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a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 302 | c | divide(195, divide(subtract(const_100, 13), const_100)) | a small college reduced its faculty by approximately 13 percent to 195 professors . what was the original number of faculty members ? | "f x is the original number of faculty members , then after 13 % reduction in faculty members number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of faculty members is 224 correct answer - c" | a = 100 - 13
b = a / 100
c = 195 / b
|
a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 1 / 5 , e ) 2 | d | multiply(subtract(1, divide(3, 4)), subtract(3, divide(3, 5))) | the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 5 . the probability that none of them will be alive for 10 more yrs , is | "sol . required probability = pg . ) x p ( b ) = ( 1 β d x ( 1 β i ) = : x 1 = 1 / 5 ans . ( d )" | a = 3 / 4
b = 1 - a
c = 3 / 5
d = 3 - c
e = b * d
|
a ) 2.9 , b ) 2.2 , c ) 2.5 , d ) 2.1 , e ) 2.3 | c | multiply(divide(divide(multiply(divide(20, const_100), 100), 10), multiply(divide(20, const_100), 100)), const_100) | a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ? | "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 100 - - - 80 ? - - - 2 = > rs . 2.5 answer : c" | a = 20 / 100
b = a * 100
c = b / 10
d = 20 / 100
e = d * 100
f = c / e
g = f * 100
|
a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24 | b | subtract(divide(factorial(subtract(divide(12, const_2), const_1)), multiply(factorial(const_3), factorial(const_2))), subtract(divide(12, const_2), const_1)) | a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter . ) | "let ' s start with 4 minimum number of colors so single color code we can make 4 nos . now if we need to make 2 color combination out of 4 we can do so in 4 ! / 2 ! * 2 ! or 4 * 3 / 2 or 6 so total we can make 4 + 6 = 10 color combinations but we have 12 boxes so let ' s look at 5 we get 5 single color codes and out 5 color choices , we can choose 2 in 5 ! / 2 ! * 3 ! ways or 10 ways . so total we can have 5 + 10 = 15 color combinations . so , minimum number we need will be 5 ans is b . . . . . . ." | a = 12 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 12 / 2
i = h - 1
j = g - i
|
a ) rs . 36 , b ) rs . 72 , c ) rs . 48 , d ) rs . 96 , e ) none | d | sqrt(multiply(576, 16)) | the present worth of a sum due sometime hence is rs . 576 and the banker β s gain is rs . 16 . the true discount is | solution t . d = β p . w xb . g = β 576 x 16 = 96 . answer d | a = 576 * 16
b = math.sqrt(a)
|
a ) 425 , b ) 435 , c ) 445 , d ) 455 , e ) 465 | b | multiply(divide(subtract(90, 36), const_3_6), 29) | two trains are moving in the same direction at 90 kmph and 36 kmph . the faster train crosses a man in the slower train in 29 seconds . find the length of the faster train ? | "relative speed = ( 90 - 36 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 29 sec = 29 * 15 = 435 m . the length of the faster train = 435 m . answer : b" | a = 90 - 36
b = a / const_3_6
c = b * 29
|
a ) 12003 , b ) 12000 , c ) 12002 , d ) 12289 , e ) 12019 | b | divide(8748, subtract(const_1, multiply(divide(10, const_100), 3))) | the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs . 8748 , its purchase price was : | "explanation : = rs . 12000 answer : b ) 12000" | a = 10 / 100
b = a * 3
c = 1 - b
d = 8748 / c
|
a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5 | a | power(const_2, divide(multiply(log(8), log(9)), 3)) | solve for x the equation log 9 ( x 3 ) = log 2 ( 8 ) | log 9 ( x 3 ) = log 2 ( 8 ) : given log 2 ( 23 ) = 3 : simplify right hand side of given equation . log 9 ( x 3 ) = 3 : rewrite the above equation log 9 ( x 3 ) = log 9 ( 93 ) : rewite 3 as a log base 9 . x 3 = 93 : obtain algebraic equation from eqaution d . x = 9 : solve above for x correct answer a | a = math.log(8)
b = math.log(9)
c = a * b
d = c / 3
e = 2 ** d
|
a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 5 / 11 , e ) 4 / 10 | d | divide(divide(subtract(16, 6), add(const_1, const_1)), add(divide(subtract(16, 6), add(const_1, const_1)), 6)) | there are 6 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ? | "w = m + 6 w + m = 16 m + 6 + m = 16 2 m = 10 m = 5 w = 11 ratio : 5 : 11 ans : d" | a = 16 - 6
b = 1 + 1
c = a / b
d = 16 - 6
e = 1 + 1
f = d / e
g = f + 6
h = c / g
|
a ) 75 % , b ) 60 % , c ) 40 % , d ) 25 % , e ) 20 % | a | divide(subtract(30, 10), subtract(25, 10)) | salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 25 % vinegar , dressing p comprises what percentage of the new dressing ? | "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.25 0.2 x = 0.15 x = 0.75 = 75 % the answer is a ." | a = 30 - 10
b = 25 - 10
c = a / b
|
a ) 120 , b ) 116 , c ) 112 , d ) 108 , e ) 104 | a | multiply(2, divide(135, add(2, 16))) | water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 135 grams of water ? | "( 16 / 18 ) * 144 = 120 grams the answer is a ." | a = 2 + 16
b = 135 / a
c = 2 * b
|
a ) 3 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours | a | divide(63, add(16, 5)) | a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 63 km downstream . | "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 63 / 21 = 3 hours option a" | a = 16 + 5
b = 63 / a
|
