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a ) 43 , b ) 26 , c ) 33 , d ) 21 , e ) 28 | b | divide(subtract(multiply(48, const_4), 140), const_2) | a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be : | "b 26 let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 26 ." | a = 48 * 4
b = a - 140
c = b / 2
|
a ) 1980 , b ) 1998 , c ) 198 , d ) 200 , e ) 20 | c | subtract(multiply(multiply(add(const_3, const_4), const_1000), divide(1, 10)), multiply(divide(divide(1, 10), const_100), multiply(add(const_3, const_4), const_1000))) | when 1 / 10 percent of 2,000 is subtracted from 1 / 10 of 2,000 , the difference is | "( 1 / 10 ) * 2000 - ( 1 / 10 ) % * 2000 = 200 - ( 1 / 1000 ) * 2000 = 200 - 2 = 198 the answer is c ." | a = 3 + 4
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4
h = g * 1000
i = f * h
j = d - i
|
a ) 2875 , b ) 2654 , c ) 2645 , d ) 2456 , e ) 2522 | e | subtract(multiply(power(add(const_1, divide(divide(20, const_4), const_100)), const_3), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))) | find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quarterly | principal = rs . 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = rs . [ 16000 x ( 1 + ( 5 / 100 ) ) 3 ] = rs . 18522 . ci . = rs . ( 18522 - 16000 ) = rs . 2522 answer : e | a = 20 / 4
b = a / 100
c = 1 + b
d = c ** 3
e = 4 * 4
f = e * 100
g = math.sqrt(100)
h = f * g
i = d * h
j = 4 * 4
k = j * 100
l = math.sqrt(100)
m = k * l
n = i - m
|
a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4 | e | divide(subtract(51, multiply(const_3, 9)), multiply(const_3, const_2)) | a number is doubled and 9 is added . if the resultant is trebled , it becomes 51 . what is that number ? | "let the number be x . then , 3 ( 2 x + 9 ) = 51 2 x = 8 = > x = 4 answer : e" | a = 3 * 9
b = 51 - a
c = 3 * 2
d = b / c
|
a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4 | b | inverse(add(divide(subtract(35, 25), subtract(40, 35)), const_1)) | a certain quantity of 40 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ? | "original quantity = a substituted quantity = b then : ( a * 0.4 + 0.25 * b Ρ Π° Ρ 0.4 * b ) / a = 0.35 0.4 + ( b / a ) * ( - 0.15 ) = 0.35 b / a = - 0.05 / - 0.15 = 1 / 3 answer : b" | a = 35 - 25
b = 40 - 35
c = a / b
d = c + 1
e = 1/(d)
|
a ) 31 , b ) 33.33 , c ) 35 , d ) 37 , e ) 39.33 | b | divide(subtract(350, 250), 3) | on the first day of her vacation , louisa traveled 250 miles . on the second day , traveling at the same average speed , she traveled 350 miles . if the 250 - mile trip took 3 hours less than the 350 - mile trip , what was the average speed , in miles per hour ? | "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 250 / t = 350 / ( t + 3 ) - - > 5 / t = 7 / ( t + 3 ) - - > 5 t + 15 = 7 t - - - - > 2 t = 15 . t = 7.5 - - - - > ( rate ) = 250 / 7.5 = 33.33 answer : b" | a = 350 - 250
b = a / 3
|
a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 % | e | add(6.5, multiply(divide(5, const_100), 90)) | a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ? | "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e ." | a = 5 / 100
b = a * 90
c = 6 + 5
|
a ) 21600 , b ) 3778 , c ) 12788 , d ) 18000 , e ) 2881 | a | multiply(multiply(const_3, const_60), const_60) | if an object travels at six feet per second , how many feet does it travel in one hour ? | "explanation : if an object travels at 6 feet per second it covers 6 x 60 feet in one minute , and 6 x 60 x 60 feet in one hour . answer = 21600 answer : a ) 21600" | a = 3 * const_60
b = a * const_60
|
a ) 150 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm | a | multiply(sqrt(divide(67.5, 30)), const_100) | 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq . m . find the length of each stone slab ? | "area of each slab = 67.5 / 30 m 2 = 2.25 m 2 length of each slab β 2.25 = 1.5 m = 150 cm" | a = 67 / 5
b = math.sqrt(a)
c = b * 100
|
a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12 | e | subtract(subtract(40, 25), const_3) | machine r takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine r to make 40 widgets ? | i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of r is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and r reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of r . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer | a = 40 - 25
b = a - 3
|
a ) rs . 28 , b ) rs . 280 , c ) rs . 140 , d ) rs . 70 , e ) rs . 80 | b | divide(multiply(480, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 answer : b | a = 100 + 19
b = 480 * a
c = 100 - 15
d = 100 + 19
e = c + d
f = b / e
|
['a ) 1.04', 'b ) 1.12', 'c ) 1.24', 'd ) 1.4', 'e ) 1.5'] | b | multiply(divide(add(const_100, 40), const_100), divide(subtract(const_100, 20), const_100)) | a gardener changed the size of his rectangle shaped garden by increasing it ' s length by 40 % & decreasing is ' s width by 20 % . find area of new garden . | a 1 = l * b a 2 = ( l * 140 / 100 ) * ( b * 80 / 100 ) = 1.12 * lb so , area of garden is by 1.12 times of old area . answer : b | a = 100 + 40
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
|
a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54 | b | divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2) | the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and dennison have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ? | "if steve and dennison submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ." | a = 80 * 0
b = 2 * a
c = 100 - 25
d = c / 100
e = 160 * d
f = e * 0
g = b - f
h = g / 2
|
a ) 0 , b ) 191 , c ) 375 , d ) 875 , e ) 965 | b | divide(multiply(190, 191), const_4) | what is the sum of the integers from - 190 to 191 inclusive ? | "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 191 / 2 = 0.5 number of items ( n ) = b - a + 1 = 191 - ( - 190 ) + 1 = 195 + 191 = 382 . sum = average * n = 0.5 * 382 = 191 . answer is b" | a = 190 * 191
