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MNLP_M2_rag_dataset

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crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 40 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 40 % , so the manufacturing must have been $ 60 . answer = ( e ) ."
a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 60
e
subtract(divide(50, divide(50, const_100)), multiply(divide(50, divide(50, const_100)), divide(40, const_100)))
divide(n1,const_100)|divide(n0,const_100)|divide(n1,#0)|multiply(#2,#1)|subtract(#2,#3)|
general
E
a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km / hr in the same direction . in how much time will the train pass the jogger ?
"speed of train relative to jogger = 27 - 9 = 18 km / hr . = 18 * 5 / 18 = 5 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 5 = 72 sec . answer : b"
a ) 76 sec , b ) 72 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
b
divide(add(240, 120), multiply(subtract(27, 9), divide(divide(const_10, const_2), divide(subtract(27, 9), const_2))))
add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)|
general
B
if the sides of a triangle are 30 cm , 26 cm and 10 cm , what is its area ?
"the triangle with sides 30 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : option c"
a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
c
divide(multiply(26, 10), const_2)
multiply(n1,n2)|divide(#0,const_2)|
geometry
C
a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 27 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
"let x be the wholesale price . then 1.8 x = 27 and x = 27 / 1.8 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 3 more . the answer is c ."
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
c
subtract(multiply(divide(27, add(const_1, divide(80, 100))), const_2), 27)
divide(n0,n2)|add(#0,const_1)|divide(n1,#1)|multiply(#2,const_2)|subtract(#3,n1)|
general
C
calculate how long it will take a swimmer to swim a distance of 8 km against the current of a river which flows at 1.4 km / hr , given that he can swim in still water at 3 km / h
swim in still water at = 3 speed of river = 1.4 us = 3 - 1.4 = 1.6 distance = 8 t = 8 / 1.6 = 5 answer : e
a ) 20 seconds , b ) 3 , c ) 4 , d ) 1 , e ) 5
e
divide(8, subtract(3, 1.4))
subtract(n2,n1)|divide(n0,#0)
gain
E
how many digits are required to write numbers between 1 to 100 .
"explanation : single digits are from 1 to 9 = 9 digits doubt digits are from 10 to 99 = 90 x 2 = 180 digits 100 needs 3 digits . total 192 digits correct option : c"
a ) 196 , b ) 158 , c ) 192 , d ) 200 , e ) none
c
add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(1, const_100), const_1), const_3))
subtract(const_10,const_1)|subtract(n0,const_100)|add(#1,const_1)|multiply(#0,const_10)|multiply(#3,const_2)|multiply(#2,const_3)|add(#4,#0)|add(#6,#5)|
general
C
a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 61 , how many questions did student a answer correctly ?
"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 61 ( subtracting twice of incorrect from correct ) 3 x = 261 x = 87 answer : e"
a ) 55 , b ) 60 , c ) 73 , d ) 81 , e ) 87
e
subtract(100, divide(subtract(100, 61), const_3))
subtract(n0,n1)|divide(#0,const_3)|subtract(n0,#1)|
general
E
on a sum of money , the simple interest for 2 years is rs . 320 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - simple interest for 2 years is rs . 320 = > simple interest for first year = 320 / 2 = 160 = > similarly , simple interest for second year is also 160 compound interest for first year = 160 compound interest for second year = 340 - 160 = 180 we can see that compound interest for second year is more than simple interest for second year by 180 - 160 = 20 i . e . , rs . 20 is the simple interest on rs . 160 for 1 year r = 100 Γ— si / pt = ( 100 Γ— 20 ) / ( 160 Γ— 1 ) = 12.5 % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r Γ— si ) / ( 2 Γ— 100 ) difference between the compound interest and simple interest = 340 - 320 = 20 ( r Γ— si ) / ( 2 Γ— 100 ) = 20 ( r Γ— 320 ) / ( 2 Γ— 100 ) = 20 r = 20 Γ— 100 Γ— 2320 = 12.5 % answer : option c
a ) 15 % , b ) 14.25 % , c ) 12.5 % , d ) 10.5 % , e ) 11.5 %
c
divide(multiply(const_100, subtract(subtract(340, divide(320, 2)), divide(320, 2))), divide(320, 2))
divide(n1,n0)|subtract(n2,#0)|subtract(#1,#0)|multiply(#2,const_100)|divide(#3,#0)
gain
C
rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 8 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
"let the amount lent at 7 % be rs . x amount lent at 8 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 8 / 100 ( 6000 - x ) = 480 - x / 100 = > 480 - 1 / 100 x = 450 = > x = 3000 amount lent at 10 % = 3000 required ratio = 3000 : 3000 = 5 : 5 answer : b"
a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 2
b
divide(divide(subtract(multiply(450, const_100), multiply(6000, 7)), subtract(8, 7)), divide(subtract(multiply(450, const_100), multiply(6000, 7)), subtract(8, 7)))
multiply(n3,const_100)|multiply(n0,n1)|subtract(n2,n1)|subtract(#0,#1)|divide(#3,#2)|divide(#4,#4)|
gain
B
each child has 2 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?