a ) 7 , b ) 7 1 / 3 , c ) 7 1 / 2 , d ) 4 , e ) 7 1 / 2 | b | divide(add(subtract(15, 12), subtract(12, subtract(multiply(divide(40, const_60), 15), multiply(divide(40, const_60), 12)))), subtract(multiply(divide(40, const_60), 15), multiply(divide(40, const_60), 12))) | john and jacob set out together on bicycle traveling at 15 and 12 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john two hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible ) | "john ' s speed - 15 miles / hr jacob ' s speed - 12 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 2 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 2 hour 40 min ( i . e 8 / 3 hr ) = 12 x 8 / 3 = 32 miles . now , when john starts riding back , the distance between them is 22 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 12 = 3 miles / hr . thus , to cover 22 miles at 3 miles / hr , john will take 22 / 3 = 7 1 / 3 hours answer b" | a = 15 - 12
b = 40 / const_60
c = b * 15
d = 40 / const_60
e = d * 12
f = c - e
g = 12 - f
h = a + g
i = 40 / const_60
j = i * 15
k = 40 / const_60
l = k * 12
m = j - l
n = h / m
|
a ) 266 sec , b ) 180 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec | b | divide(add(1200, 600), divide(1200, 120)) | a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 600 m long ? | "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : b" | a = 1200 + 600
b = 1200 / 120
c = a / b
|
a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 % | d | multiply(divide(multiply(choose(const_4, const_1), const_2), choose(6, 3)), multiply(multiply(const_5, const_5), const_4)) | two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability v that jane will be on the same committee as albert ? | "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability v = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d" | a = math.comb(4, 1)
b = a * 2
c = math.comb(6, 3)
d = b / c
e = 5 * 5
f = e * 4
g = d * f
|
a ) 50 kmh , b ) 60 kmh , c ) 70 kmh , d ) 80 kmh , e ) 90 kmh | d | divide(subtract(sqrt(add(multiply(multiply(const_2, multiply(120, 40)), const_4), power(40, const_2))), 40), const_2) | if a car had traveled 40 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 120 km , at what speed did it travel ? | "time = distance / speed difference in time = 1 / 2 hrs 120 / x - 120 / ( x + 40 ) = 1 / 2 substitute the value of x from the options . - - > x = 80 - - > 120 / 80 - 120 / 120 = 3 / 2 - 1 = 1 / 2 answer : d" | a = 120 * 40
b = 2 * a
c = b * 4
d = 40 ** 2
e = c + d
f = math.sqrt(e)
g = f - 40
h = g / 2
|
a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 5991 | a | subtract(multiply(add(5, const_1), 3500), add(add(add(add(3435, 3927), 3855), 4230), 3562)) | a grocer has a sale of rs . 3435 , rs . 3927 , rs . 3855 , rs . 4230 and rs . 3562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ? | "explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) Γ’ β¬ β 19009 ] = rs . ( 21000 Γ’ β¬ β 19009 ) = rs . 1991 . answer a" | a = 5 + 1
b = a * 3500
c = 3435 + 3927
d = c + 3855
e = d + 4230
f = e + 3562
g = b - f
|
a ) 5 / 5 , b ) 1 / 2 , c ) 5 / 1 , d ) 5 / 7 , e ) 5 / 2 | b | divide(const_2, choose(add(const_3, const_3), const_3)) | what is the probability of getting a number less than 4 when a die is rolled ? | "total number of outcomes possible when a die is rolled = 6 ( β΅ any one face out of the 6 faces ) i . e . , n ( s ) = 6 e = getting a number less than 4 = { 1 , 2 , 3 } hence , n ( e ) = 3 the probability = 3 / 6 = 1 / 2 . answer : b" | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
|
a ) 150 m , b ) 230 m , c ) 290 m , d ) 310 m , e ) 420 m | b | subtract(multiply(divide(add(120, 80), const_3_6), 9), 270) | a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 second . what is the length of the other train ? | relative speed = 120 + 80 = 200 * 5 / 18 = 500 / 9 m / s let the length of the other train be x meters x + 270 / 9 = 500 / 9 x = 230 m answer is b | a = 120 + 80
b = a / const_3_6
c = b * 9
d = c - 270
|
a ) 10 sec , b ) 16 sec , c ) 13 sec , d ) 67 sec , e ) 8 sec | e | multiply(multiply(multiply(const_0_2778, subtract(60, 40)), 40), inverse(multiply(const_0_2778, add(60, 40)))) | two trains of equal length , running with the speeds of 60 and 40 kmph , take 40 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ? | "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 40 d = 40 * 100 / 18 = 2000 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2000 / 9 * 18 / 500 = 8 sec answer : e" | a = 60 - 40
b = const_0_2778 * a
c = b * 40
d = 60 + 40
e = const_0_2778 * d
f = 1/(e)
g = c * f
|
a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 6 : 5 | e | divide(multiply(2, 3), 3) | a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is : | "explanation : dog : hare = ( 2 * 3 ) leaps of hare : 3 leaps of hare = 6 : 5 . answer : e ) 6 : 5" | a = 2 * 3
b = a / 3
|
a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 11 | e | divide(22, const_2) | in a group of pigs and hens , the number of legs are 22 more than twice the number of heads . the number of pigs is | explanation : let the number of pigs be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 22 4 x + 2 y = 2 x + 2 y + 22 2 x = 22 x = 11 answer : e | a = 22 / 2
|
a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5 | d | subtract(multiply(add(2, const_4), 2), 2) | x + y = 19 , and x + 3 y = 1 . find the value of x + 2 y | add these two equations 2 x + 4 y = 20 divide by 2 ( to get x + 2 y ) answer will be d . 10 | a = 2 + 4
b = a * 2
c = b - 2
|
