</gadget>
<output>46</output>
<result>46</result>


if y > 0 , ( 2 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

Explanation: "soln : - can be reduced to y / 10 + 3 y / 10 = 2 y / 5 = 40 % answer : a"

multiply(const_100, add(divide(2, 20), divide(3, 10)))

<gadget id="calculator">2 / 20</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/10) + (3/10)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">100 * (2/5)</gadget>
<output>40</output>
<result>40</result>


at a loading dock , each worker on the night crew loaded 2 / 3 as many boxes as each worker on the day crew . if the night crew has 5 / 6 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?

Explanation: let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 2 y / 3 ) = 5 xy / 9 the total number of boxes is xy + 5 xy / 9 = 14 xy / 9 the fraction loaded by the day crew is xy / ( 14 xy / 9 ) = 9 / 14 the answer is d .

divide(multiply(6, 3), add(multiply(6, 3), multiply(2, 5)))

<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">18 + 10</gadget>
<output>28</output>
<gadget id="calculator">18 / 28</gadget>
<output>9/14 = around 0.642857</output>
<result>9/14 = around 0.642857</result>


if a train , travelling at a speed of 90 kmph , crosses a pole in 6 sec , then the length of train is ?

Explanation: "e e = 90 * 5 / 18 * 6 = 150 m"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>
<gadget id="calculator">25 * 6</gadget>
<output>150</output>
<result>150</result>


find the number of different prime factors of 25650

Explanation: explanation : l . c . m of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19 3 , 2 , 5,19 number of different prime factors is 4 . answer : option a

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


the mean of 50 observations was 36 . it was found later that an observation 58 was wrongly taken as 43 . the corrected new mean is ?

Explanation: "correct sum = ( 36 * 50 + 58 - 43 ) = 1815 . correct mean = 1815 / 50 = 36.3 answer : e"

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 43)), 50)

<gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 43</gadget>
<output>5</output>
<gadget id="calculator">1_800 + 5</gadget>
<output>1_805</output>
<gadget id="calculator">1_805 / 50</gadget>
<output>361/10 = around 36.1</output>
<result>361/10 = around 36.1</result>


in a school of 450 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?

Explanation: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 450 * 18 / 100 = 81 answer : d"

divide(multiply(450, subtract(const_100, add(add(44, 28), 10))), const_100)

<gadget id="calculator">44 + 28</gadget>
<output>72</output>
<gadget id="calculator">72 + 10</gadget>
<output>82</output>
<gadget id="calculator">100 - 82</gadget>
<output>18</output>
<gadget id="calculator">450 * 18</gadget>
<output>8_100</output>
<gadget id="calculator">8_100 / 100</gadget>
<output>81</output>
<result>81</result>


find the volume and surface area of a cuboid 16 m long , 14 m broad and 7 m high .

Explanation: volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d

multiply(add(multiply(16, 7), add(multiply(16, 14), multiply(14, 7))), const_2)

<gadget id="calculator">16 * 7</gadget>
<output>112</output>
<gadget id="calculator">16 * 14</gadget>
<output>224</output>
<gadget id="calculator">14 * 7</gadget>
<output>98</output>
<gadget id="calculator">224 + 98</gadget>
<output>322</output>
<gadget id="calculator">112 + 322</gadget>
<output>434</output>
<gadget id="calculator">434 * 2</gadget>
<output>868</output>
<result>868</result>


3 - twentieths of the members of a social club are retirees who are also bridge players , 5 - twentieths of the members are retirees , and one - half of the members are bridge players . if 120 of the members are neither retirees nor bridge players , what is the total number of members in the social club ?

Explanation: { total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c

multiply(subtract(120, multiply(5, const_4)), const_2)

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">120 - 20</gadget>
<output>100</output>
<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<result>200</result>


the total marks obtained by a student in mathematics and physics is 80 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .

Explanation: let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 80 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 80 + 20 ) / 2 = 50 . answer : d

<gadget id="calculator">80 + 20</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>50</result>


the perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?

Explanation: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : b"

<gadget id="calculator">(2.5 * 44) / 2</gadget>
<output>55</output>
<result>55</result>


the principal that amounts to rs . 4903 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?

Explanation: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4903 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4076 . answer : b"

divide(4903, power(add(1, divide(add(6, divide(1, 4)), const_100)), 3))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">6 + (1/4)</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(25/4) / 100</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 + (1/16)</gadget>
<output>17/16 = around 1.0625</output>
<gadget id="calculator">(17/16) ** 3</gadget>
<output>4_913/4_096 = around 1.199463</output>
<gadget id="calculator">4_903 / (4_913/4_096)</gadget>
<output>20_082_688/4_913 = around 4_087.662935</output>
<result>20_082_688/4_913 = around 4_087.662935</result>


in a group of 95 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?

Explanation: "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 95 - 59 = 36 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 95 = 36 + 32 + 36 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - e"

<gadget id="calculator">36 + 32</gadget>
<output>68</output>
<gadget id="calculator">68 - 59</gadget>
<output>9</output>
<gadget id="calculator">36 - 9</gadget>
<output>27</output>
<result>27</result>


the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 80 cents more than the commodity y ?

Explanation: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 80 = $ 1.00 cents on commodity y , which will take 10 years . the answer is b ."

add(2001, divide(add(divide(80, const_100), subtract(4.40, 4.20)), subtract(divide(30, const_100), subtract(4.40, 4.20))))

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">4.4 - 4.2</gadget>
<output>0.2</output>
<gadget id="calculator">(4/5) + 0.2</gadget>
<output>1</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) - 0.2</gadget>
<output>0.1</output>
<gadget id="calculator">1 / 0.1</gadget>
<output>10</output>
<gadget id="calculator">2_001 + 10</gadget>
<output>2_011</output>
<result>2_011</result>


there are 13 clubs in a full deck of 52 cards . in a certain game , you pick a card from a standard deck of 52 cards . if the card is a club , you win . if the card is not a club , the person replaces the card to the deck , reshuffles , and draws again . the person keeps repeating that process until he picks a club , and the point is to measure how many draws it took before the person picked a club and , thereby , won . what is the probability that one will pick the first club on the forth draw or later ?

Explanation: favorable case = the club is picked in the third draw or later unfavorable cases = the club is picked in either first draw , second draw or third draws probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case 1 : probability of club picked in first draw = 13 / 52 = 1 / 4 unfavorable case 2 : probability of club picked in second draw ( i . e . first draw is not club ) = ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 unfavorable case 3 : probability of club picked in third draw ( i . e . first and 2 nd draws are not clubs ) = ( 39 / 52 ) * ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 3 / 4 ) * ( 1 / 4 ) = 9 / 64 total unfavorable probability = ( 1 / 4 ) + ( 3 / 16 ) + ( 9 / 64 ) = ( 16 / 64 ) + ( 12 / 64 ) + ( 9 / 64 ) = 37 / 64 i . e . , favorable probability = 1 - ( 37 / 64 ) = 27 / 64 answer : option e

multiply(multiply(divide(subtract(52, 13), 52), divide(subtract(52, 13), 52)), divide(subtract(52, 13), 52))

<gadget id="calculator">52 - 13</gadget>
<output>39</output>
<gadget id="calculator">39 / 52</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * (3/4)</gadget>
<output>9/16 = around 0.5625</output>
<gadget id="calculator">(9/16) * (3/4)</gadget>
<output>27/64 = around 0.421875</output>
<result>27/64 = around 0.421875</result>


the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 70 , and what number ?