2 * 8 = 16 . answer is a .
a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
a
multiply(2, 8)
multiply(n0,n2)|
general
A
what is ( 16 ^ 7 + 16 ) / 16 ?
"( 16 ^ 7 + 16 ) / 16 = 16 * ( 16 ^ 6 + 1 ) / 16 = 16 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is b ."
a ) 15467118 , b ) 16777217 , c ) 17827343 , d ) 18047455 , e ) 19357579
b
divide(add(power(16, 7), 16), 16)
power(n0,n1)|add(n0,#0)|divide(#1,n0)|
general
B
what is the sum of all even numbers from 1 to 701 ?
"explanation : 700 / 2 = 350 350 * 351 = 122850 answer : d"
a ) 122821 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 128111
d
divide(multiply(1, 701), const_4)
multiply(n0,n1)|divide(#0,const_4)|
general
D
the charge for a single room at hotel p is 40 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
"p = 0.6 r = 0.9 g r = 0.9 g / 0.6 = 1.5 * g thus r is 50 % greater than g . the answer is d ."
a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) e . 150 %
d
multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 40), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 40), subtract(const_100, 10)), const_100)), const_100)
subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)|
gain
D
how many of the positive factors of 20 are not factors of 24
"factors of 20 - 1 , 2 , 4,5 , 10 , 20 factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12 and 24 comparing both , we have 3 factors of 20 which are not factors of 24 - 5 , 10,20 answer : b"
a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
b
divide(24, 20)
divide(n1,n0)|
other
B
- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 190 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
"since 190 students answered yes only for subject m , then the remaining 310 students who answered yes for subject m , also answered yes for subject r . so , 310 students answered yes for both subjects . if 310 students answered yes for both subjects , then 400 - 310 = 90 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 90 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 90 + 300 ) = 210 students did not answer yes for either subject . answer : b ."
a ) 100 , b ) 210 , c ) 300 , d ) 400 , e ) 500
b
subtract(800, add(add(190, subtract(500, 190)), subtract(400, subtract(500, 190))))
subtract(n0,n7)|add(n7,#0)|subtract(n3,#0)|add(#1,#2)|subtract(n6,#3)|
general
B
two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km / hr and 36 km / hr . the time of crossing each other , if they run in the opposite direction is
explanation : total distance to be covered = 156.62 + 100 = 256.62 m trains are running in opposite directions , hence relative speed = 30 + 36 = 66 km / hr = 18.33 m / sec time = distance / relative speed = 256.62 / 18.33 sec = 14 sec therefore , the time of crossing each other in the opposite direction is 14 seconds . answer : b
a ) 322 sec , b ) 14 sec , c ) 11 sec , d ) 13 sec , e ) 34 sec
b
divide(add(156.62, 100), multiply(add(30, 36), const_0_2778))
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)
physics
B
if the perimeter of a rectangular park is 1000 m , its length when its breadth is 200 m is ?
2 ( l + 200 ) = 1000 = > l = 300 m answer : d
a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400
d
subtract(divide(1000, const_2), 200)
divide(n0,const_2)|subtract(#0,n1)|
physics
D
if x is to be chosen at random from the integers between 1 to 6 , inclusive , and y is to be chosen at random from the integers between 7 and 11 , inclusive , what is the probability that x + y will be even ?
"x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 6 * 2 / 5 = 1 / 5 p ( x and y are both odd ) = 3 / 6 * 3 / 5 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a ."
a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
a
divide(add(multiply(const_2, const_2), multiply(const_3, const_2)), multiply(6, subtract(6, 1)))
multiply(const_2,const_2)|multiply(const_2,const_3)|subtract(n1,n0)|add(#0,#1)|multiply(n1,#2)|divide(#3,#4)|
general
A
mahesh can do a piece of work in 60 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
"work done by mahesh in 60 days = 20 * 1 / 60 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 2 / 3 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 3 / 2 = 45 days answer is a"
a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 30
a
divide(const_1, divide(subtract(const_1, multiply(20, divide(const_1, 60))), 30))
divide(const_1,n0)|multiply(n1,#0)|subtract(const_1,#1)|divide(#2,n2)|divide(const_1,#3)|
physics
A
the average of 6 observations is 13 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
let seventh observation = x . then , according to the question we have = > ( 78 + x ) / 7 = 12 = > x = 6 . hence , the seventh observation is 6 . answer : d
a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
d
subtract(multiply(subtract(13, 1), add(6, 1)), multiply(13, 6))
add(n0,n2)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#2)|subtract(#3,#1)
general
D
3 numbers are in the ratio 3 : 5 : 7 . the largest number is 56 . what is the difference between smallest and largest number ?
the three numbers are 3 x , 5 x , and 7 x . the largest number is 56 = 7 * 8 , so x = 8 . the smallest number is 3 * 8 = 24 . 56 - 24 = 32 the answer is d .
a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
d
subtract(56, multiply(3, divide(56, 7)))
divide(n4,n3)|multiply(n0,#0)|subtract(n4,#1)
other
D
a scuba diver descends at a rate of 32 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 6400 feet below the sea level . . how long will he take to reach the ship ?