b = a / 4
|
a ) 2387 , b ) 2888 , c ) 9000 , d ) 2837 , e ) 2271 | c | add(9000, divide(multiply(16, 2), divide(3, const_3.0))) | 9000 + 16 2 / 3 % of ? = 10500 | "explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c" | a = 16 * 2
b = 3 / 3
c = a / b
d = 9000 + c
|
a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 100 % | c | multiply(subtract(divide(3, 2), const_1), const_100) | the ratio of the cost price and selling price is 2 : 3 . the profit percent is ? | let the c . p . = $ 2 x then s . p . = $ 3 x then , gain = 3 x - 2 x = $ x gain % = x / 2 x * 100 = 50 % answer is c | a = 3 / 2
b = a - 1
c = b * 100
|
a ) 3 / 10 , b ) 6 / 17 , c ) 9 / 25 , d ) 10 / 33 , e ) 12 / 35 | c | divide(multiply(divide(6, 10), const_100), multiply(divide(10, 6), const_100)) | 10 is 6 % of a , and 6 is 10 % of b . c equals b / a . what is the value of c ? | "6 a / 100 = 10 a = 500 / 3 b / 10 = 6 b = 60 c = b / a = 60 * 3 / 500 = 9 / 25 the answer is c ." | a = 6 / 10
b = a * 100
c = 10 / 6
d = c * 100
e = b / d
|
a ) 26 , b ) 28 , c ) 48 , d ) 26 , e ) 28 | c | multiply(multiply(const_pi, 4), 12) | the slant height of a cone is 12 cm and radius of the base is 4 cm , find the curved surface of the cone ? | "Ο * 12 * 4 = 48 answer : c" | a = math.pi * 4
b = a * 12
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(5, 2) | points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 5 cm , and bd = 6 cm , what is cd , in centimeters ? | putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 5 ( ac = 5 ) d - 8 ( bd = 6 ) cd is 8 - 5 = 3 . ans c | a = 5 - 2
|
a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24 | b | divide(subtract(100, 8), 3) | in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 8 and the other one , that is cheaper , costs $ 3 . the factory holds a $ 100 worth stock of 25 modules . how many of the modules in the stock are of the cheaper kind ? | "so the number of $ 3 modules must be 20 so that the leftover 5 modules are of $ 8 which will give a total value $ 100 . 20 * 3 + 5 * 8 = 60 + 40 = 100 . answer : b" | a = 100 - 8
b = a / 3
|
a ) a ) 8239 , b ) b ) 2900 , c ) c ) 1000 , d ) d ) 2393 , e ) e ) 2009 | c | multiply(multiply(subtract(4, 3), 500), 3) | a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is b ' s share ? | "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 500 = > x = 500 . b ' s share = rs . 2 x = 2 * 500 = rs . 1000 . answer : c" | a = 4 - 3
b = a * 500
c = b * 3
|
a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 19.1 , e ) e ) 24 | d | max(multiply(subtract(add(55, 10), const_1), subtract(divide(10, 20), divide(10, 55))), const_4) | due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 20 = 10 * 3 = 30 time difference = 19.1 ans : d" | a = 55 + 10
b = a - 1
c = 10 / 20
d = 10 / 55
e = c - d
f = b * e
g = max(f)
|
a ) 83.33 , b ) 210 , c ) 112 , d ) 120 , e ) 160 | b | multiply(divide(const_100, 10), 21) | a 21 % stock yielding 10 % is quoted at : | "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 21 , money invested = rs . ( 100 / 10 x 21 ) = rs . 210 . Γ’ Λ Β΄ market value of rs . 100 stock = rs . 210 answer b" | a = 100 / 10
b = a * 21
|
a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622 | e | subtract(859622, reminder(859622, 456)) | which no . need to add to 859622 to get a no . exactly divisible by 456 ? | dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 β 62 = 394 should be added to 859622 . e | a = 859622 - reminder
|
a ) 54 , b ) 432 , c ) 864 , d ) 2,916 , e ) 148,824 | c | multiply(multiply(4, subtract(4, const_1)), multiply(9, 4)) | right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 4 β€ x β€ 2 and 4 β€ y β€ 9 , then how many different triangles can be drawn that will meet these conditions ? | "we have the rectangle with dimensions 9 * 4 ( 9 horizontal dots and 4 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 4 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 3 c 1 , ( 4 - 1 = 3 as 1 vertical dot is already occupied by a ) . 9 c 1 * 4 c 1 * 8 c 1 * 3 c 1 = 864 . answer : c ." | a = 4 - 1
b = 4 * a
c = 9 * 4
d = b * c
|
a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | a | multiply(40, const_1) | at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ? | "well , first let β s take care of the β totals β . the numbers in the β totals β row must add up . if 90 are females , the other 250 β 90 = 160 must be males . similarly , the numbers in the β totals β column must add up . if 40 are managers , then the other 250 β 40 = 210 must be associates . now , in the β associate β row , 135 + e = 210 , which means e = 75 β the other 75 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the β female β column : b + 75 = 90 , which means b = 15 . there are fifteen female managers in this company . thus , the answer = ( a ) ." | a = 40 * 1
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a ) 15 % , b ) 12 % , c ) 8 % , d ) 7 % , e ) 5 % | b | multiply(divide(subtract(12005, 9800), subtract(multiply(9800, 8), multiply(5, 12005))), const_100) | a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is | "explanation : simple interest for 3 years = ( rs . 12005 - rs . 9800 ) = rs . 2205 simple interest for 5 years = 22053 Γ 5 = rs . 3675 principal ( p ) = ( rs . 9800 - rs . 3675 ) = rs . 6125 r = 100 Γ si / pt = 100 Γ 3675 / 6125 Γ 5 = 12 % answer : option b" | a = 12005 - 9800
b = 9800 * 8
c = 5 * 12005
d = b - c
e = a / d
f = e * 100
|
a ) 5 / 24 , b ) 6 / 24 , c ) 2 / 15 , d ) 8 / 24 , e ) 9 / 24 | c | subtract(divide(3, 5), divide(3, 15)) | if 3 / p = 5 & 3 / q = 15 then p - q = ? | "p = 3 / 5 , q = 3 / 15 = > q = 1 / 5 therefore p - q = ( 3 / 5 ) - ( 1 / 5 ) = 2 / 15 answer : c" | a = 3 / 5
b = 3 / 15
c = a - b
|