a ) 69 . , b ) 135 . , c ) 81 . , d ) 91 . , e ) 108 . | b | subtract(subtract(470, 300), subtract(250, divide(multiply(250, 86), const_100))) | in the fifth grade at parkway elementary school there are 470 students . 300 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? | "total students = 470 boys = 300 , girls = 170 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 170 - 35 = 135 . correct option : b" | a = 470 - 300
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
|
a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 30.00 sec , e ) 72.0 sec | d | divide(add(110, 390), multiply(60, const_0_2778)) | how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length ? | "d = 110 + 390 = 500 m s = 60 * 5 / 18 = 50 / 3 t = 500 * 3 / 50 = 30 sec answer : d" | a = 110 + 390
b = 60 * const_0_2778
c = a / b
|
a ) 10 days , b ) 12 days , c ) 13 days , d ) 9 days , e ) 14 days | a | multiply(divide(const_1, add(divide(const_1, 9), divide(const_1, 12))), 3) | a can finish a work in 24 days , b in 9 days and c in 12 days . b and c start the work but are forced to leave after 3 days . when a done the work ? | "b + c = = > 1 / 9 + 1 / 12 = 7 / 36 b , c = in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done a 24 * 5 / 12 = 10 days answer a" | a = 1 / 9
b = 1 / 12
c = a + b
d = 1 / c
e = d * 3
|
a ) 901 , b ) 989 , c ) 990 , d ) 971 , e ) 1,001 | d | subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), const_0.5)) | in a recent election , james received 1.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ? | "james = ( 1.5 / 100 ) * 2000 = 30 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 30 = 971 answer : option d" | a = 1000 + 1000
b = 1000 + 1000
c = b * 0
d = a - c
|
a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24 | b | add(multiply(add(multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, const_2)), power(const_100, const_2))), add(multiply(divide(2, const_100), power(const_100, const_2)), power(const_100, const_2))), divide(4, const_100)), multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, const_2)), power(const_100, const_2)))) | jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 10 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ? | if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 726.24 . answer : b . | a = 3 / 100
b = 2 / 100
c = 100 ** 2
d = b * c
e = 100 ** 2
f = d + e
g = a * f
h = 2 / 100
i = 100 ** 2
j = h * i
k = 100 ** 2
l = j + k
m = g + l
n = 4 / 100
o = m * n
p = 3 / 100
q = 2 / 100
r = 100 ** 2
s = q * r
t = 100 ** 2
u = s + t
v = p * u
w = o + v
|
a ) 22 , b ) 16 , c ) 27 , d ) 28 , e ) 20 | b | multiply(4, 4) | walking 4 / 3 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ? | "speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b" | a = 4 * 4
|
a ) 242 , b ) 232 , c ) 236 , d ) 240 , e ) 244 | e | subtract(1256, add(4, multiply(gcd(1256, lcm(lcm(7, 12), 16)), lcm(lcm(7, 12), 16)))) | which is the least number that must be subtracted from 1256 so that the remainder when divided by 7 , 12 , 16 is 4 ? | "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1256 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 244 . e" | a = math.lcm(7, 12)
b = math.lcm(a, 16)
c = math.gcd(1256, b)
d = math.lcm(7, 12)
e = math.lcm(d, 16)
f = c * e
g = 4 + f
h = 1256 - g
|
a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24 | a | divide(divide(divide(divide(divide(divide(108, const_2), const_2), const_2), const_2), const_3), const_3) | if n is the smallest integer such that 108 times n is the square of an integer , what is the value of n ? | "108 can written as = 2 * 2 * 3 * 3 * 3 - - > 2 ^ 2 * 3 ^ 3 - - - ( 1 ) so for 108 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 2 in ( 1 ) even option a is correct" | a = 108 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 3
f = e / 3
|
a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 325 | e | add(multiply(40, const_2), 60) | of the 500 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ? | "300 prefer x ( group 1 ) ; 200 prefer y ( group 2 ) . city y needs 375 people : letall 200 who prefer y ( entire group 2 ) be relocated there , the rest 175 will be those who prefer x from group 1 ; city x needs 125 people : 300 - 175 = 125 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 200 + 125 = 325 . answer : e ." | a = 40 * 2
b = a + 60
|
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | a | subtract(subtract(multiply(3, 6), add(subtract(11, 6), 3)), 6) | the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 11 . what is the last numbers ? | "a + b + c = 18 b + c + d = 15 a + d = 11 a β d = 3 a + d = 11 2 d = 8 d = 4 answer : a" | a = 3 * 6
b = 11 - 6
c = b + 3
d = a - c
e = d - 6
|
a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 43 | e | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 35), 50)), divide(multiply(const_100, 35), 50))) | if the cost price of 50 articles is equal to the selling price of 35 articles , then the gain or loss percent is ? | "percentage of profit = 15 / 35 * 100 = 43 % answer : e" | a = 100 * 35
b = a / 50
c = 100 - b
d = 100 * 35
e = d / 50
f = c / e
g = 100 * f
|
a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 3 / 5 , e ) 9 / 7 | d | add(subtract(1, divide(3, 4)), subtract(divide(3, 4), divide(1, 4))) | a batch of cookies was divided amomg 3 tins : 3 / 4 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin | "this will help reduce the number of variables you have to deal with : g + b = 3 / 4 r = 1 / 3 b = 1 / 4 we can solve for g which is 1 / 2 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 1 / 2 + 1 / 3 ) = 1 / 2 x = 3 / 5 answer : d" | a = 3 / 4