"time taken to reach = 6400 / 32 = 200 minutes answer : a"
a ) 200 minutes , b ) 240 minutes , c ) 220 minutes , d ) 210 minutes , e ) 77 minutes
a
divide(6400, 32)
divide(n1,n0)|
gain
A
a company that ships boxes to a total of 13 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 )
"back - solving is the best way to solve this problem . you basically need 13 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
a ) 6 , b ) 5 , c ) 8 , d ) 9 , e ) 10
b
subtract(divide(factorial(subtract(divide(13, const_2), const_1)), multiply(factorial(const_3), factorial(const_2))), subtract(divide(13, const_2), const_1))
divide(n0,const_2)|factorial(const_3)|factorial(const_2)|multiply(#1,#2)|subtract(#0,const_1)|factorial(#4)|divide(#5,#3)|subtract(#6,#4)|
general
B
right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 10 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
"lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 10 * ( a + e ) = = > 9 a = 11 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 e / 9 * 11 = 220 + 12 e or ( 121 / 9 - 12 ) e = 220 or 13 / 9 e = 220 e = 220 * 9 / 13 = 152.3 b"
a ) $ 110 , b ) $ 152.3 , c ) $ 180 , d ) $ 220 , e ) $ 260
b
divide(multiply(22, const_100), subtract(multiply(add(10, 1), 10), add(const_100, 20)))
add(n0,n1)|add(n3,const_100)|multiply(n4,const_100)|multiply(#0,n2)|subtract(#3,#1)|divide(#2,#4)|
general
B
if ( a + b ) = 16 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
"given a + b = 16 = > a = 16 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 16 - b + 3 - c = > 19 - ( b + c ) = > 19 - 9 = 10 . option a . . ."
a ) 10 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
a
subtract(add(16, 3), 9)
add(n0,n2)|subtract(#0,n1)|
general
A
the largest 4 digit number exactly divisible by 66 is ?
"largest 4 - digit number = 9999 66 ) 9999 ( 151 9966 largest number : 9966 answer : d"
a ) 9935 , b ) 9939 , c ) 9944 , d ) 9966 , e ) 9960
d
square_area(const_pi)
square_area(const_pi)|
general
D
if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 60 / r years . if pat ' s parents invested $ 7,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 20 years later , when pat is ready for college ?
"since investment doubles in 60 / r years , then for r = 6 it ' ll double in 60 / 6 = ~ 10 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 20 years investment will become $ 7,000 * 2 = $ 14,000 . answer : b"
a ) $ 20000 , b ) $ 14000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
b
divide(multiply(multiply(add(const_2, const_3), const_1000), 6), const_2)
add(const_2,const_3)|multiply(#0,const_1000)|multiply(n2,#1)|divide(#2,const_2)|
general
B
8 * 8 * 8 * 8 = 2 ^ ?
"solution : 2 ^ 3 * 2 ^ 3 * 2 ^ 3 * 2 ^ 3 = 2 ^ ( 3 + 3 + 3 + 3 ) = 2 ^ 12 answer : 12 option : e"
a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
e
multiply(8, 8)
multiply(n0,n1)|
general
E
if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ? .
if both 5 ^ 2 & 3 ^ 3 are factors , then they must be present in the number . leaving rest of the prime factors and splitting 6 ^ 2 into 3 ^ 2 * 2 ^ 3 . the number is lacking 5 ^ 2 & a 3 , so that 5 ^ 2 and 3 ^ 3 is a factor . hence the smallest number is 5 ^ 2 * 3 = 75 answer : d
a ) 25 , b ) 27 , c ) 45 , d ) 75 , e ) 125
d
multiply(power(5, 2), 3)
power(n0,n1)|multiply(n2,#0)
other
D
60 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
"orange + mango - apple = 7 mango + apple - orange = 10 apple = 60 orange + mango + apple = 4 60 + 10 + 4 - 7 = 67 like apple answer : e"
a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 67
e
add(add(subtract(60, 4), 7), subtract(10, 7))
subtract(n0,n3)|subtract(n2,n1)|add(n1,#0)|add(#2,#1)|
general
E
in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.0 , 9.0 , 6.0 , and 8.8 , what was the point value of the dive ?
"degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.8 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8 + 8.8 ) = 24.3 point of value of the dive = 24 * 3.2 = 77.76 answer e"
a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 77.76
e
multiply(add(add(7.5, 8.0), 8.8), 3.2)
add(n4,n5)|add(n8,#0)|multiply(n3,#1)|
general
E
the average weight of 25 girls increases by 1 kg when a new girl comes in place of one of them weighing 55 kg . what might be the weight of the new girl ?
"total weight increased = 25 x 1 kg = 25 kg . weight of new person = 55 + 25 kg = 80 kg answer : d"
a ) 85 kg , b ) 90 kg , c ) 83 kg , d ) 80 kg , e ) 82 kg
d
add(multiply(25, 1), 55)
multiply(n0,n1)|add(n2,#0)|
general
D
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 16 cm height . what is the diameter of each sphere ?
"volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 64 cm ^ 3 r = 4 cm d = 8 cm the answer is c ."
a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
c
multiply(divide(divide(divide(divide(multiply(divide(volume_cylinder(divide(16, const_2), 16), const_pi), const_3), const_4), 12), const_4), const_4), const_2)
divide(n1,const_2)|volume_cylinder(#0,n2)|divide(#1,const_pi)|multiply(#2,const_3)|divide(#3,const_4)|divide(#4,n0)|divide(#5,const_4)|divide(#6,const_4)|multiply(#7,const_2)|
physics
C
the average of 11 numbers is 10.7 . if the average of first 6 is 10.5 and that of the last 6.00001 is 11.4 the sixth number is ?
explanation : 1 to 11 = 11 * 10.7 = 117.7 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.4 = 68.4 63 + 68.4 = 131.4 – 117.7 = 13.7 6 th number = 13.7 d )
a ) 9 , b ) 9.2 , c ) 10 , d ) 13.7 , e ) 12
d
subtract(add(multiply(11.4, 6), multiply(10.5, 6)), multiply(11, 10.7))
multiply(n2,n5)|multiply(n2,n3)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2)
general
D
the area of a triangle is with base 3 m and height 10 m ?
"1 / 2 * 3 * 5 = 15 m 2 answer : c"
a ) 88 m 2 , b ) 10 m 2 , c ) 66 m 2 , d ) 15 m 2 , e ) 31 m 2
c
triangle_area(3, 10)
triangle_area(n0,n1)|
geometry
C
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 26 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
"1 h - - - - - 5 ? - - - - - - 60 12 h rs = 26 + 21 = 47 t = 12 d = 47 * 12 = 564 answer : b"
a ) 288 , b ) 564 , c ) 877 , d ) 278 , e ) 178
b
add(multiply(divide(60, subtract(21, 26)), 26), multiply(divide(60, subtract(21, 26)), 21))
subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(#2,#3)|
physics
B
a school has received 30 % of the amount it needs for a new building by receiving a donation of $ 500 each from people already solicited . people already solicited represent 60 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
"let us suppose there are 100 people . 60 % of them donated $ 30000 ( 500 * 60 ) $ 30000 is 30 % of total amount . so total amount = 30000 * 100 / 60 remaining amount is 70 % of total amount . 70 % of total amount = 30000 * ( 100 / 60 ) * ( 70 / 100 ) = 35000 this amount has to be divided by 40 ( remaining people are 40 ) so per head amount is 35000 / 40 = $ 875 ; answer : e"
a ) $ 200 , b ) $ 250 , c ) $ 100 , d ) $ 350 , e ) $ 875
e
divide(multiply(divide(multiply(divide(60, const_100), 500), divide(30, const_100)), divide(60, const_100)), divide(30, const_100))
divide(n2,const_100)|divide(n0,const_100)|multiply(n1,#0)|divide(#2,#1)|multiply(#3,#0)|divide(#4,#1)|
general
E
what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7
explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a
a ) 2 / 15 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
a
subtract(divide(4, 5), divide(2, 3))
divide(n3,n5)|divide(n0,n1)|subtract(#0,#1)
general
A
find the compound interest on $ 1200 for 4 years at 20 % p . a . if ci is component yearly ?
"a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 4 = $ 2488 ci = $ 1288 answer is c"
a ) $ 120 , b ) $ 150 , c ) $ 1288 , d ) $ 250 , e ) $ 300
c
subtract(multiply(1200, power(add(const_1, divide(20, const_100)), 4)), 1200)
divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0)|
gain
C
find a sum for 1 st 6 prime number ' s ?
"required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option a"
a ) 41 , b ) 28 , c ) 30 , d ) 34 , e ) 36
a
add(add(add(add(add(add(add(add(const_2, const_3), add(const_2, const_3)), add(add(const_2, const_3), const_2)), add(6, const_2)), add(add(6, const_2), const_2)), add(add(add(6, const_2), const_2), const_4)), add(add(add(add(6, const_2), const_2), const_4), const_2)), add(add(add(add(add(6, const_2), const_2), const_4), const_2), const_4))
add(const_2,const_3)|add(n1,const_2)|add(#0,#0)|add(#0,const_2)|add(#1,const_2)|add(#2,#3)|add(#4,const_4)|add(#5,#1)|add(#6,const_2)|add(#7,#4)|add(#8,const_4)|add(#9,#6)|add(#11,#8)|add(#12,#10)|
general
A
in a games hour 4 different types of players came to the ground ? cricket 15 , hokey 12 , football 13 , softball 15 . how many players are present in the ground ?
"total number of players = 15 + 12 + 13 + 15 = 55 answer is c"
a ) 70 , b ) 52 , c ) 55 , d ) 49 , e ) 50
c
add(add(15, 12), add(13, 15))
add(n1,n2)|add(n3,n4)|add(#0,#1)|
physics
C
points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction s of the area of triangle abc is the area of triangle xyz ?