a ) rs . 120 , b ) rs . 60 , c ) rs . 128 , d ) rs . 130 , e ) rs . 140 | a | multiply(divide(96, 8), 10) | a invested some money in 8 % stock at 96 . if b wants to invest in an equally good 10 % stock , he must purchase a stock worth of : | "solution for an income of rs . 8 , investment = rs . 96 . for an income of rs . 10 , investment = rs . ( 96 / 8 x 10 ) = rs . 120 answer a" | a = 96 / 8
b = a * 10
|
a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 121 | e | floor(add(const_1, multiply(divide(log(2), log(const_10)), 400))) | how many digits 2 ^ 400 has ? | "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e" | a = math.log(2)
b = math.log(10)
c = a / b
d = c * 400
e = 1 + d
f = math.floor(e)
|
a ) 20 / 11 , b ) 16 / 11 , c ) 17 / 11 , d ) 10 / 11 , e ) 19 / 11 | d | divide(4, add(divide(40, const_100), 4)) | a committee is reviewing a total of 40 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ? | "say x = y = 10 . in this case we would have : 40 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 40 color films , thus total of 44 films were selected . color films thus compose 40 / 44 = 10 / 11 of the selected films . answer : d" | a = 40 / 100
b = a + 4
c = 4 / b
|
a ) 6 / 25 , b ) 5 / 16 , c ) 4 / 9 , d ) 3 / 7 , e ) 2 / 5 | e | inverse(add(divide(const_12, 8), const_1)) | a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ? | let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 8 ( 1 - x ) p 12 xp = 8 p - 8 xp 20 xp = 8 p x = 2 / 5 the answer is e . | a = 12 / 8
b = a + 1
c = 1/(b)
|
a ) 1211 , b ) 1231 , c ) 1251 , d ) 1271 , e ) 1291 | d | add(multiply(divide(add(50, 70), const_2), add(subtract(70, 50), const_1)), add(divide(subtract(70, 50), const_2), const_1)) | if x is equal to the sum of the integers from 50 to 70 , inclusive , and y is the number of even integers from 50 to 70 , inclusive , what is the value of x + y ? | "x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d ." | a = 50 + 70
b = a / 2
c = 70 - 50
d = c + 1
e = b * d
f = 70 - 50
g = f / 2
h = g + 1
i = e + h
|
a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14 | a | divide(add(12, subtract(power(12, const_2), multiply(36, const_4))), const_2) | 12 times a positive integer is more than its square by 36 , then the positive integer is | "explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a" | a = 12 ** 2
b = 36 * 4
c = a - b
d = 12 + c
e = d / 2
|
a ) 8 , b ) 12 , c ) 14 , d ) 15 , e ) 17 | a | inverse(subtract(divide(const_1, 4), divide(const_1, 8))) | renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ? | "renu Γ’ β¬ β’ s one day Γ’ β¬ β’ s work = 1 / 8 suma Γ’ β¬ β’ s one day Γ’ β¬ β’ s work = 1 / 4 - 1 / 8 = 1 / 8 suma can do it alone in 8 days . answer : a" | a = 1 / 4
b = 1 / 8
c = a - b
d = 1/(c)
|
a ) 0.34 , b ) 0.44 , c ) 0.54 , d ) 0.64 , e ) 0.74 | c | multiply(divide(90, multiply(multiply(const_5, const_5), const_4)), divide(60, multiply(multiply(const_5, const_5), const_4))) | 90 percent of the members of a study group are women , and 60 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ? | "say there are 100 people in that group , then there would be 0.9 * 0.60 * 100 = 54 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 54 / 100 . answer : c" | a = 5 * 5
b = a * 4
c = 90 / b
d = 5 * 5
e = d * 4
f = 60 / e
g = c * f
|
a ) 298 m , b ) 188 m , c ) 240 m , d ) 178 m , e ) 189 m | c | divide(12, subtract(divide(12, 10), 12)) | a train covers a distance of 12 km in 10 min . if it takes 12 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 12 = 240 m . answer : c" | a = 12 / 10
b = a - 12
c = 12 / b
|
a ) $ 1,292 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 12,917 , e ) $ 20,796 | a | power(const_2, divide(log(divide(add(add(4, 9), const_100), const_100)), const_12)) | a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 310000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ? | 0.04 x + 0.09 y = 310000 [ 1 ] 0.04 x = 0.80 * 310000 = 248000 [ 2 ] 248000 + 0.09 y = 310000 - - > 0.09 y = 62000 [ 3 ] 248000 / 12 = 258333.3333 [ 4 ] 62000 / 12 = 5166.67 [ 5 ] adding [ 4,5 ] we get : 25833 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.292 , ans a | a = 4 + 9
b = a + 100
c = b / 100
d = math.log(c)
e = d / 12
f = 2 ** e
|
a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400 | e | multiply(5000, divide(1600, add(5000, 15000))) | x and y started a business by investing rs . 5000 / - and rs . 15000 / - respectively . find the x β s share out of a total profit of rs . 1600 : | x = rs . 5000 / - y = rs . 15000 / - x share 1 part & y share 3 parts total 4 parts - - - - - > rs . 1600 / - - - - - > 1 part - - - - - - - > rs . 400 / - x share = 1 part - - - - - > rs . 400 / - e | a = 5000 + 15000
b = 1600 / a
c = 5000 * b
|
a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000 | b | divide(multiply(multiply(add(const_2, const_3), const_1000), 8), const_2) | if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 48 / r years . if pat ' s parents invested $ 5,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ? | "since investment doubles in 48 / r years , then for r = 8 it ' ll double in 48 / 8 = ~ 6 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 3 = $ 15,000 . answer : b ." | a = 2 + 3
b = a * 1000
c = b * 8
d = c / 2
|
a ) 11 , b ) 17 , c ) 16 , d ) 13 , e ) 12 | a | add(divide(subtract(89, 9), 7), const_1) | how many multiples of 7 are there between 9 and 89 , 9 and 89 inclusive ? | "7 multiples are . . . 14 , 21,28 , 35,42 , 49,56 , 63,70 , 77,84 , . . . , . . . , the answer is = 11 answer is a" | a = 89 - 9
b = a / 7
c = b + 1
|
a ) 8 rs . , b ) 7 rs . , c ) 6 rs . , d ) 4 rs . , e ) 5 rs . | c | divide(90, multiply(const_3, 5)) | 5 men are equal to as many women as are equal to 7 boys . all of them earn rs . 90 only . men β s wages are ? | 5 m = xw = 7 b 5 m + xw + 7 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : c | a = 3 * 5
b = 90 / a