b = 1 - a
c = 3 / 4
d = 1 / 4
e = c - d
f = b + e
|
a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1260 | e | multiply(divide(divide(factorial(10), factorial(subtract(10, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2)) | 10 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ? | "no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )" | a = math.factorial(10)
b = 10 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(8)
g = 8 - 2
h = math.factorial(g)
i = f / h
j = i / 2
k = e * j
|
a ) rs . 4500 , b ) rs . 4700 , c ) rs . 4800 , d ) rs . 5000 , e ) rs . 5100 | e | subtract(multiply(add(5, const_1), 6500), add(add(add(add(6400, 7000), 6800), 7200), 6500)) | a grocer has a sale of rs . 6400 , rs . 7000 , rs . 6800 , rs . 7200 and rs . 6500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ? | "total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e" | a = 5 + 1
b = a * 6500
c = 6400 + 7000
d = c + 6800
e = d + 7200
f = e + 6500
g = b - f
|
a ) 3 : 4 , b ) 6 : 13 , c ) 5 : 6 , d ) 13 : 10 , e ) 4 : 3 | b | divide(multiply(divide(add(5, const_1), const_2), 6), multiply(divide(add(12, const_1), const_2), 6)) | given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ? | the first nine positive multiples of six are { 6 , 12 , 18 , 24,30 } the first twelve positive multiples of six are { 6 , 12 , 18 , 24 , 30 , 36,42 , 48 , 54 , 60 , 66 , 72 } both sets are evenly spaced , thus their median = mean : a = 18 and b = ( 36 + 42 ) / 2 = 39 - - > a / b = 18 / 39 = 6 / 13 . answer : b . | a = 5 + 1
b = a / 2
c = b * 6
d = 12 + 1
e = d / 2
f = e * 6
g = c / f
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a ) rs . 610 , b ) rs . 612 , c ) rs . 614 , d ) rs . 616 , e ) none of these | b | subtract(multiply(power(add(const_1, divide(divide(4, 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 . 7500 at 4 % per annum for 2 years , compounded annually . | "explanation : amount = [ 7500 Γ ( 1 + 4100 ) 2 ] = ( 7500 Γ 2625 Γ 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b" | a = 4 / 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
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a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 4 / 5 | d | divide(const_4, add(0,0, const_10)) | in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,9 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ? | "the area of the right triangle is ( 1 / 2 ) * 4 * 9 = 18 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 18 = 2 / 9 the answer is d ." | a = 0 + 0
b = 4 / a
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a ) 12 , b ) 12.5 , c ) 20 , d ) 13.5 , e ) 14 | c | divide(divide(const_2, divide(5, const_100)), const_2) | if a sum of money doubles itself in 5 years at simple interest , the ratepercent per annum is | "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 5 ) = 20 option c" | a = 5 / 100
b = 2 / a
c = b / 2
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a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 28 , e ) $ 29 | d | subtract(multiply(52, const_2), 76) | elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 52 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ? | "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d" | a = 52 * 2
b = a - 76
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a ) 33008 , b ) 24000 , c ) 28000 , d ) 48000 , e ) 81122 | d | subtract(76000, multiply(const_60, const_100)) | a started a business with an investment of rs . 70000 and after 9 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 76000 , then the share of b is ? | "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 3 ) = 7 : 12 total profit = rs . 76000 share of b = 12 / 19 ( 76000 ) = rs . 48000 answer : d" | a = const_60 * 100
b = 76000 - a
|
a ) 18 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | b | divide(110, multiply(7, const_3.0)) | how many 7 in between 1 to 110 ? | "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 21 7 ' s between 1 to 110 answer : b" | a = 7 * 3
b = 110 / a
|
a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1800 , d ) rs . 2000 , e ) none of these | c | multiply(divide(divide(multiply(15, const_2), 10), add(divide(multiply(15, const_2), 10), divide(multiply(15, const_2), 15))), 3000) | a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get : | "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a β s amount = 120 Γ 15 = rs . 1800 . answer : option c" | a = 15 * 2
b = a / 10
c = 15 * 2
d = c / 10
e = 15 * 2
f = e / 15
g = d + f
h = b / g
i = h * 3000
|
a ) a ) 34500 , b ) b ) 36099 , c ) c ) 36000 , d ) d ) 38007 , e ) e ) 42000 | c | subtract(78000, multiply(const_60, const_100)) | a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 78000 , then the share of b is ? | "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 78000 share of b = 6 / 13 ( 78000 ) = rs . 36000 answer : c" | a = const_60 * 100
b = 78000 - a
|
a ) 17.36 , b ) 20.45 , c ) 23.87 , d ) 26.92 , e ) 29.56 | b | divide(divide(90, 5280), multiply(3, divide(1, const_3600))) | if an object travels 90 feet in 3 seconds , what is the object β s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet ) | "90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ." | a = 90 / 5280
b = 1 / 3600
c = 3 * b
d = a / c
|