"if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives s = 1 / 9 . a"
a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
a
divide(divide(power(const_4, const_2), const_2), divide(power(add(const_10, const_2), const_2), const_2))
add(const_10,const_2)|power(const_4,const_2)|divide(#1,const_2)|power(#0,const_2)|divide(#3,const_2)|divide(#2,#4)|
geometry
A
potato chips are on sale , buy 2 get 1 free . there are only 9 bags of chips left ( 4 plain and 5 bbq ) . a shopper randomly grabs 3 bags . what is the probability the shopper will grab exactly 3 bags of bbq chips ?
combination probability formula : ncr = n ! / [ r ! ( n - r ) ! ] total possible , select 3 bags from 9 bags = 9 c 3 = 9 ! / [ 3 ! ( 9 - 3 ) ! ] = 84 . to have 3 bbq there must be 0 plain , select 0 plain from 4 = 4 c 0 = 1 . and , select 3 bbq from 5 = 5 c 3 = 10 . 3 bbq and 0 plain = ( 1 ) ( 10 ) = 10 probability = ( number outcomes favorable ) / ( total number outcomes ) = 10 / 84 = 5 / 42 answer : d
a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 42 , e ) 7 / 42
d
multiply(divide(subtract(subtract(5, const_1), const_1), subtract(subtract(9, const_1), const_1)), multiply(divide(5, 9), divide(subtract(5, const_1), subtract(9, const_1))))
divide(n4,n2)|subtract(n4,const_1)|subtract(n2,const_1)|divide(#1,#2)|subtract(#1,const_1)|subtract(#2,const_1)|divide(#4,#5)|multiply(#0,#3)|multiply(#6,#7)
probability
D
if 40 honey bees make 40 grams of honey in 40 days , then 1 honey bee will make 1 gram of honey in how many days ?
"explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 40 : : 40 : x honey 40 : 1 = > 1 x 40 x x = 40 x 1 x 40 = > x = 40 . answer : c"
a ) 1 , b ) 3.5 , c ) 40 , d ) 49 , e ) 30
c
divide(1, divide(1, 40))
divide(n3,n0)|divide(n3,#0)|
physics
C
find the value of 72516 x 9999 = m ?
"72516 x 9999 = 72516 x ( 10000 - 1 ) = 72516 x 10000 - 72516 x 1 = 725160000 - 72516 = 725087484 c"
a ) 456578972 , b ) 436567874 , c ) 725087484 , d ) 725117481 , e ) 357889964
c
multiply(subtract(9999, const_4), 72516)
subtract(n1,const_4)|multiply(#0,n0)|
general
C
solution a is made up of alcohol and water mixed in the ratio of 21 : 4 by volume ; solution b is made up of alcohol and water mixed in the ratio of 2 : 3 by volume . if solution a and solution b are mixed in the ratio of 5 : 6 by volume , what percent of the resultant mixture is alcohol ?
let mixture after mixing a and b is 110 ml ( number assumed for calculation because of 5 : 6 ) now solution a is 50 ml and solu b is 60 ml further in a 100 ml a contains 84 ml alch so 50 ml contain 42 ml in mix b 100 ml solution contain 40 ml alc , 60 ml of b , it will be 24 ml alcohol . so 42 + 24 = 66 in 110 ml solution which is 60 % answer : c
a ) 32.5 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) can not be determined
c
multiply(add(multiply(divide(21, add(21, 4)), divide(5, add(5, 6))), multiply(divide(2, add(2, 3)), divide(6, add(5, 6)))), const_100)
add(n0,n1)|add(n4,n5)|add(n2,n3)|divide(n0,#0)|divide(n4,#1)|divide(n2,#2)|divide(n5,#1)|multiply(#3,#4)|multiply(#5,#6)|add(#7,#8)|multiply(#9,const_100)
other
C
a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 35 ) + 2 = 2 ( x + 2 ) x + 37 = 2 x + 4 x = 33 . answer : e"
a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 33 years
e
divide(subtract(35, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))
multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)|
general
E
one night 16 percent of the female officers on a police force were on duty . if 160 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
"let x be the number of female police officers on the police force . the number of female police officers on duty was 80 . 0.16 x = 80 x = 500 the answer is a ."
a ) 500 , b ) 650 , c ) 800 , d ) 950 , e ) 1100
a
divide(divide(160, const_2), divide(16, const_100))
divide(n1,const_2)|divide(n0,const_100)|divide(#0,#1)|
gain
A
the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 3 years ?
"formula : ( after = 100 denominator ago = 100 numerator ) 10000 Γ— 120 / 100 ^ 3 = 17280 b )"
a ) 14300 , b ) 17280 , c ) 14500 , d ) 14600 , e ) 15400
b
add(10000, multiply(divide(multiply(10000, 20), const_100), 3))
multiply(n0,n1)|divide(#0,const_100)|multiply(#1,n2)|add(n0,#2)|
gain
B
a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
"total subjects = 4 + 3 + 3 = 10 max subjects by 1 teacher = 2 so , min of teachers required = 10 / 2 = 5 answer : b"
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
b
divide(add(add(4, 3), 3), 2)
add(n0,n1)|add(n2,#0)|divide(#1,n3)|
general
B
a and b can do a piece of work in 7 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
"c = 1 / 4 Γ’ € β€œ 1 / 7 = 3 / 28 = > 28 / 3 = 9 1 / 3 days answer : b"
a ) 33 , b ) 9 1 / 3 , c ) 30 , d ) 88 , e ) 11
b
inverse(subtract(4, divide(4, 7)))
divide(n1,n0)|subtract(n1,#0)|inverse(#1)|
physics
B
everyone shakes hands with everyone else in a room . total number of handshakes is 120 . number of persons = ?