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a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(100, reminder(5, 7)) | when positive integer n is divided by 4 , the remainder is 2 . when n is divided by 7 , the remainder is 5 . how many values less than 100 can n take ? | "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 3 . . c" | a = 100 - reminder
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a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 2 , e ) 4 / 7 | d | divide(divide(16, 15), divide(8, 15)) | if p ( a ) = 8 / 15 , p ( b ) = 4 / 15 , and p ( a Γ’ Λ Βͺ b ) = 16 / 15 find p ( b | a ) | "p ( b | a ) = p ( a Γ’ Λ Βͺ b ) / p ( a ) p ( b | a ) = ( 16 / 15 ) / ( 8 / 15 ) = 2 . d" | a = 16 / 15
b = 8 / 15
c = a / b
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a ) 89 kmph , b ) 92 kmph , c ) 75 kmph , d ) 65 kmph , e ) 66 kmph | e | divide(add(90, 42), const_2) | the speed of a car is 90 km in the first hour and 42 km in the second hour . what is the average speed of the car ? | "s = ( 90 + 42 ) / 2 = 66 kmph e" | a = 90 + 42
b = a / 2
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a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2 | c | subtract(divide(divide(48, const_1), const_3), const_3) | in how many ways can the integer 48 be expressed as a product of two different positive integers ? | "method 1 : listing all multiples since given number is small 48 = 1 * 48 , 2 * 24 , 3 * 16 , 4 * 12 , 6 * 8 = > 5 ways method 2 : express given number as prime factors 48 = 6 * 8 = 2 * 3 * 2 ^ 3 = 2 ^ 4 * 3 total number of factors = ( 4 + 1 ) ( 1 + 1 ) = 5 * 2 = 10 since the given number is not a perfect square , there will be exact 5 pairs possible of the given 10 factors = > 5 ways option c" | a = 48 / 1
b = a / 3
c = b - 3
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a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 % | e | multiply(divide(subtract(multiply(subtract(const_1, divide(46, const_100)), const_100), subtract(subtract(const_100, 40), multiply(divide(40, const_100), subtract(const_100, 40)))), subtract(subtract(const_100, 40), multiply(divide(40, const_100), subtract(const_100, 40)))), const_100) | if w is 40 percent less than x , x is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ? | given w = 0.6 x , x = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer . | a = 46 / 100
b = 1 - a
c = b * 100
d = 100 - 40
e = 40 / 100
f = 100 - 40
g = e * f
h = d - g
i = c - h
j = 100 - 40
k = 40 / 100
l = 100 - 40
m = k * l
n = j - m
o = i / n
p = o * 100
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a ) 2 hr 30 min , b ) 2 hr , c ) 4 hr , d ) 1 hr 15 min , e ) none of these | a | divide(5, divide(add(multiply(divide(1, 20), const_60), divide(2, 2)), const_2)) | a boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes . how long will it take to go 5 km in stationary water ? | "explanation : speed upstream = 2 / 2 = 1 km / hr speed downstream = 1 / ( ( 20 / 60 ) ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 5 km in still water = 5 / 2 = 2 ( 1 / 2 ) hours = 2 hour 30 minutes . answer : option a" | a = 1 / 20
b = a * const_60
c = 2 / 2
d = b + c
e = d / 2
f = 5 / e
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a ) s . 9621 , b ) s . 6921 , c ) s . 10210 , d ) s . 6261 , e ) s . 6361 | c | multiply(8000, power(add(const_1, divide(5, const_100)), 5)) | the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 5 years is | "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 5 = rs 10210 answer : c" | a = 5 / 100
b = 1 + a
c = b ** 5
d = 8000 * c
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a ) 30 , b ) 27 , c ) 35 , d ) 33 , e ) 37 | a | multiply(divide(140, 14), 3) | pencils , pens and exercise books in a shop are in the ratio of 14 : 4 : 3 . if there are 140 pencils , the number of exercise books in the shop is : | explanation : let pencils = 14 x , pens = 4 x & exercise books = 3 x . now , 14 x = 140 hence x = 10 number of exercise books = 3 x = 30 answer : a | a = 140 / 14
b = a * 3
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a ) 240 meters , b ) 360 meters , c ) 280 meters , d ) 600 meters , e ) can not be determined | c | subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 16)) | a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds . what is the length of the platform in meters ? | "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 16 * 20 = 320 = length of train length of platform = 600 - 320 = 280 answer : c" | a = 72 * 1000
b = a / 3600
c = b * 30
d = 72 * 1000
e = d / 3600
f = e * 16
g = c - f
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a ) 2 , b ) can not be determined , c ) 4 , d ) 6 , e ) 10 | b | subtract(10050, 10000) | in a quiz the points in each round for the first , second , third and fourth position were 10050 , 2010 . no other points were given . rachel participated in several rounds in the competition and the product of her score was 10000 . in how many rounds did she participate ? | correct answer is b because we are given that there wo n ' t be any points awarded for rounds other than 1 st four position . thus , it may happen that she played 150 rounds out of only 8 rounds were there in which she was awarded some points . | a = 10050 - 10000
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | divide(factorial(subtract(add(const_4, 2), const_1)), multiply(factorial(2), factorial(subtract(const_4, const_1)))) | how many positive integers less than 50 have a reminder 2 when divided by 7 ? | "take the multiples of 7 and add 2 0 x 7 + 2 = 2 . . . . 6 x 7 + 2 = 44 there are 7 numbers answer e" | a = 4 + 2
b = a - 1
c = math.factorial(b)
d = math.factorial(2)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
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a ) 13 , b ) 16 , c ) 34 , d ) 43 , e ) 42 | b | sqrt(divide(multiply(square_area(8), 2), inverse(const_2))) | the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the area of the field . what is the length of the field ? | "explanation : a / 2 = 8 * 8 = > a = 8 * 8 * 2 x * 2 x = 8 * 8 * 2 x = 8 = > 2 x = 16 answer : option b" | a = square_area * (
