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a ) - 11 , b ) β 12 , c ) 11 , d ) 12 , e ) 10 | c | add(add(4, 3), subtract(subtract(8, 3), 1)) | simplify : ( 4 + 3 ) + ( 8 - 3 - 1 ) | solution : ( 4 + 3 ) + ( 8 - 3 - 1 ) = 7 + ( 8 - 3 - 1 ) = 7 + 8 - 3 - 1 = 15 - 1 = 11 answer : ( c ) | a = 4 + 3
b = 8 - 3
c = b - 1
d = a + c
|
a ) 140 , b ) 272 , c ) 278 , d ) 277 , e ) 112 | a | multiply(divide(multiply(56, const_1000), const_3600), 9) | a train running at the speed of 56 km / hr crosses a pole in 9 seconds . find the length of the train ? | "speed = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec length of train ( distance ) = speed * time ( 140 / 9 ) * 9 = 140 meter answer : a" | a = 56 * 1000
b = a / 3600
c = b * 9
|
a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 90000 | e | multiply(multiply(multiply(multiply(9, const_10), const_10), const_10), const_10) | how many 9 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 123454321 . | take the task of building palindromes and break it intostages . stage 1 : select the 9 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 8 th , 7 th , 6 th , 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 9 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 90000 ways ) answer : e | a = 9 * 10
b = a * 10
c = b * 10
d = c * 10
|
a ) 20 % , b ) 40 % , c ) 66.67 % , d ) 80 % , e ) 100 % | c | subtract(const_100, divide(subtract(const_100, 60), add(const_1, divide(20, const_100)))) | when sold at a 60 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ? | "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 40 or x = 33.33 . . . marked price was 100 so . . . so answer is 66.67 % . . c" | a = 100 - 60
b = 20 / 100
c = 1 + b
d = a / c
e = 100 - d
|
a ) rs . 28,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these | a | 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))) | jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 56,000 after completion of one year . what will be madhu ' s share of profit ? | "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 56,000 i . e . rs . 28,000 answer : a" | a = 4 * 2
b = 2 + 3
c = b * 2
d = a * c
e = d * 100
f = 2 + 3
g = f * 100
h = g * 100
i = e + h
j = 2 + 3
k = j * 2
l = k / 2
m = 4 * 3
n = l / m
o = i * n
|
a ) 4.7 kmph , b ) 3.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph | b | add(divide(1, divide(add(const_60, 48), const_60)), 3) | a start walking from a place at a uniform speed of 3 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b . | "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 3 + 5 / 9 = 3.55 answer b" | a = const_60 + 48
b = a / const_60
c = 1 / b
d = c + 3
|
a ) s . 150 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60 | a | multiply(600, divide(25, const_100)) | find the 25 % of rs . 600 . | "explanation : 25 % of 600 = > 25 / 100 * 600 = rs . 150 answer : a" | a = 25 / 100
b = 600 * a
|
a ) 10.7 % , b ) 19 % , c ) 18 % , d ) 14 % , e ) 16 % | a | multiply(divide(subtract(60900, add(42000, 13000)), add(42000, 13000)), const_100) | ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 60900 . what is his profit percent ? | "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 60900 profit ( % ) = ( 60900 - 55000 ) / 55000 * 100 = 10.7 % answer : a" | a = 42000 + 13000
b = 60900 - a
c = 42000 + 13000
d = b / c
e = d * 100
|
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | divide(divide(10, const_2), const_2) | an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 10 - meter platform and caught it after it had traveled 29.65 meters . how many times did the ball bounce ? | "ans : 6 division of total diatance travelled will be 10 + 10 + 5 + 2.5 + 1.25 + 0.6 + 0.3 ans b" | a = 10 / 2
b = a / 2
|
a ) 2 : 1 , b ) 3 : 1 , c ) 4 : 1 , d ) 6 : 1 , e ) 8 : 1 | c | multiply(2, 2) | if the length of the sides of two cubes are in the ratio 2 : 1 , what is the ratio of their total surface area ? | "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 2 x ) ^ 2 = 24 x ^ 2 . the ratio of surface areas is 4 : 1 . the answer is c ." | a = 2 * 2
|
a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55 | a | divide(multiply(choose(5, 3), choose(5, 4)), 5) | a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ? | "there 3 questions in part a out of which 4 question can be chosen as = 5 c 3 . similarly , 5 questions can be chosen from 10 questions of part b as = 5 c 4 . hence , total number of ways , = 5 c 3 * 5 c 4 = [ 5 ! / ( 2 ! 3 ! ) ] * [ 5 ! / ( 4 ! * 1 ) ] = { 10 } * { 5 * 4 ! / ( 4 ! ) } = 10 * 5 = 50 . a" | a = math.comb(5, 3)
b = math.comb(5, 4)
c = a * b
d = c / 5
|
a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3150 km | e | multiply(30, 42) | a walks at 30 kmph and 30 hours after his start , b cycles after him at 42 kmph . how far from the start does b catch up with a ? | "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 42 = 30 x = 3150 km answer is e" | a = 30 * 42
|
a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph | d | divide(subtract(12, 8), const_2) | what is the speed of the stream if a canoe rows upstream at 8 km / hr and downstream at 12 km / hr | "sol . speed of stream = 1 / 2 ( 12 - 8 ) kmph = 2 kmph . answer d" | a = 12 - 8
b = a / 2
|
['a ) 6.67 %', 'b ) 12.5 %', 'c ) 18.75 %', 'd ) 25 %', 'e ) 31.25 %'] | e | subtract(subtract(multiply(multiply(divide(circumface(150), 150), const_3), const_2), const_4), const_2) | obra drove 150 Ο meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 Ο square meters , what percentage of the circular track did obra drive ? | area enclosed by the circular track on which she drove is 57,600 Ο square meters so , Ο ( r ^ 2 ) = 57,600 Ο - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 Ο r = 480 Ο therefore , part of circumference covered = 150 Ο / 480 Ο = 31.25 % hence , answer is e . | a = circumface / (