a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4 | a | divide(add(divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1)), subtract(7, multiply(2, divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1))))), 3) | if 2 x + y = 7 and x + 2 y = 5 , then xy / 3 = | "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 xy / 3 = 3 * 1 / 3 = 1 a" | a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l
n = m / 3
|
a ) 1180 , b ) 1330 , c ) 1540 , d ) 1760 , e ) 1920 | b | multiply(subtract(const_1, divide(3, 21)), 21) | there are 21 students in a class . in how many different ways can a committee of 3 students be formed ? | "21 c 3 = 21 * 20 * 19 / 6 = 1330 the answer is b ." | a = 3 / 21
b = 1 - a
c = b * 21
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a ) 15 years , b ) 15.5 years , c ) 16 years , d ) 17 years , e ) can not be computed | e | subtract(16, 15) | the average age of boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is | "clearly , to find the average , we ought to know the numbers of boys , girls or students in the class , neither of which has been given . so the data provided is inadequate . answer : e" | a = 16 - 15
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a ) 20 , b ) 25 , c ) 30 , d ) 55 , e ) 100 | e | subtract(multiply(multiply(divide(800, subtract(add(divide(divide(25, const_100), divide(20, const_100)), const_1), divide(25, const_100))), divide(divide(25, const_100), divide(20, const_100))), subtract(const_1, divide(20, const_100))), multiply(divide(800, subtract(add(divide(divide(25, const_100), divide(20, const_100)), const_1), divide(25, const_100))), subtract(const_1, divide(25, const_100)))) | of 800 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ? | "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 800 = 1.25 b + b - 0.25 b - - > b = 400 , a = 1.25 b = 500 and { both } = 0.25 b = 100 . the number of students who read only book a is { a } - { both } = 500 - 100 = 400 ; the number of students who read only book b is { b } - { both } = 400 - 100 = 300 ; the difference is 400 - 300 = 100 . answer : e ." | a = 25 / 100
b = 20 / 100
c = a / b
d = c + 1
e = 25 / 100
f = d - e
g = 800 / f
h = 25 / 100
i = 20 / 100
j = h / i
k = g * j
l = 20 / 100
m = 1 - l
n = k * m
o = 25 / 100
p = 20 / 100
q = o / p
r = q + 1
s = 25 / 100
t = r - s
u = 800 / t
v = 25 / 100
w = 1 - v
x = u * w
y = n - x
|
a ) 993.2 , b ) 586.21 , c ) 534.33 , d ) 543.33 , e ) 646.33 | b | divide(multiply(power(add(divide(5, const_100), const_1), 2), 1090), 2) | what annual payment will discharge a debt of rs . 1090 due in 2 years at the rate of 5 % compound interest ? | explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b | a = 5 / 100
b = a + 1
c = b ** 2
d = c * 1090
e = d / 2
|
a ) rs . 22941.18 , b ) rs . 32941.18 , c ) rs . 52941.18 , d ) rs . 62941.18 , e ) none of these | c | divide(multiply(divide(multiply(54000, const_100), add(const_100, 20)), const_100), subtract(const_100, 15)) | a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was : | "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 Γ£ β 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 Γ£ β 45000 ] = rs . 52941.18 correct option : c" | a = 54000 * 100
b = 100 + 20
c = a / b
d = c * 100
e = 100 - 15
f = d / e
|
a ) 399 , b ) 272 , c ) 666 , d ) 277 , e ) 311 | c | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1), 3) | the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ? | "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 Γ’ β¬ β 6 = 666 * 1 = 666 answer : c" | a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
|
a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 9 | e | subtract(add(6, 4), const_1) | how many 0 ' s are there in the binary form of 6 * 1024 + 4 * 64 + 2 | 6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e | a = 6 + 4
b = a - 1
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a ) 87 / 36 , b ) 36 / 17 , c ) 7 / 6 , d ) 62 / 3 , e ) 5 / 4 | d | subtract(divide(add(multiply(const_10, 7), 7), 4), divide(add(const_10, 4), 3)) | what is 7 1 / 4 - 4 2 / 3 divided by 7 / 8 - 3 / 4 ? | "7 1 / 4 - 4 2 / 3 = 29 / 4 - 14 / 3 = ( 87 - 56 ) / 12 = 31 / 12 7 / 8 - 3 / 4 = ( 7 - 6 ) / 8 = 1 / 8 so 31 / 12 / 1 / 8 = 31 / 12 * 8 = 62 / 3 answer - d" | a = 10 * 7
b = a + 7
c = b / 4
d = 10 + 4
e = d / 3
f = c - e
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a ) rs . 200 , b ) rs . 350 , c ) rs . 475 , d ) rs . 425 , e ) none of these | c | divide(subtract(multiply(30, 350), multiply(15, 225)), 15) | the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be | "average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c" | a = 30 * 350
b = 15 * 225
c = a - b
d = c / 15
|
a ) 489.66 , b ) 406.07 , c ) 406.04 , d ) 306.03 , e ) 306.01 | a | subtract(multiply(8000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 8000) | find out the c . i on rs . 8000 at 4 % p . a . compound half - yearly for 1 1 / 2 years | "a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a" | a = 4 / 100
b = 1 + a
c = 3 / 2
d = b ** c
e = 8000 * d
f = e - 8000
|
a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes . | c | divide(20, 20) | jayes can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ? | rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min | a = 20 / 20