b = a / 2
c = 1/(2)
d = math.sqrt(b)
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a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | b | add(subtract(subtract(const_1000, const_10), multiply(multiply(const_10, multiply(78, 78)), multiply(const_4, const_2))), const_10) | how many three digit numbers n are divisible by 78 or 91 ? | "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b" | a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
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a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10 | c | divide(add(11, 5), const_2) | in one hour , a boat goes 11 km along the stream and 5 km against the stream . the sped of the boat in still water ( in km / hr ) is : | "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 kmph . answer c" | a = 11 + 5
b = a / 2
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a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 . | a | divide(subtract(5, const_1), const_2) | arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 5 from the product of their ages a year from today . what is their age today ? | "ad = ( a + 1 ) ( d + 1 ) - 5 0 = a + d - 4 a + d = 4 a = d ( as they are twin brothers ) a = d = 2 a is the answer" | a = 5 - 1
b = a / 2
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a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 180 sec , e ) 168 sec | d | divide(900, subtract(multiply(54, const_0_2778), multiply(36, const_0_2778))) | a and b go around a circular track of length 900 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ? | "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 900 / ( 36 * 5 / 18 ) , 900 / ( 54 * 5 / 18 ) } = lcm ( 90 , 60 ) = 180 sec . answer : d" | a = 54 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 900 / c
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a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days | e | multiply(const_3, 12) | working together , jose and jane can complete an assigned task in 12 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 48 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose | assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 12 12 ( x + y ) = xy next , we ' re told 1 job takes 48 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 48 x + y = 96 so xy = 1152 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 36 days for jose and 32 days for jane . answer : e | a = 3 * 12
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a ) 120 , b ) 130 , c ) 150 , d ) 180 , e ) 250 | d | divide(multiply(divide(15, multiply(multiply(divide(const_1, const_4), divide(const_1, const_3)), divide(const_2, add(const_2, const_3)))), 40), const_100) | one fourth of one third of two fifth of a number is 15 . what will be the 40 % of that number is ? | "( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer d" | a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3
e = 2 / d
f = c * e
g = 15 / f
h = g * 40
i = h / 100
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a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | b | multiply(divide(22, add(4, 7)), 4) | the ages of ashley and mary are in the ratio 4 : 7 . the sum of their ages is 22 . find the ages of ashley . | a : m = 4 : 7 let the ages of a & m be x & 22 - x x / 22 - x = 4 / 7 x = 8 a = 8 yrs answer : b | a = 4 + 7
b = 22 / a
c = b * 4
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a ) 20 sec , b ) 12 sec , c ) 30 sec , d ) 50 sec , e ) 1 min | b | divide(180, add(8, 7)) | two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 180 meters , after what time will they meet at the starting point ? | "they meet every 180 / 7 + 8 = 12 sec answer is b" | a = 8 + 7
b = 180 / a
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a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 30 minutes , e ) 40 minutes | d | multiply(add(const_3, 6), 5) | a clock shows the time as 12 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ? | "there are 6 hours in between 12 a . m . to 6 p . m . 6 * 5 = 30 minutes . answer : d" | a = 3 + 6
b = a * 5
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a ) 3944 , b ) 2882 , c ) 2999 , d ) 2667 , e ) 1392 | e | multiply(square_perimeter(sqrt(36)), 58) | what will be the cost of building a fence around a square plot with area equal to 36 sq ft , if the price per foot of building the fence is rs . 58 ? | "let the side of the square plot be a ft . a 2 = 36 = > a = 6 length of the fence = perimeter of the plot = 4 a = 24 ft . cost of building the fence = 24 * 58 = rs . 1392 . answer : e" | a = math.sqrt(36)
b = square_perimeter * (
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a ) $ 1000 , b ) $ 2000 , c ) $ 1800 , d ) $ 1500 , e ) $ 1600 | c | multiply(divide(4, add(add(2, 4), 5)), 4500) | a person want to give his money of $ 4500 to his 4 children a , b , c , d in the ratio 2 : 4 : 5 : 4 . what is the a + b share ? | "a ' s share = 4500 * 2 / 15 = $ 600 b ' s share = 4500 * 4 / 15 = $ 1200 a + b = $ 1800 answer is c" | a = 2 + 4
b = a + 5
c = 4 / b
d = c * 4500
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a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700 | a | multiply(divide(351, divide(add(const_100, 30), const_100)), 2) | if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y = | "before price increase price = y after 30 % price increase price = y + ( 30 / 100 ) * y = 1.3 y = 351 ( given ) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a" | a = 100 + 30
b = a / 100
c = 351 / b
d = c * 2