b = a * 150
c = b * 3
d = c - 2
e = d - 4
|
a ) 600 , b ) 610 , c ) 500 , d ) 520 , e ) 720 | b | multiply(305, const_2) | on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 305 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ? | "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 305 ) = 2 + 2 ( extra ) = > 2 x - 610 = x = > x = 610 . answer : b" | a = 305 * 2
|
a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000 | d | subtract(divide(negate(subtract(multiply(20, 8), multiply(30, 8))), divide(10, const_100)), subtract(multiply(20, 8), multiply(30, 8))) | at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 10 percent . what was the store ' s actual revenue from corsages that day ? | "let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 8 ) + 30 ( y - 8 ) = r - . 1 r = > 20 x + 160 + 30 y - 240 = . 9 r = > 20 x + 30 y = . 9 r + 80 . . . . . . . . . . . . ( 2 ) so , r = . 9 r + 80 = > r = 800 the answer is d ." | a = 20 * 8
b = 30 * 8
c = a - b
d = negate / (
e = 10 / 100
f = d - e
|
a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20 | e | multiply(divide(10, 20), 40) | two pots are in side - by - side . one pot , which is 20 inches tall , casts a shadow that is 10 inches long . the other pot is 40 inches tall . compute , in inches , the length of the shadow that the taller pot casts . | the ratio of shadow to height is constant , so if x is the length of the shadow , then 20 / 10 = 40 / x and x = 20 . correct answer e | a = 10 / 20
b = a * 40
|
a ) 3800 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3603 | a | subtract(19000, multiply(divide(4, 5), 19000)) | income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 19000 , then find his savings ? | "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 19000 = > x = 3800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3800 . answer : a" | a = 4 / 5
b = a * 19000
c = 19000 - b
|
a ) - 0.61 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71 | a | divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 7) | ( ( - 1.9 ) ( 0.6 ) β ( 2.6 ) ( 1.2 ) ) / 7.0 = ? | dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.61 answer a | a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
|
a ) - 8 , b ) - 4 , c ) 0 , d ) 4 , e ) 8 | c | multiply(negate(multiply(divide(60, 2), 2)), 11) | if 9 a - b = 10 b + 60 = - 12 b - 2 a , what is the value of 11 a + 11 b ? | "( i ) 9 a - 11 b = 60 ( ii ) 2 a + 22 b = - 60 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ." | a = 60 / 2
b = a * 2
c = negate * (
|
a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 462 $ | e | multiply(multiply(0.65, 55), 12) | in a fuel station the service costs $ 2.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ? | 12 * 2.75 + 0.65 * 12 * 55 = 462 hence - e | a = 0 * 65
b = a * 12
|
a ) 96 , b ) 94 , c ) 86 , d ) 74 , e ) 48 | e | divide(20, 240) | find 20 % of 240 | "we know that r % of m is equal to r / 100 Γ m . so , we have 20 % of 240 20 / 100 Γ 240 = 48 answer : e" | a = 20 / 240
|
a ) 1 , b ) 0 , c ) - 1 , d ) 2 , e ) 4 | a | subtract(subtract(12, add(1, 4)), 6) | if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 12 . what is the value of f ( 6 ) ? | "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 12 then f ( 5 ) = 12 - 5 = 7 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 7 - 6 = 1 . answer : a . questions on funtions to practice :" | a = 1 + 4
b = 12 - a
c = b - 6
|
a ) $ 318 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286 | a | add(multiply(18, add(const_3, const_4)), multiply(12, subtract(23, add(const_3, const_4)))) | if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 12.00 / day for each additional week , how much does it cost to stay for 23 days ? | total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 12 = 16 * 12 = 192 $ total charge = 126 + 192 = 318 $ answer a | a = 3 + 4
b = 18 * a
c = 3 + 4
d = 23 - c
e = 12 * d
f = b + e
|
a ) 4.5 , b ) 5 , c ) 2.25 , d ) 5.7 , e ) 6.5 | c | multiply(divide(9, 12), 3) | when a number is divided by 3 & then multiply by 12 the answer is 9 what is the no . ? | "if $ x $ is the number , x / 3 * 12 = 9 = > 4 x = 9 = > x = 2.25 c" | a = 9 / 12
b = a * 3
|
['a ) 20', 'b ) 24', 'c ) 48', 'd ) 72', 'e ) 120'] | c | multiply(factorial(const_4), const_2) | juan and his five friends will sit on six fixed seats around a circular table . if juan must sit on the seat closest to the window and jamal must sit next to juan , in how many can juan and his five friends sit ? | j = juan , f = jamal since j is always fixed , set j , set f relative to j , then see how many options there are : j f 4 3 2 1 = 24 or f j 4 3 2 1 = 24 24 + 24 = 48 β¦ c answer : c | a = math.factorial(4)
b = a * 2
|
a ) 24 , b ) 26 , c ) 25 , d ) 27 , e ) 28 | b | divide(subtract(subtract(20, multiply(20, divide(8, const_10))), subtract(14, multiply(14, divide(9, const_10)))), divide(const_1, const_10)) | lucia ' s sells kale at x dollar per pound for the first 20 pounds and . 8 x for every subsequent pound . amby ' s price is x per pound for the first 14 pounds and . 9 x for subsequent pounds . what is the minimum number of pounds over 15 for which lucia ' s becomes an equal or better deal ? | for amy ' s deal to be better , the cost has to be less or equal to lucia ' s assuming ' n ' is the number of pounds of kale , the equation is 20 x + ( n - 20 ) ( 0.8 x ) < = 14 x + ( n - 14 ) ( 0.9 x ) resolve it : = = > 20 x + 0.8 nx - 16 x < = 14 x + 0.9 nx - 12.6 x = = > 2.6 x < = 0.1 nx = = > 26 x < = nx = = > x ( n - 26 ) > = 0 as x can not be 0 , = = > n - 26 > = 0 = = > n > = 26 so the minimum value is 26 ' b ' would be the correct answer | a = 8 / 10