"in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 120 or n ( n - 1 ) = 240 or n = 16 answer is ( e )"
a ) a . 14 , b ) b . 12 , c ) c . 11 , d ) d . 15 , e ) e . 16
e
divide(divide(multiply(120, const_2), const_3), const_4)
multiply(n0,const_2)|divide(#0,const_3)|divide(#1,const_4)|
general
E
a question paper has 2 parts , a & b , each containing 6 questions . if a student has to choose 4 from part a & 3 from part b , in how many ways can he choose the questions ?
"there 6 questions in part a out of which 4 question can be chosen as = 6 c 4 . similarly , 3 questions can be chosen from 6 questions of part b as = 6 c 3 . hence , total number of ways , = 6 c 4 * 6 c 3 = [ 6 ! / ( 2 ! 4 ! ) ] * [ 6 ! / ( 3 ! * 3 ! ) ] = { 15 } * { 6 * 5 * 4 * 3 / ( 3 * 2 * 1 ) } = 300 . d"
a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140
d
divide(multiply(choose(6, 4), choose(6, 3)), 6)
choose(n1,n2)|choose(n1,n3)|multiply(#0,#1)|divide(#2,n1)|
probability
D
find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm
"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c"
a ) 178 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
c
quadrilateral_area(15, 18, 20)
quadrilateral_area(n2,n1,n0)|
physics
C
a certain company reported that the revenue on sales increased 60 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
"assume the revenue in 2000 to be 100 . then in 2003 it would be 160 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 160 ) / 160 = 20 / 160 = 13 % answer : e ."
a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 13 %
e
multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(60, const_100))), add(const_1, divide(60, const_100))), const_100)
divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(#2,#3)|divide(#4,#3)|multiply(#5,const_100)|
gain
E
sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 06 : 00 and starts climbing at a constant pace . ken starts climbing only at 08 : 00 , when sari is already 800 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
both sari and ken climb in the same direction . speed of sari = 800 / 2 = 400 meters / hr ( since she covers 800 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 800 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 800 + 50 ) / ( 500 - 400 ) = 8.5 hrs starting from 8 : 00 , in 8.5 hrs , the time will be 16 : 30 answer ( a )
a ) 16.3 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
a
add(divide(add(800, 50), subtract(500, divide(800, const_2))), 8)
add(n4,n6)|divide(n4,const_2)|subtract(n5,#1)|divide(#0,#2)|add(n2,#3)
physics
A
the length of rectangle is thrice its breadth and its perimeter is 48 m , find the area of the rectangle ?
"2 ( 3 x + x ) = 48 l = 18 b = 6 lb = 18 * 6 = 108 answer : b"
a ) 432 , b ) 108 , c ) 252 , d ) 992 , e ) 212
b
multiply(multiply(divide(48, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(48, add(multiply(const_3, const_2), multiply(const_1, const_2))))
multiply(const_2,const_3)|multiply(const_1,const_2)|add(#0,#1)|divide(n0,#2)|multiply(#3,const_3)|multiply(#3,#4)|
geometry
B
if a 2 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
"the area a of the large cube is 2 * 2 * 6 = 24 square cm . the area of the 8 small cubes is 8 * 6 = 48 = 2 a , an increase of 100 % . the answer is b ."
a ) 50 % , b ) 100 % , c ) 150 % , d ) 200 % , e ) 250 %
b
multiply(const_100, divide(multiply(surface_cube(1), surface_cube(2)), surface_cube(2)))
surface_cube(n1)|surface_cube(n0)|multiply(#0,#1)|divide(#2,#1)|multiply(#3,const_100)|
geometry
B
at a kennel with 80 dogs , 45 of the dogs wear tags and 40 wear flea collars . if 6 of the dogs wear both , then how many of the dogs wear neither a collar nor tags ?
dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 ) dogs wear neither a collar nor tags = 80 - 79 dogs wear neither a collar nor tags = 80 - 79 hence , answer will be 1 answer : a
a ) 1 , b ) 6 , c ) 34 , d ) 79 , e ) 85
a
subtract(80, subtract(add(45, 40), 6))
add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)
other
A
a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ?
imo it should be c that is 3 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 200 1 b + 6 c = 220 solving both we get b that is bat = 40 and c that is ball = 30 new equation 210 to be divided in equal 3 b + 3 c = 210 3 * 40 + 3 * 30 = 210 120 + 90 = 210
['a ) 1', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 5']
c
divide(210, add(subtract(220, multiply(6, divide(subtract(220, divide(200, const_2)), 4))), divide(subtract(220, divide(200, const_2)), 4)))
divide(n2,const_2)|subtract(n5,#0)|divide(#1,n1)|multiply(n4,#2)|subtract(n5,#3)|add(#2,#4)|divide(n6,#5)
geometry
C
there were two candidates in an election . winner candidate received 62 % of votes and won the election by 408 votes . find the number of votes casted to the winning candidate ?