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a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48 | b | multiply(subtract(multiply(divide(subtract(const_100, 22), const_100), divide(add(const_100, 86), const_100)), const_1), const_100) | if price of t . v set is reduced by 22 % , then its sale increases by 86 % , find net effect on sale value | "- a + b + ( ( - a ) ( b ) / 100 ) = - 22 + 86 + ( - 22 * 86 ) / 100 = - 22 + 86 - 19 = 45 answer : b" | a = 100 - 22
b = a / 100
c = 100 + 86
d = c / 100
e = b * d
f = e - 1
g = f * 100
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a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36 | a | subtract(add(floor(divide(76, const_3)), floor(divide(76, add(const_1, const_4)))), multiply(floor(divide(76, multiply(const_3, add(const_1, const_4)))), const_2)) | there are 76 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ? | "editing my solution : number of switches = 76 number of switches turned on by a : 3 , 6 , . . . 75 = 25 number of switches turned on by b : 5 , 10 , . . . . 75 = 15 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 25 - 6 ) + ( 15 - 6 ) = 28 answer : a" | a = 76 / 3
b = math.floor(a)
c = 1 + 4
d = 76 / c
e = math.floor(d)
f = b + e
g = 1 + 4
h = 3 * g
i = 76 / h
j = math.floor(i)
k = j * 2
l = f - k
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a ) $ 2400 , b ) $ 3300 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600 | b | multiply(multiply(const_100, add(const_3, const_2)), divide(99, subtract(const_100, add(add(30, 20), 35)))) | each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 99 dollar , which she typically uses for gifts and charitable causes . what is jill β s net monthly salary ? | "let x be the monthly salary 15 % of 1 / 5 * x = 99 x = 3300 answer b" | a = 3 + 2
b = 100 * a
c = 30 + 20
d = c + 35
e = 100 - d
f = 99 / e
g = b * f
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['a ) 32', 'b ) 36.5', 'c ) 38.5', 'd ) 39', 'e ) 39.5'] | c | divide(circle_area(7), const_4) | a goat is tied to one corner of a square plot of side 12 m by a rope 7 m long . find the area it can graze ? | area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1 / 4 part , the goat can graze ) where r = 7 m = length of rope so area = ( 22 / 7 ) * 7 * 7 / 4 = 38.5 sq m answer : c | a = circle_area / (
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | subtract(multiply(divide(24, divide(add(100, 60), 100)), const_2), 24) | a retailer bought a hat at wholesale and marked it up 60 % to its initial price of $ 24 . by how many more dollars does he need to increase the price to achieve a 100 % markup ? | "let x be the wholesale price . then 1.6 x = 24 and x = 24 / 1.6 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 6 more . the answer is d ." | a = 100 + 60
b = a / 100
c = 24 / b
d = c * 2
e = d - 24
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a ) 0.7 , b ) 0.07 , c ) 0.007 , d ) 7 , e ) none of these | b | power(divide(divide(000343, const_1000), const_1000), divide(const_1, const_3)) | the cube root of . 000343 is | "explanation : ( . 000343 ) 1 / 3 = ( 343 / 106 ) 1 / 3 = ( 7 * 7 * 7 / 102 * 102 * 102 ) 1 / 3 = 7 / 102 = 7 / 100 = 0.07 answer b" | a = 343 / 1000
b = a / 1000
c = 1 / 3
d = b ** c
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a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6 | d | divide(divide(multiply(200, multiply(15, const_2)), const_1000), divide(15, const_10)) | a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 200 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ? | "the distance between the nest and the ditch is 200 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 200 = 6000 . d = st 6000 / 1.5 = t , i think we can take 6000 meters as 6 km , then only we get t = 4 . ( 1000 meters = 1 km ) d )" | a = 15 * 2
b = 200 * a
c = b / 1000
d = 15 / 10
e = c / d
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a ) a ) 148 , b ) b ) 210 , c ) c ) 63 , d ) d ) 248 , e ) e ) 258 | c | divide(multiply(divide(30, const_100), divide(12, subtract(divide(3, add(const_3, const_4)), divide(40, const_100)))), const_2) | 3 seventh of a number is 12 more than 40 % of that number . what will be the 30 % of that number ? | 3 / 7 x β 40 / 100 x = 12 x = 35 * 12 35 * 12 * 30 / 100 = 126 / 2 = 63 answer : c | a = 30 / 100
b = 3 + 4
c = 3 / b
d = 40 / 100
e = c - d
f = 12 / e
g = a * f
h = g / 2
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a ) 296 , b ) 252 , c ) 344 , d ) 388 , e ) none of these | c | add(power(add(4, const_10), const_2), multiply(const_12, const_12)) | the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ? | let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c | a = 4 + 10
b = a ** 2
c = 12 * 12
d = b + c
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a ) 90 , b ) 98 , c ) 60 , d ) 88 , e ) 12 | a | divide(multiply(multiply(divide(add(150, 150), multiply(8, add(const_1, const_2))), const_2), const_3600), const_1000) | two trains , each 150 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ? | "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 150 + 150 ) / 8 = 3 x = > x = 25 / 2 . so , speed of the faster train = 50 / 2 = 25 * 18 / 5 = 90 km / hr . answer : a" | a = 150 + 150
b = 1 + 2
c = 8 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
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a ) 30 km , b ) 40 km , c ) 70 km , d ) 80 km , e ) 90 km | c | multiply(35, multiply(divide(40, gcd(40, 35)), divide(15, const_60))) | with an average speed of 40 km / hr a car reaches its destination on time . if it goes with an average speed of 35 km / h , it is late by 15 minutes . the total journey is ? | let the total journey be x km . x / 35 - x / 40 = 15 / 60 solving for x , we get x = 70 therefore , total journey = 70 km . answer : c | a = math.gcd(40, 35)
b = 40 / a
c = 15 / const_60
d = b * c
e = 35 * d