b = 20 * a
c = 20 - b
d = 9 / 10
e = 14 * d
f = 14 - e
g = c - f
h = 1 / 10
i = g / h
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(multiply(7, divide(subtract(multiply(2, 4), 1), subtract(multiply(6, 3), multiply(2, 11)))), add(multiply(11, divide(subtract(multiply(2, 4), 1), subtract(multiply(6, 3), multiply(2, 11)))), 4)) | when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 1 . what is the value of 7 y β x ? | "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y - 3 = x 7 y - x = 3 the answer is c ." | a = 2 * 4
b = a - 1
c = 6 * 3
d = 2 * 11
e = c - d
f = b / e
g = 7 * f
h = 2 * 4
i = h - 1
j = 6 * 3
k = 2 * 11
l = j - k
m = i / l
n = 11 * m
o = n + 4
p = g - o
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(5, const_2) | in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 140800 , how many purple chips were selected ? | 140800 = 1 * 5 ^ 2 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c . | a = 5 - 2
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a ) 400 , b ) 500 , c ) 700 , d ) none of these , e ) 506 | c | divide(const_100.0, divide(07, 49)) | evaluate 49 / . 07 | "explanation : 49 / . 07 = 4900 / 7 = 700 option c" | a = 7 / 49
b = 100 / 0
|
a ) $ 28,000 , b ) $ 25,000 , c ) $ 20,000 , d ) $ 35,000 , e ) $ 39,000 | e | multiply(subtract(divide(multiply(subtract(const_100, const_10), const_1000), subtract(multiply(subtract(const_100, const_10), const_1000), multiply(multiply(const_0_25, const_100), const_1000))), const_1), const_100) | an employee β s annual salary was increased 30 % . if her old annual salary equals $ 30,000 , what was the new salary ? | "old annual salary = $ 30,000 salary increase = 30 % . original salary = $ 30,000 * 30 / 100 = $ 9000 new salary = $ 30,000 + $ 9000 = $ 39,000 hence e ." | a = 100 - 10
b = a * 1000
c = 100 - 10
d = c * 1000
e = const_0_25 * 100
f = e * 1000
g = d - f
h = b / g
i = h - 1
j = i * 100
|
a ) 1000 , b ) 1200 , c ) 1300 , d ) 1800 , e ) 2500 | e | subtract(negate(50), multiply(subtract(3,5, 7,9), divide(subtract(3,5, 7,9), subtract(1, 3,5)))) | 1 , 3,5 , 7,9 , . . . . 50 find term of sequnce | "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n β 1 ) l ) sn = 12 n ( 2 a + ( n β 1 ) l ) s 50 = 12 Γ 50 Γ ( 2 Γ 1 + ( 50 β 1 ) Γ 2 ) s 50 = 12 Γ 50 Γ ( 2 Γ 1 + ( 50 β 1 ) Γ 2 ) = 25 Γ ( 2 + 49 Γ 2 ) = 25 Γ ( 2 + 49 Γ 2 ) = 25 Γ ( 2 + 98 ) = 25 Γ ( 2 + 98 ) = 2500 = 2500 . e" | a = negate - (
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a ) $ 5306 , b ) $ 6120 , c ) $ 5136 , d ) $ 5405 , e ) $ 5500 | a | add(5000, divide(multiply(5000, 6), const_100)) | david deposited $ 5000 to open a new savings account that earned 6 percent annual interest , compounded semi - annually . if there were no other transactions in the account , what the amount of money in david account one year after the account was opened ? | approach # 1 : 6 percent annual interest compounded semi - annually - - > 3 % in 6 moths . for the first 6 moths interest was 3 % of $ 5000 , so $ 150 ; for the next 6 moths interest was 3 % of $ 5000 , plus 3 % earned on previous interest of $ 150 , so $ 150 + $ 6 = $ 156 ; total interest for one year was $ 150 + $ 156 = $ 306 , hence balance after one year was $ 5000 + $ 306 = $ 5306 . answer : a . | a = 5000 * 6
b = a / 100
c = 5000 + b
|
a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these | d | multiply(1000, 10) | ( 1000 ) 7 Γ· ( 10 ) 17 = ? | explanation : = ( 103 ) 7 / ( 10 ) 17 = ( 10 ) 21 / ( 10 ) 17 = 10 ( 4 ) = 10000 option d | a = 1000 * 10
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a ) 67.6 , b ) 1.58 , c ) 2.47 , d ) 3.54 , e ) 6.51 | a | add(divide(subtract(300, 100), 3), const_1) | how many multiples of 3 are there between 100 and 300 ( both are inclusive ) ? | "the answer is ( 300 - 100 ) / 3 + 1 = 67.6 answer is a" | a = 300 - 100
b = a / 3
c = b + 1
|
a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50 | b | divide(multiply(const_3, const_5), 50) | find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ? | let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 } n ( x ) = 15 , n ( s ) = 50 hence , the required probability is 15 / 50 . answer : b | a = 3 * 5
b = a / 50
|
a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 1.250 kg , e ) none of these | d | multiply(divide(divide(multiply(subtract(const_100, 90), 10), const_100), subtract(const_100, 20)), const_100) | fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 10 kg of fresh grapes ? | "the weight of non - water in 10 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 10 Γ’ Λ β 0.1 = x Γ’ Λ β 0.8 - - > x = 1.25 answer : d" | a = 100 - 90
b = a * 10
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
|
a ) 70 , b ) 75 , c ) 87.5 , d ) 90 , e ) 92.5 | b | multiply(divide(6, add(10, 6)), 200) | two trains , a and b , started simultaneously from opposite ends of a 200 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 200 - mile trip in 10 hours ; train b , traveling at a constant rate , completed the 200 - mile trip in 6 hours . how many miles had train a traveled when it met train b ? | "as the ratio of the rates of a and b is 6 to 10 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 6 / ( 6 + 10 ) = 6 / 16 of 200 miles : 200 * 6 / 16 = 75 miles . answer : b ." | a = 10 + 6
b = 6 / a
c = b * 200
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a ) 11 liters , b ) 11.2 liters , c ) 12.5 liters , d ) 13.78 liters , e ) 13.33 liters | e | divide(subtract(multiply(divide(25, const_100), 200), multiply(divide(20, const_100), 200)), subtract(const_1, divide(25, const_100))) | a mixture of 200 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ? | "number of liters of water in 200 liters of the mixture = 20 % of 120 = 20 / 100 * 200 = 40 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 40 + p ) and total volume of mixture is ( 200 + p ) . ( 40 + p ) = 25 / 100 * ( 200 + p ) 160 + 4 p = 200 + p p = 13.33 liters . answer : e" | a = 25 / 100