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a ) 15 , b ) 30 , c ) 31 , d ) 37 , e ) 46 | d | subtract(divide(subtract(subtract(120, 10), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(120, const_2), multiply(3, const_4)), 3), 3), 3), const_2)) | how many even number in the range between 10 to 120 inclusive are not divisible by 3 | "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d" | a = 120 - 10
b = a - 2
c = b / 2
d = 120 - 2
e = 3 * 4
f = d - e
g = f - 3
h = g - 3
i = h / 3
j = i / 2
k = c - j
|
a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | e | divide(multiply(multiply(const_1000, const_100), 0.037), divide(74000, const_1000)) | in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 74000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ? | 0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e | a = 1000 * 100
b = a * 0
c = 74000 / 1000
d = b / c
|
a ) 18 , b ) 28 , c ) 40 , d ) 38 , e ) 59 | c | divide(multiply(subtract(62, 2), 2), add(2, const_1)) | if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ? | "let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c" | a = 62 - 2
b = a * 2
c = 2 + 1
d = b / c
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a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 days , e ) 3 days | e | subtract(add(inverse(add(inverse(15), inverse(10))), 10), const_3) | a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ? | "work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e" | a = 1/(15)
b = 1/(10)
c = a + b
d = 1/(c)
e = d + 10
f = e - 3
|
a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | e | subtract(power(2, 2), 4) | for the symbol , m β n = n ^ 2 β m for all values of m and n . what is the value of 4 β 2 ? | "4 β 2 = 4 - 4 = 0 answer : e" | a = 2 ** 2
b = a - 4
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a ) 462 , b ) 674 , c ) 672 , d ) 960 , e ) none | a | multiply(subtract(divide(62, const_100), multiply(subtract(const_1, divide(60, const_100)), divide(50, const_100))), 1100) | in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ? | "solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer literate = 682 - 220 = 462 . answer : option a" | a = 62 / 100
b = 60 / 100
c = 1 - b
d = 50 / 100
e = c * d
f = a - e
g = f * 1100
|
a ) 48 , b ) 47 , c ) 40 , d ) 42 , e ) 47 | e | add(48, const_1) | total 48 matches are conducted in knockout match type . how many players will be participated in that tournament ? | "47 players answer : e" | a = 48 + 1
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a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 26 m , e ) 12 m | d | multiply(divide(130, 45), subtract(45, 36)) | in 130 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by : | "distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d" | a = 130 / 45
b = 45 - 36
c = a * b
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a ) 25 , b ) 37.5 , c ) 50 , d ) 52.5 , e ) 75 | d | add(subtract(const_100, 69), subtract(90, 69)) | at a certain university , 69 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ? | "answer is 75 % total women = 69 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 21 % but question wants to know the percent of men that are tenured 21 % / 40 % = 52.5 % d" | a = 100 - 69
b = 90 - 69
c = a + b
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a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30 | d | multiply(divide(26, 26), 26) | in a dairy farm , 26 cows eat 26 bags of husk in 26 days . in how many days one cow will eat one bag of husk ? | "explanation : one bag of husk = 26 cows per day β 26 Γ 1 Γ 26 = 1 Γ 26 Γ x for one cow = 26 days answer : d" | a = 26 / 26
b = a * 26
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a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | c | divide(subtract(34, 16), subtract(16, 14)) | the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ? | "14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c ." | a = 34 - 16
b = 16 - 14
c = a / b
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a ) Β½ , b ) 21 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500 | b | subtract(0.650, divide(1, 8)) | the number 0.650 is how much greater than 1 / 8 ? | "let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b" | a = 1 / 8
b = 0 - 650
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a ) 60.32 % , b ) 61.54 % , c ) 62.21 % , d ) 62.76 % , e ) 63.87 % | b | divide(1092, add(5, 8)) | if $ 1092 are divided between worker a and worker b in the ratio 5 : 8 , what is the share that worker b will get ? | "worker b will get 8 / 13 = 61.54 % the answer is b ." | a = 5 + 8
b = 1092 / a
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a ) 8 / 58 , b ) 9 / 25 , c ) 1 / 26 , d ) 6 / 25 , e ) 8 / 45 | c | divide(subtract(52, multiply(const_4, const_4)), 52) | a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ? | "here n ( s ) = 52 let e be the event of getting queen of the club or king of kings n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer ( c )" | a = 4 * 4
b = 52 - a
c = b / 52
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a ) 12.9 , b ) 12.5 , c ) 11.3 , d ) 12.2 , e ) 12.1 | c | divide(multiply(17, 1000), add(1000, 500)) | 1000 men have provisions for 17 days . if 500 more men join them , for how many days will the provisions last now ? | "1000 * 17 = 1500 * x x = 11.3 answer : c" | a = 17 * 1000
b = 1000 + 500
c = a / b