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a ) 12 , b ) 1 , c ) 1728 , d ) 1717 , e ) 4 | d | subtract(1729, 12) | find the remainder q when 12 ^ 190 is divided by 1729 ? | 12 ^ ( 190 ) can be written as . ( ( 12 ^ 3 ) ^ 63 ) * 12 . 12 ^ 3 when divided by 1729 gives a remainder q - 1 . so in the numerator we have - 12 . now acccording to remainder theorm the answer will be 1729 - 12 = 1717 . d | a = 1729 - 12
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a ) 18 , b ) 99 , c ) 22 , d ) 26 , e ) 71 | c | subtract(divide(multiply(70, 100), const_100), divide(multiply(60, 80), const_100)) | how much 70 % of 100 is greater than 60 % of 80 ? | "( 70 / 100 ) * 100 β ( 60 / 100 ) * 80 70 - 48 = 22 answer : c" | a = 70 * 100
b = a / 100
c = 60 * 80
d = c / 100
e = b - d
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a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8 | e | divide(subtract(10, const_2), 10) | the main line train starts at 5.00 am and the harbor line train starts at 5.02 am . each train has the frequency of 10 minutes . if a guy goes in the morning at a random time what is the probability of he getting main line train ? | out of 10 minutes there is only 2 minutes chance of getting harbour line train and there is 8 minutes chance for getting main line train . so , probability = 8 / 10 = 0.8 answer : e | a = 10 - 2
b = a / 10
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a ) 20 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none | a | multiply(subtract(subtract(add(const_1, divide(60, const_100)), multiply(add(const_1, divide(60, const_100)), divide(25, const_100))), const_1), const_100) | an uneducated retailer marks all his goods at 60 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ? | "sol . let c . p . = rs . 100 . then , marked price = rs . 160 . s . p . = 75 % of rs . 160 = rs . 120 . β΄ gain % = 20 % . answer a" | a = 60 / 100
b = 1 + a
c = 60 / 100
d = 1 + c
e = 25 / 100
f = d * e
g = b - f
h = g - 1
i = h * 100
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a ) 253 mph . , b ) 275 mph . , c ) 296 mph . , d ) 278 mph . , e ) 235 mph . | a | divide(add(multiply(350, 23), multiply(420, 23)), subtract(420, 350)) | a plane flies 420 miles with the wind and 350 miles against the wind in the same length of time . if the speed of the wind is 23 mph , what is the speed of the plain in still air ? | the speed of the plane in still air = x miles / hour the speed of the wind is 23 mph speed with the wind = ( x + 23 ) mph speed against the wind = ( x β 23 ) mph time = distance / speed according to the problem , 420 / ( x + 23 ) = 350 / ( x β 23 ) 420 ( x β 23 ) = 350 ( x + 23 ) 420 x β 9660 = 350 x + 805 420 x β 350 x = 8050 + 9660 70 x = 17710 x = 17710 / 70 x = 253 therefore , the speed of the plane in still air = 253 mph . correct answer a | a = 350 * 23
b = 420 * 23
c = a + b
d = 420 - 350
e = c / d
|
a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000 | e | divide(subtract(divide(multiply(80000, 20), const_100), 9000), divide(10, const_100)) | rs 80000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 9000 find money given by 10 % ? | "let first parrt is x and second part is y then x + y = 80000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 9000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 90000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 90000 = 80000 + y so y = 10000 then x = 80000 - 10000 = 70000 first part = 70000 answer : e" | a = 80000 * 20
b = a / 100
c = b - 9000
d = 10 / 100
e = c / d
|
a ) 450 , b ) 465.12 , c ) 475 , d ) 500.15 , e ) 200 | b | divide(multiply(50, 4), divide(43, const_100)) | at the end of year x , automobile installment credit accounted for 43 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 50 billion of credit , or 1 / 4 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ? | system of equations a = ( 43 / 100 ) c ( 1 / 4 ) a = 50 - - > a = 200 substitution 200 = ( 43 / 100 ) c c = ( 100 / 43 ) 200 calculate 200 / 43 * 100 - the the correct answer is 465.12 . the correct answer is b . | a = 50 * 4
b = 43 / 100
c = a / b
|
a ) 12 , b ) 6 , c ) 8 , d ) 18 , e ) 33 | b | lcm(1, 3) | what is the lowest positive integer that is divisible by 1 through 3 , inclusive ? | "the integer should be divisible by : 1 , 2 , and 3 . the least common multiple of these integers is lcm = 1 * 2 * 3 = 6 answer : b" | a = math.lcm(1, 3)
|
a ) 1680 , b ) 1420 , c ) 1120 , d ) 970 , e ) 740 | b | divide(add(subtract(1.85, divide(65, 100)), multiply(divide(divide(10, 100), 100), 250)), divide(divide(10, 100), 100)) | a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.85 ? | "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.85 - $ 0.65 = $ 1.20 the charge for the next 1100 grams is $ 1.10 which leaves a charge of $ 0.10 the weight is somewhere between 1350 and 1450 . the answer is b ." | a = 65 / 100
b = 1 - 85
c = 10 / 100
d = c / 100
e = d * 250
f = b + e
g = 10 / 100
h = g / 100
i = f / h
|
a ) 14 , b ) 12 , c ) 10 , d ) 8 , e ) 7.5 | e | floor(divide(60, add(4, const_1))) | during a certain two - week period , 60 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ? | "total movies = 100 . comedies = 60 . action + drama = 40 . since there were 5 times as many dramas as action movies , then action + 4 * action = 40 - - > action = a = 8 . comedies = 60 = 7.5 a . answer : e" | a = 4 + 1
b = 60 / a
c = math.floor(b)
|
a ) rs 8.81 , b ) rs 9.81 , c ) rs 10.81 , d ) rs 11.81 , e ) none of these | d | divide(multiply(9, add(const_100, 5)), subtract(const_100, 20)) | a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % | "explanation : 85 : 9 = 105 : x x = ( 9 Γ 105 / 85 ) = rs 11.81 option d" | a = 100 + 5
b = 9 * a
c = 100 - 20
d = b / c
|
a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 9 | b | multiply(const_2, const_2) | if 21 / 22 = 0 . 95.45 , what is the 57 th digit to the right of the decimal point of the fraction ? | we are not concerned what 21 / 22 means . . we have to look at the decimal . . 0.9544 means 0.95454545 . . . . so leaving first digit to the right of decimal , all odd numbered digits are 4 and all even numbered are 5 . . here 57 is odd , so ans is 4 answer is b | a = 2 * 2