b = a * 200
c = 20 / 100
d = c * 200
e = b - d
f = 25 / 100
g = 1 - f
h = e / g
|
a ) 100 , b ) 120 , c ) 125 , d ) 350 , e ) 252 | e | divide(multiply(choose(10, 5), choose(10, 10)), 10) | a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 5 from part a & 10 from part b , in how many ways can he choose the questions ? | "there 5 questions in part a out of which 10 question can be chosen as = 10 c 5 similarly , 10 questions can be chosen from 10 questions of part b as = 10 c 10 . hence , total number of ways , = 10 c 5 * 10 c 10 = [ 10 ! / ( 5 ! 5 ! ) ] * [ 10 ! / ( 0 ! * 10 ) ] = { 10 * 9 * 8 * 7 * 6 / ( 5 * 4 * 3 * 2 * 1 ) } * 10 ! / 1 * 10 ! = 252 e" | a = math.comb(10, 5)
b = math.comb(10, 10)
c = a * b
d = c / 10
|
a ) 27 , b ) 16 , c ) 18 , d ) 20 , e ) 24 | a | divide(log(divide(multiply(const_3, const_10), add(const_4, const_1))), log(power(divide(multiply(const_2, const_10), add(const_4, const_1)), divide(const_1, 12)))) | on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 240,000 ? | "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 240 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 240,000 = 3 years total 27 years . answer a" | a = 3 * 10
b = 4 + 1
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1
g = e / f
h = 1 / 12
i = g ** h
j = math.log(i)
k = d / j
|
a ) 0.1402 , b ) 0.001402 , c ) 1.4021 , d ) 0.01402 , e ) none of these | d | multiply(divide(14.02, 0.001), const_100) | 14.02 Γ£ β 0.001 = ? | "14.02 Γ£ β 0.001 = 0.01402 the answer is d ." | a = 14 / 2
b = a * 100
|
a ) 720 , b ) 420 , c ) 300 , d ) 30 , e ) 333 | b | subtract(subtract(subtract(divide(divide(divide(factorial(17), factorial(subtract(17, 3))), factorial(3)), const_2), 17), 17), const_10) | mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 17 candidates . she plans to have one working interview with 3 of the 17 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ? | "420 . answer b" | a = math.factorial(17)
b = 17 - 3
c = math.factorial(b)
d = a / c
e = math.factorial(3)
f = d / e
g = f / 2
h = g - 17
i = h - 17
j = i - 10
|
a ) 3.4 , b ) 4.5 , c ) 6.2 , d ) 5.7 , e ) 6.9 | a | divide(subtract(multiply(5, 5), multiply(2, 4)), 5) | the average ( arithmetic mean ) of 5 numbers is 5 . if 2 is subtracted from each of 4 of the numbers , what is the new average ? | let the numbers be a , b , c , d , e , f so , total of these 5 numbers must be 25 or , a + b + c + d + e = 25 so , 12 must be subtracted from the total sum i . e a + b + c + d + e - 8 or , 25 - 8 = 17 hence average of the 5 numbers now is 17 / 5 = > 3.4 so , answer will be a | a = 5 * 5
b = 2 * 4
c = a - b
d = c / 5
|
['a ) q = 16', 'b ) q = 32', 'c ) 64', 'd ) 128', 'e ) 512'] | b | multiply(8, 4) | the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 Ο Β· r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many q grams ? | weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b ) | a = 8 * 4
|
a ) 29 , b ) 92 , c ) 41 , d ) 32 , e ) 23 | c | divide(add(34, 48), const_2) | a man can row upstream at 34 kmph and downstream at 48 kmph , and then find the speed of the man in still water ? | "us = 34 ds = 48 m = ( 48 + 34 ) / 2 = 41 answer : c" | a = 34 + 48
b = a / 2
|
a ) 12 , b ) 18 , c ) 14 , d ) 20 , e ) 22 | c | multiply(7, divide(multiply(add(7, 6), subtract(6, multiply(divide(5, add(7, 5)), 6))), subtract(multiply(6, 7), multiply(7, 5)))) | a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 6 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ? | "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 6 ) = ( 7 / 16 ) * v 1 ( v 1 - 6 ) / v 1 = 3 / 4 6 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 6 = 24 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 24 = 14 litres . answer : c" | a = 7 + 6
b = 7 + 5
c = 5 / b
d = c * 6
e = 6 - d
f = a * e
g = 6 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
|
a ) 1840 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000 | a | divide(multiply(multiply(13, 2300), 16), add(multiply(16, 16), 4)) | one ton has 2300 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ? | "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2300 pound = 13 * 2300 * 16 ounces . hence the answer is ( 13 * 2300 * 16 ) / 260 = 1840 . answer : a ." | a = 13 * 2300
b = a * 16
c = 16 * 16
d = c + 4
e = b / d
|
a ) 1.8 , b ) 1.9 , c ) 1.2 , d ) 1.7 , e ) 1.3 | c | multiply(divide(multiply(add(2, 1.2), subtract(2, 1.2)), add(add(2, 1.2), subtract(2, 1.2))), const_2) | a man can row 2 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ? | "m = 2 s = 1.2 ds = 2.4 us = 0.8 x / 1.2 + x / 0.8 = 1 x = 0.6 d = 0.6 * 2 = 1.2 answer : c" | a = 2 + 1
b = 2 - 1
c = a * b
d = 2 + 1
e = 2 - 1
f = d + e
g = c / f
h = g * 2
|
a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 24.26 | e | divide(add(211, divide(multiply(15, 211), const_100)), 10) | total dinning bill for 10 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share | 211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 10 = 24.26 answer : e | a = 15 * 211
b = a / 100
c = 211 + b
d = c / 10
|
a ) 200 , b ) 278 , c ) 282 , d ) 400 , e ) 270 | d | multiply(divide(multiply(subtract(add(multiply(divide(const_100, subtract(const_100, 40)), 1000), multiply(divide(const_100, add(const_100, 40)), 1000)), add(1000, 1000)), const_100), add(multiply(divide(const_100, subtract(const_100, 40)), 1000), multiply(divide(const_100, add(const_100, 40)), 1000))), const_100) | a shopkeeper buys two articles for rs . 1000 each and then sells them , making 40 % profit on the first article and 40 % loss on second article . find the net profit or loss percent ? | "profit on first article = 40 % of 1000 = 400 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d" | a = 100 - 40