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a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 5 km | c | multiply(multiply(divide(divide(47, const_60), add(add(divide(const_1, 3), divide(const_1, 4)), divide(const_1, 5))), const_3), const_1000) | a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance is ? | "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 = > x = 1 . total distance = 3 * 1 = 3 km ." | a = 47 / const_60
b = 1 / 3
c = 1 / 4
d = b + c
e = 1 / 5
f = d + e
g = a / f
h = g * 3
i = h * 1000
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a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | subtract(subtract(5, 2), 2) | if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > β 1 , 3 > x > 0 , and x + 2 < 4 , then x is | "0 < x < 7 , 0 < x < 15 , 5 > x > β 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ." | a = 5 - 2
b = a - 2
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a ) 9 , b ) 8 , c ) 3 , d ) 0 , e ) 2 | e | multiply(divide(1, 1), const_100) | 1 + 1 | e | a = 1 / 1
b = a * 100
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a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90 | c | multiply(divide(2, add(3, 2)), 150) | rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 150 . what is the share of rahul ? | "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 150 * 2 / 5 = $ 60 answer is c" | a = 3 + 2
b = 2 / a
c = b * 150
|
a ) 1000 yards , b ) 1200 yards , c ) 1400 yards , d ) 1600 yards , e ) 1800 yards | b | multiply(300, const_4) | a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b | if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b | a = 300 * 4
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a ) 7 , b ) 6 , c ) 5 , d ) 2 , e ) 3 | d | divide(subtract(38, multiply(const_4, 7)), 5) | a pineapple costs rs 7 each and a watermelon costs rs . 5 each . if i spend rs 38 on total what is the number of pineapple i purchased ? | explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d | a = 4 * 7
b = 38 - a
c = b / 5
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a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 5 : 4 , e ) 2 : 3 | d | divide(sqrt(25), sqrt(16)) | the sub - duplicate ratio of 25 : 16 is | "root ( 25 ) : root ( 16 ) = 5 : 4 answer : d" | a = math.sqrt(25)
b = math.sqrt(16)
c = a / b
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a ) 9 / 4 , b ) 12 / 5 , c ) 56 / 9 , d ) 15 / 4 , e ) 20 / 3 | c | divide(8, 7) | in Ξ΄ pqs above , if pq = 7 and ps = 8 , then | "there are two ways to calculate area of pqs . area remains same , so both are equal . 7 * 8 / 2 = pr * 9 / 2 pr = 56 / 9 c" | a = 8 / 7
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a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs | d | divide(1250, 50) | ajay can ride 50 km in 1 hour . in how many hours he can ride 1250 km ? | "1 hour he ride 50 km he ride 1250 km in = 1250 / 50 * 1 = 25 hours answer is d" | a = 1250 / 50
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a ) 31 kmph , b ) 16 kmph , c ) 19 kmph , d ) 15 kmph , e ) 14 kmph | d | divide(add(multiply(divide(const_3, const_2), const_3.0), 2), subtract(divide(const_3, const_2), 1)) | a boat covers a certain distance downstream in 1 hour , while it comes back in 11 Γ’ Β β 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ? | "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x Γ’ Λ β 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 Γ’ Β β 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 11 Γ’ Β β 2 hour since distance = speed Γ£ β time , we have ( x + 3 ) Γ£ β 1 = ( x - 3 ) 3 / 2 2 ( x + 3 ) = 3 ( x - 3 ) 2 x + 6 = 3 x - 9 x = 6 + 9 = 15 kmph answer : d" | a = 3 / 2
b = a * 3
c = b + 2
d = 3 / 2
e = d - 1
f = c / e
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a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 58 | e | divide(multiply(87, 24), 36) | in a division , a student took 87 as divisor instead of 36 . his answer was 24 . the correct answer is - | x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e | a = 87 * 24
b = a / 36
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a ) 199 , b ) 209 , c ) 219 , d ) 229 , e ) 239 | d | multiply(add(divide(subtract(subtract(26, 10), const_2), const_2), 10), divide(add(subtract(26, 10), const_2), const_2)) | what is the sum of all digits for the number 10 ^ 26 - 51 ? | "10 ^ 26 is a 27 - digit number : 1 followed by 26 zeros . 10 ^ 26 - 51 is a 26 - digit number : 24 9 ' s and 49 at the end . the sum of the digits is 24 * 9 + 4 + 9 = 229 . the answer is d ." | a = 26 - 10
b = a - 2
c = b / 2
d = c + 10
e = 26 - 10
f = e + 2
g = f / 2
h = d * g
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a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90 | c | divide(const_180, const_3) | what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube . | "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c" | a = const_180 / 3
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a ) 1260 , b ) 1320 , c ) 1200 , d ) 1250 , e ) none of these | a | subtract(multiply(6000, power(add(const_1, divide(10, const_100)), const_2)), 6000) | what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum . | solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a | a = 10 / 100
b = 1 + a
c = b ** 2
d = 6000 * c
e = d - 6000