"w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 408 62 % - - - - - - - - ? = > 1054 answer : b"
a ) 288 , b ) 1054 , c ) 788 , d ) 298 , e ) 177
b
divide(multiply(divide(408, divide(subtract(62, subtract(const_100, 62)), const_100)), 62), const_100)
subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)|
gain
B
john makes $ 60 a week from his job . he earns a raise and now makes $ 110 a week . what is the % increase ?
"increase = ( 50 / 60 ) * 100 = ( 5 / 6 ) * 100 = 83.33 % . b"
a ) 16 % , b ) 83.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
b
multiply(divide(subtract(110, 60), 60), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
B
if 10 % of 30 % of 50 % of a number is 90 , then what is the number ?
"let the number be a given , 10 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 1 / 10 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 6000 . answer : b"
a ) 4000 , b ) 6000 , c ) 4400 , d ) 4500 , e ) none of these
b
divide(90, multiply(multiply(divide(50, const_100), divide(30, const_100)), divide(10, const_100)))
divide(n0,const_100)|divide(n2,const_100)|divide(n1,const_100)|multiply(#1,#2)|multiply(#0,#3)|divide(n3,#4)|
gain
B
weights of two friends ram and shyam are in the ratio 1 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
solution : given ratio of ram and shayam ' s weight = 1 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 1 / 5 or , x = 16 % . answer : option d
a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
d
add(15, multiply(subtract(15, 10), divide(1, 5)))
divide(n0,n1)|subtract(n4,n2)|multiply(#0,#1)|add(n4,#2)
gain
D
two trains are traveling from point a to point b such that the speed of first train is 65 kmph and the speed of 2 train is 29 kmph . where is the distance b / w a and b such that the slower train reached 5 hrs late compared to the faster ?
answer : b
a ) 3 , b ) 65 , c ) 9 , d ) 5 , e ) 31
b
speed(multiply(65, divide(multiply(29, 5), subtract(65, 29))), divide(multiply(29, 5), subtract(65, 29)))
multiply(n2,n3)|subtract(n0,n2)|divide(#0,#1)|multiply(n0,#2)|speed(#3,#2)
physics
B
a train 100 m long crosses a platform 200 m long in 15 sec ; find the speed of the train ?
"d = 100 + 200 = 300 t = 15 s = 300 / 15 * 18 / 5 = 72 kmph answer : c"
a ) 94 kmph , b ) 58 kmph , c ) 72 kmph , d ) 94 kmph , e ) 59 kmph
c
subtract(multiply(15, multiply(200, const_0_2778)), 100)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
physics
C
a envelop weight 8.5 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
"800 * 8.5 6800.0 gm 6.8 kg answer : b"
a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
b
divide(multiply(8.5, 800), const_1000)
multiply(n0,n1)|divide(#0,const_1000)|
general
B
a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 70 percent of its games that season , what was the total number of games that the team played ?
"70 % is 30 % - points above 40 % and 10 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 1 : 3 . so the team played a total of 30 + 90 = 120 games . the answer is c ."
a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 180
c
divide(multiply(30, divide(40, const_100)), subtract(divide(80, const_100), divide(70, const_100)))
divide(n0,const_100)|divide(n2,const_100)|divide(n3,const_100)|multiply(n1,#0)|subtract(#1,#2)|divide(#3,#4)|
gain
C
a box contain red , blue and green colored balls . the number of red balls is 80 and the number of blue balls is 60 . the number of green balls subtracted from the number of red balls is the same as the number of green balls added with the number of blue balls . then the number of green balls is ?
answer let the number of green balls be x . then , x - 60 = 80 - x Γ’ ‑ ’ 2 x = 80 + 60 = 140 Γ’ ‑ ’ 2 x = 140 Γ’ Λ† Β΄ x = 70 correct option : b
a ) 80 , b ) green balls = 70 , c ) 60 , d ) 85 , e ) 140
b
divide(subtract(80, 60), const_2)
subtract(n0,n1)|divide(#0,const_2)
general
B
a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 24 gallons of gasoline ?
so 12.2 * 24 = 292 . . imo option d is correct answer . .
a ) 190 , b ) 284.6 , c ) 300 , d ) 292 , e ) 312
d
multiply(12.2, 24)
multiply(n0,n2)
general
D
the perimeter of a semi circle is 126 cm then the radius is ?