Explanation: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 answer : b"

subtract(add(add(20, 40), 60), add(add(multiply(5, const_3), 10), 70))

<gadget id="calculator">20 + 40</gadget>
<output>60</output>
<gadget id="calculator">60 + 60</gadget>
<output>120</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 + 10</gadget>
<output>25</output>
<gadget id="calculator">25 + 70</gadget>
<output>95</output>
<gadget id="calculator">120 - 95</gadget>
<output>25</output>
<result>25</result>


if 28 % of a number exceeds 18 % of it by 7.2 , then find the number ?

Explanation: use the elimination method to find the correct option . of all the options only 90 fits 28 % of 90 = 25.2 18 % of 90 = 16.2 25.2 - 16.2 = 7.2 required number is 90 . answer : e

add(divide(7.2, divide(subtract(28, 18), const_100)), 18)

<gadget id="calculator">28 - 18</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">7.2 / (1/10)</gadget>
<output>72</output>
<gadget id="calculator">72 + 18</gadget>
<output>90</output>
<result>90</result>


how many factors of 60 are odd numbers greater than 1 ?

Explanation: prime factors of 60 are 2 ^ 2,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors d is the answer

<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>3</result>


a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent e of the distribution is less than m + d ?

Explanation: d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d

subtract(const_100, divide(subtract(const_100, 68), const_2))

<gadget id="calculator">100 - 68</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<result>84</result>


village p ’ s population is 1150 greater than village q ' s population . if village q ’ s population were reduced by 200 people , then village p ’ s population would be 4 times as large as village q ' s population . what is village q ' s current population ?

Explanation: p = q + 1150 . p = 4 ( q - 200 ) . 4 ( q - 200 ) = q + 1150 . 3 q = 1950 . q = 650 . the answer is c .

divide(add(1150, multiply(200, 4)), const_3)

<gadget id="calculator">200 * 4</gadget>
<output>800</output>
<gadget id="calculator">1_150 + 800</gadget>
<output>1_950</output>
<gadget id="calculator">1_950 / 3</gadget>
<output>650</output>
<result>650</result>


together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours e would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?

Explanation: say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job e in 44 hours . answer : c .

it can not be determined from the information above .

divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">(1/4) + (1/11)</gadget>
<output>15/44 = around 0.340909</output>
<gadget id="calculator">(15/44) / 15</gadget>
<output>1/44 = around 0.022727</output>
<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>


jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 50,000 after completion of one year . what will be madhu ' s share of profit ?

Explanation: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 50,000 i . e . rs . 25,000 answer : c"

multiply(add(multiply(multiply(multiply(const_4, 2), multiply(add(2, const_3), 2)), const_100), multiply(multiply(add(2, const_3), const_100), const_100)), divide(divide(multiply(add(2, const_3), 2), 2), multiply(const_4, const_3)))

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">80 * 100</gadget>
<output>8_000</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 * 100</gadget>
<output>50_000</output>
<gadget id="calculator">8_000 + 50_000</gadget>
<output>58_000</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">58_000 * (5/12)</gadget>
<output>72_500/3 = around 24_166.666667</output>
<result>72_500/3 = around 24_166.666667</result>


in a certain school , the ratio of boys to girls is 5 to 13 . if there are 160 more girls than boys , how many boys are there ?

Explanation: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 160 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 160 . so 1 part corresponds to 160 / 8 = 20 and so 5 parts correspond to 5 * 10 = 100 . a"

subtract(divide(160, subtract(const_1, divide(5, 13))), 160)

<gadget id="calculator">5 / 13</gadget>
<output>5/13 = around 0.384615</output>
<gadget id="calculator">1 - (5/13)</gadget>
<output>8/13 = around 0.615385</output>
<gadget id="calculator">160 / (8/13)</gadget>
<output>260</output>
<gadget id="calculator">260 - 160</gadget>
<output>100</output>
<result>100</result>


ajay can walk 4 km in 1 hour . in how many hours he can walk 40 km ?

Explanation: "1 hour he walk 4 km he walk 40 km in = 40 / 4 * 1 = 10 hours answer is b"

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