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a ) 5 / 8 , b ) 3 / 4 , c ) 7 / 8 , d ) 157 / 64 , e ) 143 / 128 | e | subtract(const_1, add(multiply(inverse(power(2, 8)), 8), add(inverse(power(2, 8)), inverse(power(2, 8))))) | a fair 2 sided coin is flipped 8 times . what is the probability that tails will be the result at least twice , but not more than 8 times ? | "at least twice , but not more than 8 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times , 8 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 8 c 2 / 2 ^ 8 + 8 c 3 / 2 ^ 8 + 8 c 4 / 2 ^ 8 + 8 c 5 / 2 ^ 8 + 8 c 6 / 2 ^ 8 + 8 c 7 / 2 ^ 8 = 143 / 128 option : e" | a = 2 ** 8
b = 1/(a)
c = b * 8
d = 2 ** 8
e = 1/(d)
f = 2 ** 8
g = 1/(f)
h = e + g
i = c + h
j = 1 - i
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a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 6 | e | sqrt(54) | the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 54 . what is the rate of interest per annum ? | "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 54 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 54 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 54 r 2 = ( 54 * 2 ) / 3 = 36 = > r = 6 rate = 6 % answer : option e" | a = math.sqrt(54)
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a ) 1 : 2 , b ) 3 : 5 , c ) 5 : 7 , d ) 1 : 4 , e ) 2 : 1 | d | multiply(divide(1, 2), multiply(divide(1, 2), divide(2, 2))) | find the compound ratio of ( 1 : 2 ) , ( 2 : 3 ) and ( 3 : 4 ) is | "required ratio = 1 / 2 * 2 / 3 * 3 / 4 = 1 / 4 = 1 : 4 answer is d" | a = 1 / 2
b = 1 / 2
c = 2 / 2
d = b * c
e = a * d
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a ) 4 / 7 , b ) 5 / 9 , c ) 2 / 3 , d ) 10 / 11 , e ) none of these | c | divide(add(1, 1), add(2, 1)) | if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is | explanation : let the required fraction be a / b . then β a / b + 1 = 1 / 2 β 2 a β b = 1 - - - - ( 1 ) β a + 1 / b = 1 β a β b = β 1 β a β b = β 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c | a = 1 + 1
b = 2 + 1
c = a / b
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a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | b | divide(120, multiply(2, 3)) | if the ratio of two number is 2 : 3 and lcm of the number is 120 then what is the number . | "product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b" | a = 2 * 3
b = 120 / a
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a ) 244.83 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01 | a | subtract(multiply(4000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 4000) | find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years | "a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a" | a = 4 / 100
b = 1 + a
c = 3 / 2
d = b ** c
e = 4000 * d
f = e - 4000
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a ) 1 : 4 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 5 : 4 | e | divide(divide(const_100, add(const_100, 40)), divide(const_100, add(const_100, 75))) | bert and rebecca were looking at the price of a condominium . the price of the condominium was 40 % more than bert had in savings , and separately , the same price was also 75 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings . | suppose bert had 100 so price becomes 140 , this 140 = 1.75 times r ' s saving . . so r ' s saving becomes 80 so required ratio is 100 : 80 = 5 : 4 answer : e | a = 100 + 40
b = 100 / a
c = 100 + 75
d = 100 / c
e = b / d
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a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60 | e | multiply(5, 12) | walking at 5 / 6 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is | "let v be her normal speed and let t be her normal time . d = ( 5 / 6 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 5 / 6 ) v * ( t + 12 ) t / 6 = 10 t = 60 the answer is e ." | a = 5 * 12
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a ) 1 minutes , b ) 12 minute , c ) 120 minutes , d ) 10000 minutes , e ) 1000 minutes | b | multiply(divide(12, 12), 12) | if 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers ? | "we can try the logic of time and work , our work is to kill the deers so 12 ( lions ) * 12 ( min ) / 12 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 12 answer : b" | a = 12 / 12
b = a * 12
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a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes | d | divide(subtract(18, divide(18, divide(add(6, 18), subtract(18, 6)))), const_1) | a man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ? | let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) . | a = 6 + 18
b = 18 - 6
c = a / b
d = 18 / c
e = 18 - d
f = e / 1
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a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3 | a | divide(multiply(45000, const_12), multiply(27000, add(const_4, const_3))) | x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ? | "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 Γ 12 : 27000 Γ 9 = 45 Γ 12 : 27 Γ 9 = 15 Γ 12 : 9 Γ 9 = 20 : 9 answer is a" | a = 45000 * 12
b = 4 + 3
c = 27000 * b
d = a / c
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a ) 20 , b ) 55 / 4 , c ) 25 , d ) 14 , e ) 13 | b | multiply(divide(multiply(subtract(15, 4), divide(5, const_60)), 4), const_60) | the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ? | "after passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 4 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 11 / 12 miles to meet the waiting cyclist . the hiker will need 55 / 4 mins to cover the remaining 11 / 12 miles . so the answer is b ." | a = 15 - 4
b = 5 / const_60
c = a * b
d = c / 4
e = d * const_60
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