b = 100 / a
c = b * 1000
d = 100 + 40
e = 100 / d
f = e * 1000
g = c + f
h = 1000 + 1000
i = g - h
j = i * 100
k = 100 - 40
l = 100 / k
m = l * 1000
n = 100 + 40
o = 100 / n
p = o * 1000
q = m + p
r = j / q
s = r * 100
|
a ) 15 / 29 , b ) 5 / 8 , c ) 5 / 16 , d ) 1 / 2 , e ) 13 / 27 | a | divide(divide(5, 8), add(const_1, divide(1, 4))) | sawyer is mixing up a salad dressing . regardless of the number of servings , the recipe requires that 5 / 8 of the finished dressing mix be peanut oil , 1 / 4 vinegar , and the remainder an even mixture of salt , pepper and sugar . if sawyer accidentally doubles the vinegar and forgets the sugar altogether , what proportion of the botched dressing will be peanut oil ? | peanut oil = 5 / 8 = 15 / 24 - - > 15 parts out of 24 ; vinegar = 1 / 4 = 6 / 24 - - > 6 parts out of 24 ; salt + pepper + sugar = 1 - ( 15 / 24 + 6 / 24 ) = 3 / 24 , so each = 1 / 24 - - > 1 part out of 24 each ; if vinegar = 12 ( instead of 6 ) and sugar = 0 ( instead of 1 ) then total = 15 + 12 + 1 + 1 + 0 = 29 parts out of which 15 parts are peanut oil - - > proportion = 15 / 29 . answer : a . | a = 5 / 8
b = 1 / 4
c = 1 + b
d = a / c
|
a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 300 | e | multiply(divide(multiply(subtract(add(multiply(divide(const_100, subtract(const_100, 30)), 1000), multiply(divide(const_100, add(const_100, 30)), 1000)), add(1000, 1000)), const_100), add(multiply(divide(const_100, subtract(const_100, 30)), 1000), multiply(divide(const_100, add(const_100, 30)), 1000))), const_100) | a shopkeeper buys two articles for rs . 1000 each and then sells them , making 30 % profit on the first article and 30 % loss on second article . find the net profit or loss percent ? | "profit on first article = 30 % of 1000 = 300 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e" | a = 100 - 30
b = 100 / a
c = b * 1000
d = 100 + 30
e = 100 / d
f = e * 1000
g = c + f
h = 1000 + 1000
i = g - h
j = i * 100
k = 100 - 30
l = 100 / k
m = l * 1000
n = 100 + 30
o = 100 / n
p = o * 1000
q = m + p
r = j / q
s = r * 100
|
a ) 18 , b ) 10 , c ) 13 , d ) 14 , e ) 16 | c | divide(subtract(74, multiply(const_3, 11)), multiply(const_3, const_2)) | a number is doubled and 11 is added . if resultant is doubled , it becomes 74 . what is that number | "explanation : = > 2 ( 2 x + 11 ) = 74 = > 4 x + 22 = 74 = > 4 x = 52 = > x = 13 option c" | a = 3 * 11
b = 74 - a
c = 3 * 2
d = b / c
|
a ) 6 days , b ) 5 days , c ) 7 days , d ) 8 days , e ) 10 days | a | divide(const_1, subtract(divide(const_1, 4), divide(const_1, 12))) | raja and ram can together complete a piece of work in 4 days . if raja alone can complete the same work in 12 days , in how many days can ram alone complete that work ? | ( raja + ram ) ' s 1 days work = 1 / 4 raja 1 day work = 1 / 2 ram 1 day work = ( 1 / 4 - 1 / 12 ) = 1 / 6 = = > 6 days answer a | a = 1 / 4
b = 1 / 12
c = a - b
d = 1 / c
|
a ) 75 kgs , b ) 64 kgs , c ) 37.5 kgs , d ) 65 kgs , e ) 70 kgs | c | add(divide(multiply(20, subtract(const_100, 25)), const_100), 60) | fresh grapes contain 60 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ? | "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 60 = 40 % of whole weight ) , so 20 * 0.75 = x * 0.4 - - > x = 37.5 . answer : c" | a = 100 - 25
b = 20 * a
c = b / 100
d = c + 60
|
a ) 237 , b ) 287 , c ) 197 , d ) 660 , e ) 720 | d | multiply(330, const_2) | on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 330 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ? | "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 330 ) = 2 + 2 ( extra ) = > 2 x - 660 = x = > x = 660 . answer : d" | a = 330 * 2
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | subtract(divide(7, const_2), multiply(617, 617)) | what is the remainder when 617 + 1176 is divided by 7 ? | "617 + 1176 mod 7 = > 617 % 7 + 1176 % 7 = > 1 + 0 = > 1 % 7 = > 1 answer : a" | a = 7 / 2
b = 617 * 617
c = a - b
|
a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 8 | c | divide(const_1, subtract(divide(const_1, 4), divide(const_1, 12))) | a and b together can complete a piece of work in 4 days . if a alone can complete the same work in 12 days , in how many days can b alone complete that work ? | "a and b ' s one day work = 1 / 4 a ' s 1 day ' s work = 1 / 12 b ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 12 ) = 2 / 12 = 1 / 6 hence b alone can complete the work in 6 days . answer is option c" | a = 1 / 4
b = 1 / 12
c = a - b
d = 1 / c
|
a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec | e | multiply(divide(300, multiply(90, const_1000)), const_3600) | a train 300 m long , running with a speed of 90 km / hr will pass a tree in ? | "speed = 90 * 5 / 18 = 25 m / sec time taken = 300 * 1 / 25 = 12 sec answer : e" | a = 90 * 1000
b = 300 / a
c = b * 3600
|
a ) 4 , b ) 18 , c ) 15 , d ) 20 , e ) 24 | b | divide(subtract(multiply(75, 30), 1800), subtract(75, 50)) | tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 75 ? | you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 18 * 50 600 1800 - 900 0900 12 75.00 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is b | a = 75 * 30
b = a - 1800
c = 75 - 50
d = b / c
|
a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | e | floor(divide(log(divide(21000, 2.134)), log(10))) | if x is an integer and 2.134 Γ 10 ^ x is less than 21000 , what is the greatest possible value for x ? | "if x = 4 2.134 Γ 10 ^ 4 = 21340 > 21000 so , x = 3 answer : e" | a = 21000 / 2