|
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10 | d | add(add(const_2, add(const_1, const_4)), const_2) | an army β s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 20000 people who applied for the army and 196 were finally selected , what was the value of n ? | "step ( 1 ) 8000 accepted . step ( 2 ) another 40 % of 8000 = 3200 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 3200 = 1600 step ( 4 ) 50 % of 1600 = 800 step ( 5 ) 50 % of 800 = 400 step ( 6 ) 50 % of 400 = 200 70 % of 400 = 280 and last step of accepting 70 % of 280 = 196 ( our target ) total 8 steps required . ans d" | a = 1 + 4
b = 2 + a
c = b + 2
|
a ) 128 , b ) 91 , c ) 89 , d ) 61 , e ) 60 | c | add(divide(subtract(500, 50), 5), const_1) | how many multiples of 5 are there between 50 and 500 ? | "it should be mentioned whether 50 and 500 are inclusive . if 50 and 500 are inclusive , then the answer is ( 500 - 50 ) / 5 + 1 = 91 . if 50 and 500 are not inclusive , then the answer is ( 495 - 55 ) / 5 + 1 = 89 . since oa is c , then we have not inclusive case ." | a = 500 - 50
b = a / 5
c = b + 1
|
a ) 15 a . m , b ) 10 a . m , c ) 7 a . m , d ) 02 a . m , e ) 05 a . m | c | add(8, divide(subtract(110, 20), add(25, 20))) | two stations a and b are 110 km apart on a straight line . one train starts from a at 4 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ? | "suppose they meet x hours after 4 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 7 a . m . answer : c" | a = 110 - 20
b = 25 + 20
c = a / b
d = 8 + c
|
['a ) 4 m', 'b ) 5 m', 'c ) 6 m', 'd ) 7 m', 'e ) 8 m'] | a | power(divide(16128, multiply(multiply(6, 7), 6)), divide(const_1, const_3)) | the height of the wall is 6 times its width and lenght of the wall is 7 times its height . if the volume of the wall be 16128 cu . m . its width is | explanation : let width = x then , height = 6 x and length = 42 x 42 x Γ 6 x Γ x = 16128 x = 4 answer : a | a = 6 * 7
b = a * 6
c = 16128 / b
d = 1 / 3
e = c ** d
|
a ) 200 , b ) 1000 , c ) 2500 , d ) 3140 , e ) 3200 | c | add(divide(divide(100, divide(divide(divide(divide(divide(100, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(100, divide(divide(divide(divide(divide(100, const_2), const_2), const_2), const_2), const_2)), const_2)))) | find the sum of all odd numbers upto 100 . | "sol . the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 . ο required sum = ( n / 2 ) ( first term + last term ) = 50 ( 1 + 99 ) / 2 = 2500 . answer c 2500" | a = 100 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 100 / e
g = f / 2
h = 100 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 100 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o
q = g + p
|
a ) 10.30 , b ) 10 , c ) 8.45 , d ) 9.3 , e ) 11 | b | add(divide(add(110, 25), add(20, 25)), 7) | two stations p and q are 110 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ? | "explanation : assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 110 = > 20 x + 25 ( x - 1 ) = 110 = > 45 x = 135 = > x = 3 means , they meet after 3 hours after 7 am , ie , they meet at 10 am . answer : b" | a = 110 + 25
b = 20 + 25
c = a / b
d = c + 7
|
a ) 20 % , b ) 15 % , c ) 33.33 % , d ) 18 % , e ) none of these | b | multiply(divide(subtract(multiply(add(add(add(20, 5), const_10), add(divide(5, const_2), const_3)), 18), multiply(10, 18)), multiply(10, 18)), const_100) | a milk man has 10 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : | "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 10 liters of milk . therefore , profit percentage = 15 % . answer : b" | a = 20 + 5
b = a + 10
c = 5 / 2
d = c + 3
e = b + d
f = e * 18
g = 10 * 18
h = f - g
i = 10 * 18
j = h / i
k = j * 100
|
a ) 13.3 , b ) 10.8 , c ) 10.7 , d ) 11.4 , e ) 12.5 | a | add(10, subtract(9, multiply(divide(8, 7), 5))) | if * stands for / , / stands for - , + stands for * and - stands for + , then 9 / 8 * 7 + 5 - 10 = ? | 9 / 8 * 7 + 5 - 10 this expression becomes 9 - 8 / 7 * 5 + 10 after exchanging the symbols then the values for it would be 9 - 1.142 * 5 + 10 = 13.290 ( app ) = 13.3 answer : a | a = 8 / 7
b = a * 5
c = 9 - b
d = 10 + c
|
a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 152 | c | divide(multiply(12, 396), 36) | hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 36 , then the other number is ? | "12 * 396 = 36 * x x = 132 answer : c" | a = 12 * 396
b = a / 36
|
a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9 | b | floor(divide(reminder(power(36, reminder(30, add(const_4, const_1))), const_100), const_10)) | what is the tens digit of 36 ^ 30 ? | "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 30 ( dont actually calculate full values ) and answer is b : 7" | a = 4 + 1
b = 36 ** reminder
c = reminder / (
d = math.floor(c, 100)
|
a ) 1692 , b ) 1792 , c ) 1795 , d ) 1892 , e ) 1992 | b | add(add(add(const_1000, multiply(divide(divide(126, subtract(19, const_10)), 2), const_100)), multiply(subtract(19, const_10), const_10)), 2) | a 4 digit number is such that the product of all of its digits is 126 . the sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit ( 1000 digit in tens place & 10 digit in units place ) which in turn is equal to 19 . then difference of units and 1000 place of the number is , given that this difference is positive . | the number is 1792 . let the number be represented as 1000 x + 100 y + 10 z + t acc to ques , xyzt = 126 x + y + z + t = 10 x + z = 19 so , number in thousands and tens place are 1 and 9 respectively . the remaining factor is 14 which is 7 * 2 so the number is 1792 . answer : b | a = 19 - 10
b = 126 / a
c = b / 2
d = c * 100
e = 1000 + d
f = 19 - 10
g = f * 10
h = e + g
i = h + 2
|
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