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
|
a ) 42 , b ) 49 , c ) 44 , d ) 45 , e ) 46 | b | add(add(power(add(add(divide(subtract(subtract(97, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(97, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(97, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(97, const_10), const_2), const_4), const_2), const_2))) | the sum of two consecutive number is 97 . which is the larger number ? | "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 97 2 x + 1 = 97 2 x = 96 x = 48 therefore larger number is x + 1 = 49 answer : b" | a = 97 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 97 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 97 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 97 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
|
a ) 125 , b ) 165 , c ) 145 , d ) 127 , e ) 112 | d | multiply(divide(3,10, 29,66), const_100) | 3,10 , 29,66 , __ | "3 = 1 * 1 * 1 + 2 10 = 2 * 2 * 2 + 2 29 = 3 * 3 * 3 + 2 66 = 4 * 4 * 4 + 2 similarly 5 * 5 * 5 + 2 = 127 answer : d" | a = 3 / 10
b = a * 100
|
a ) 321 , b ) 276 , c ) 306 , d ) 265 , e ) 162 | c | subtract(subtract(450, divide(multiply(450, 20), const_100)), divide(multiply(subtract(450, divide(multiply(450, 20), const_100)), 15), const_100)) | the sale price sarees listed for rs . 450 after successive discount is 20 % and 15 % is ? | "explanation : 450 * ( 80 / 100 ) * ( 85 / 100 ) = 306 answer : c" | a = 450 * 20
b = a / 100
c = 450 - b
d = 450 * 20
e = d / 100
f = 450 - e
g = f * 15
h = g / 100
i = c - h
|
a ) 72 min , b ) 25.11628 min , c ) 70 min , d ) 74.11682 min , e ) 76 min | b | multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 15), multiply(const_2, 15)))), 15) | if there are 200 questions in a 3 hr examination . among these questions are 15 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ? | "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 185 x + 15 * 2 x = 180 x = 180 / 215 x = 0.837209 time taken for type a problem = 15 * 2 * 0.837209 = 25.11628 min answer : b" | a = 3 * const_60
b = 200 - 15
c = 2 * 15
d = b + c
e = a / d
f = 2 * e
g = f * 15
|
a ) 170 , b ) 160 , c ) 162 , d ) 130 , e ) 122 | c | multiply(divide(45, const_1000), const_3600) | express 45 mps in kmph ? | "45 * 18 / 5 = 162 kmph answer : c" | a = 45 / 1000
b = a * 3600
|
a ) rs . 300 , b ) rs . 56 , c ) rs . 100 , d ) rs . 240 , e ) rs . 90 | d | multiply(divide(630, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8)))) | a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a | "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = rs . 240 answer : d" | a = 3000 * 8
b = 3000 - 1000
c = 12 - 8
d = b * c
e = a + d
f = 4000 * 8
g = 4000 + 1000
h = 12 - 8
i = g * h
j = f + i
k = e + j
l = 630 / k
m = 3000 * 8
n = 3000 - 1000
o = 12 - 8
p = n * o
q = m + p
r = l * q
|
a ) 10 mps , b ) 35 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps | b | multiply(const_0_2778, 126) | express a speed of 126 kmph in meters per second ? | "126 * 5 / 18 = 35 mps answer : b" | a = const_0_2778 * 126
|
a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 9 | b | sqrt(add(power(sqrt(subtract(13, multiply(const_2, 2028))), const_2), multiply(const_4, 2028))) | the product of two numbers is 2028 and their h . c . f is 13 . the number of such pairs is ? | "let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer : b" | a = 2 * 2028
b = 13 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 2028
f = d + e
g = math.sqrt(f)
|
a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 % | e | multiply(divide(245, subtract(850, 245)), const_100) | a cricket bat is sold for $ 850 , making a profit of $ 245 . the profit percentage would be | "245 / ( 850 - 245 ) = 245 / 605 = 49 / 121 = 40 % . answer : e ." | a = 850 - 245
b = 245 / a
c = b * 100
|
a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 15 | b | divide(add(90, 60), const_2) | the speed of a car is 90 km in the first hour and 60 km in the second hour . what is the average speed of the car ? | "s = ( 90 + 60 ) / 2 = 75 kmph answer : b" | a = 90 + 60
b = a / 2
|
a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2 | e | divide(300, 600) | if shares of two persons in profits are rs . 300 and rs . 600 then ratio of their capitals is | "total profit = 1000 ratio = 300 / 600 = 1 : 2 answer : e" | a = 300 / 600
|
a ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47 | b | subtract(choose(8, 5), choose(subtract(8, 2), 2)) | a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 8 managers , if 2 managers will not attend the meeting together ? | "we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together so 6 c 5 + ( 6 c 4 * 2 c 1 ) this is 6 + 30 = 36 answer : b" | a = math.comb(8, 5)
b = 8 - 2
c = math.comb(b, 2)
d = a - c
|
a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 % | e | multiply(divide(const_3, add(const_3, const_2)), const_100) | a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % sunflower . if a customer purchases a mix of the two types of birdseed that is 50 % sunflower , what percent of the mix is brand a ? | "yes there is a simple method : consider the following method brand a : 40 % millet and 60 % sunflower brand b : 65 % millet and 35 % sunflower mix : 50 % sunflower here the weighted average is 50 % , now brand a has 60 % sunflower , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 35 % sunflower , which is 15 % less than the weighted average of mix = - 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total below = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 35 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 below average , b times - - - - - - - - - - - - - - - - - total above = - 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : e" | a = 3 + 2
b = 3 / a
c = b * 100
|
a ) 15 , b ) 16 , c ) 22 , d ) 18 , e ) 25 | b | divide(20, add(const_1, divide(25, const_100))) | sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is : | "work done by sakshi in 1 day = 1 / 20 since tanya is 25 % efficient than sakshi , she completes 25 % more work in a day than sakshi . = > tanya ' s 1 day work = 1 / 20 + 1 / 20 * 25 / 100 = 1 / 16 so time taken by tanya to finish the work = 16 days answer : b" | a = 25 / 100
b = 1 + a
c = 20 / b
|
a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000 | d | divide(1504, divide(subtract(60, subtract(const_100, 60)), const_100)) | in an election a candidate who gets 60 % of the votes is elected by a majority of 1504 votes . what is the total number of votes polled ? | let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1504 20 x / 100 = 1504 x = 1504 * 100 / 20 = 7520 answer is d | a = 100 - 60
b = 60 - a
c = b / 100
d = 1504 / c
|
a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 13 / 30 , e ) 1 / 5 | d | divide(add(21, 5), const_60) | two boats are heading towards each other at constant speeds of 5 miles / hr and 21 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ? | the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 21 = 26 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 26 * 1 / 60 = 13 / 30 miles apart . answer : d . | a = 21 + 5
b = a / const_60
|
a ) 12 , b ) 18 , c ) 22 , d ) 24 , e ) 26 | d | divide(multiply(18, 36), 27) | 36 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ? | "solution let the required number of days be x . then , less men , more days β΄ 27 : 36 : : 18 : x β 27 Γ x = 36 Γ 18 β x = 36 x 18 / 27 x = 24 . answer d" | a = 18 * 36
b = a / 27
|
a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 % | c | multiply(divide(multiply(divide(1, 3), subtract(1, divide(1, 2))), add(multiply(divide(1, 3), subtract(1, divide(1, 2))), subtract(1, divide(1, 3)))), const_100) | of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 2 , what percent of the total number of the remaining employees would then be clerical ? | "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 2 is 1200 * 1 / 2 so it reduced 600 people , so there is 600 clerical people left but since 600 people left , it also reduced from the total of 3600 so there are 3000 people total since 600 clerical left / 3000 people total you get ( c ) 20 %" | a = 1 / 3
b = 1 / 2
c = 1 - b
d = a * c
e = 1 / 3
f = 1 / 2
g = 1 - f
h = e * g
i = 1 / 3
j = 1 - i
k = h + j
l = d / k
m = l * 100
|
a ) 8 and 12 , b ) 5 and 9 , c ) 6 and 10 , d ) 5 and 10 , e ) 12 and 16 | a | add(multiply(divide(subtract(divide(60, const_3), 4), const_2), const_100), subtract(divide(60, const_3), divide(subtract(divide(60, const_3), 4), const_2))) | toby is 4 years younger than debby . thrice the sum of the ages of toby and debby equals their mother β s age . if the age of the mother is 60 , find the ages of toby and debby ? | let the age of debby be x and toby be x - 4 3 ( x + x - 4 ) = 60 x = 12 the ages of toby and debby are 8 and 12 . answer : a | a = 60 / 3
b = a - 4
c = b / 2
d = c * 100
e = 60 / 3
f = 60 / 3
g = f - 4
h = g / 2
i = e - h
j = d + i
|
a ) 294 , b ) 289 , c ) 240 , d ) 233 , e ) 200 | a | subtract(divide(multiply(multiply(2800, 18.5), 3), const_100), divide(multiply(multiply(2800, 15), 3), const_100)) | if a lends rs . 2800 to b at 15 % per annum and b lends the same sum to c at 18.5 % per annum then the gain of b in a period of 3 years is ? | "( 2800 * 3.5 * 3 ) / 100 = > 294 answer : a" | a = 2800 * 18
b = a * 3
c = b / 100
d = 2800 * 15
e = d * 3
f = e / 100
g = c - f
|
a ) 15 , b ) 20 , c ) 18 , d ) 32 , e ) 26 | e | divide(add(add(add(20, const_1), add(add(20, const_1), const_2)), add(subtract(30, 20), subtract(30, const_2))), 20) | find the average of all prime numbers between 20 and 30 | "prime numbers between 20 and 30 are 23,29 required average = ( 23 + 29 ) / 2 = 52 / 2 = 26 answer is e" | a = 20 + 1
b = 20 + 1
c = b + 2
d = a + c
e = 30 - 20
f = 30 - 2
g = e + f
h = d + g
i = h / 20
|
a ) 4 , b ) 8 , c ) 5 , d ) 6 , e ) 7 | d | multiply(4, divide(3, 4)) | a and b together can complete work in 4 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ? | "explanation : ( a + b ) one day work = 1 / 4 now a does half of the work in 3 days so a can complete the whole work in 6 days a β s one day work = 1 / 6 b β s one day work = 1 / 4 - 1 / 6 = 1 / 12 b alone can complete the work in 12 days so half of the work in 6 days answer : option d" | a = 3 / 4
b = 4 * a
|
a ) 9440 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882 | a | add(multiply(multiply(add(divide(1, const_100), divide(divide(subtract(9200, 8000), 3), 8000)), 8000), 3), 8000) | sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1 % more . she would get how much ? | "( 8000 * 3 * 1 ) / 100 = 240 9200 - - - - - - - - 9440 answer : a" | a = 1 / 100
b = 9200 - 8000
c = b / 3
d = c / 8000
e = a + d
f = e * 8000
g = f * 3
h = g + 8000
|
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7 | e | subtract(subtract(multiply(const_2, 9), 9), const_2) | john is 3 times as old as sam . if john will be twice as old as sam in 9 years , how old was sam two years ago ? | j = 3 s after 9 years j + 9 = 2 ( s + 9 ) j = 2 s + 9 2 s + 9 = 3 s s = 9 two years ago s = 9 - 2 = 7 e is the answer | a = 2 * 9
b = a - 9
c = b - 2
|
a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20 | d | divide(subtract(multiply(add(14, 23), divide(70, const_100)), 14), divide(70, const_100)) | a bowl of fruit contains 14 apples and 23 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ? | number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 23 - x ) = 37 - x 14 / ( 37 - x ) = 7 / 10 = > 20 = 37 - x = > x = 17 answer d | a = 14 + 23
b = 70 / 100
c = a * b
d = c - 14
e = 70 / 100
f = d / e
|
a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these | c | sqrt(power(49, 2)) | β ( 49 ) 2 | "explanation β ( 49 ) 2 = ? or , ? = 49 answer c" | a = 49 ** 2
b = math.sqrt(a)
|
a ) 5 / 2 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7 | a | inverse(add(divide(subtract(divide(add(inverse(add(add(const_4, const_1), const_4)), multiply(inverse(add(const_4, const_1)), const_2)), const_2), inverse(add(const_4, const_1))), divide(const_3, const_2)), inverse(add(const_4, const_1)))) | one woman and one man can build a wall together in three hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them five hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ? | "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 3 - - > ( 1 ) , w + 2 g = 1 / 3 - - > ( 2 ) and m + g = 1 / 5 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 15 , m = 2 / 15 and w = 1 / 5 . so , n = 1 / ( 2 / 5 ) = 5 / 2 option , a" | a = 4 + 1
b = a + 4
c = 1/(b)
d = 4 + 1
e = 1/(d)
f = e * 2
g = c + f
h = g / 2
i = 4 + 1
j = 1/(i)
k = h - j
l = 3 / 2
m = k / l
n = 4 + 1
o = 1/(n)
p = m + o
q = 1/(p)
|
a ) 15 sec , b ) 11.6 sec , c ) 31.6 sec , d ) 12.6 sec , e ) 23 sec | b | multiply(const_3600, divide(divide(add(170, 170), const_1000), add(55, 50))) | two trains each 170 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 55 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely . | explanation : d = 170 m + 170 m = 340 m rs = 55 + 50 = 105 * 5 / 18 = 146 / 5 t = 340 * 5 / 146 = 11.6 sec answer : option b | a = 170 + 170
b = a / 1000
c = 55 + 50
d = b / c
e = 3600 * d
|
a ) 2 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 8 / 3 , e ) 16 / 3 | e | multiply(divide(multiply(8, const_2), add(4, const_2)), const_2) | 8 cups of water are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of water should be poured into the 8 - cup bottle ? | let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : e | a = 8 * 2
b = 4 + 2
c = a / b
d = c * 2
|
a ) 7500 , b ) 2028 , c ) 2775 , d ) 10000 , e ) 6851 | d | divide(4000, subtract(subtract(const_1, divide(30, const_100)), divide(30, const_100))) | a candidate got 30 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ? | "30 % - - - - - - - - - - - l 70 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 40 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 10000 answer : d" | a = 30 / 100
b = 1 - a
c = 30 / 100
d = b - c
e = 4000 / d
|
a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | e | divide(subtract(32, 15), subtract(15, 14)) | the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 15 years old . what is the value of n ? | "14 n + 32 = 15 ( n + 1 ) n = 17 the answer is e ." | a = 32 - 15
b = 15 - 14
c = a / b
|
a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 130 | e | multiply(26, 5) | the average of 7 numbers is 26 . if each number be multiplied by 5 . find the average of new set of numbers ? | "explanation : average of new numbers = 26 * 5 = 130 answer : option e" | a = 26 * 5
|
a ) 289 , b ) 231 , c ) 100 , d ) 288 , e ) 111 | c | divide(subtract(350, 345), divide(5, const_100)) | if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 345 , the cost of the article is | "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 345 = 5 x / 20 = 5 = > x = 100 answer : c" | a = 350 - 345
b = 5 / 100
c = a / b
|
a ) 22 , b ) 48 , c ) 45 , d ) 72 , e ) 18 | a | subtract(multiply(multiply(4, 5), divide(88, add(add(multiply(3, 3), multiply(3, 5)), multiply(4, 5)))), multiply(multiply(3, 3), divide(88, add(add(multiply(3, 3), multiply(3, 5)), multiply(4, 5))))) | the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 88 , what is the difference between the ages of patrick and monica ? | "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 88 x = 2 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 2 = 22 answer a" | a = 4 * 5
b = 3 * 3
c = 3 * 5
d = b + c
e = 4 * 5
f = d + e
g = 88 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k
m = 4 * 5
n = l + m
o = 88 / n
p = i * o
q = h - p
|
a ) 144 , b ) 131 , c ) 115 , d ) 189 , e ) 45 | d | add(divide(multiply(14, subtract(14, const_1)), const_2), multiply(14, 7)) | 14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? | "there are 14 business exec and in each handshake 2 business execs are involved . hence 14 c 2 = 91 also , each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake . total = 91 + 98 = 189 ans : d" | a = 14 - 1
b = 14 * a
c = b / 2
d = 14 * 7
e = c + d
|
a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9 | d | divide(add(5, 44), 7) | 5 n - 3 > 12 and 7 n - 5 < 44 ; n must be between which numbers ? | 5 n - 3 > 12 5 n > 15 n > 3 7 n - 5 < 44 7 n < 49 n < 7 so n must be between 3 and 7 3 < n < 7 correct answer d | a = 5 + 44
b = a / 7
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | floor(divide(12, subtract(5, const_1))) | if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 12 ? | "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 12 . then 4 n < 12 and n < 3 . the largest possible integer is n = 2 . the answer is b ." | a = 5 - 1
b = 12 / a
c = math.floor(b)
|
a ) 6.24 , b ) 7.4 , c ) 7.92 , d ) 6.28 , e ) 7.24 | d | divide(const_1, subtract(divide(const_1, 4), divide(const_1, 11))) | a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? | "net part filled in 1 hour = ( 1 / 4 - 1 / 11 ) = 7 / 44 the cistern will be filled in 44 / 7 hrs i . e . , 6.28 hrs . answer : d" | a = 1 / 4
b = 1 / 11
c = a - b
d = 1 / c
|
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