"36 / 7 r = 126 = > r = 24.5 answer : d"
a ) 22 , b ) 28 , c ) 98 , d ) 24.5 , e ) 13
d
divide(126, add(const_2, const_pi))
add(const_2,const_pi)|divide(n0,#0)|
physics
D
the total of 334 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 334 - x ) . 0.20 * ( x ) + 0.25 ( 334 - x ) = 71 = > x = 250 . . answer : a ) 250"
a ) 250 , b ) 277 , c ) 278 , d ) 200 , e ) 288
a
divide(subtract(multiply(334, 25), multiply(71, const_100)), subtract(25, 20))
multiply(n0,n2)|multiply(n3,const_100)|subtract(n2,n1)|subtract(#0,#1)|divide(#3,#2)|
general
A
if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 5 * 7 * 9 = 68 then find , 7 * 9 * 11 = ?
a 106 ( 11 * 9 ) + 7 = 106
a ) 106 , b ) 49 , c ) 68 , d ) 38 , e ) 55
a
add(multiply(9, 11), 7)
multiply(n10,n14)|add(n6,#0)
general
A
the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?
"there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 250 - 168 = 281 range is therefore 128 - 42 = 86 answer e"
a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 86
e
subtract(subtract(multiply(50, add(const_2, const_3)), multiply(42, const_4)), 42)
add(const_2,const_3)|multiply(n1,const_4)|multiply(n0,#0)|subtract(#2,#1)|subtract(#3,n1)|
general
E
a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 6 tons ?
"the weight of one car and one truck is 6.75 tons . 70 / 6.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is a ."
a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
a
add(divide(70, add(0.75, 6)), divide(70, add(0.75, 6)))
add(n1,n2)|divide(n0,#0)|add(#1,#1)|
general
A
how many factors of 880 are odd numbers greater than 1 ?
when factorized , 880 has 6 prime factors . of these prime factors 2 are odd and 4 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 4 . the total number of odd factors greater than 1 are 3 . ( option a )
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
a
divide(const_60.0, multiply(const_10, const_2))
multiply(const_10,const_2)|divide(const_60.0,#0)|
other
A
joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 90 . he was allowed to drop his lowest score . after doing so , his average test score improved to 85 . what is the lowest test score that was dropped ?
"the arithmetic mean of 4 equally weighted tests was 90 . so what we can assume is that we have 4 test scores , each 90 . he dropped his lowest score and the avg went to 95 . this means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 90 . so the lowest score = 90 - 15 = 75 answer ( d )"
a ) 20 , b ) 25 , c ) 55 , d ) 75 , e ) 80
d
subtract(multiply(90, 4), multiply(85, const_3))
multiply(n0,n1)|multiply(n2,const_3)|subtract(#0,#1)|
general
D
the tax on a commodity is diminished by 16 % and its consumption increased by 15 % . the effect on revenue is ?
100 * 100 = 10000 84 * 115 = 9660 - - - - - - - - - - - 10000 - - - - - - - - - - - 340 100 - - - - - - - - - - - ? = > 3.4 % decrease answer : c
a ) 2 % , b ) 3.8 % , c ) 3.4 % , d ) 3.6 % , e ) 1 %
c
subtract(const_100, multiply(multiply(add(const_1, divide(15, const_100)), subtract(const_1, divide(16, const_100))), const_100))
divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)
general
C
evaluate : 50 - 12 * 3 * 2 = ?
"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 50 - 12 * 3 * 2 = 50 - 8 = 42 correct answer e"
a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 42
e
subtract(50, multiply(multiply(12, 3), 2))
multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|
general
E
if 15 men , working 9 hours a day , can reap a field in 16 days , in how many days will 18 men reap the field , working 8 hours a day ?
let the required number of days be x . more men , less days ( indirect proportion ) less hours per day , more days ( indirect proportion ) men 18 : 15 hours per day 8 : 9 } : : 16 : x ( 18 x 8 x x ) = ( 15 x 9 x 16 ) = x = ( 44 x 15 ) 144 = 15 hence , required number of days = 15 . answer is b .
a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) none of them
b
divide(multiply(multiply(15, 9), 16), multiply(18, 8))
multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)
physics
B
the sum of two numbers is 56 , and one of them is 12 more than the other . what are the two numbers ?
"in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 56 : word problem = 56 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 56 Γ’ Λ† ’ 12 = 44 . x = 44 / 2 = 22 . this is the first number . therefore the other number is x + 12 = 22 + 12 = 34 . the sum of 22 + 34 is 56 . b"
a ) 36 - 48 , b ) 22 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63
b
divide(subtract(56, 12), const_2)
subtract(n0,n1)|divide(#0,const_2)|
general
B
a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is :
"according to given condition vt = ( v + 3 ) ( t - 2 / 3 ) vt = ( v - 2 ) ( t + 2 / 3 ) here v is velocity in kmph , t is time in hours and 2 / 3 is value of 40 min in hour on solving we will get t = 10 / 3 and and v = 12 so distance = ( 10 / 3 ) * 12 = 40 kms answer : d"
a ) 35 , b ) 36 , c ) 37 , d ) 40 , e ) 45
d
multiply(multiply(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), divide(40, const_60)), add(const_1, divide(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), 3)))
divide(n1,const_60)|multiply(n0,n2)|subtract(n0,n2)|multiply(n2,#1)|divide(#3,#2)|divide(#4,n0)|multiply(#4,#0)|add(#5,const_1)|multiply(#7,#6)|
physics
D
walking at 5 / 6 th of its usual speed a cab is 5 mnts late . find its usual time to cover the journey ?
"new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 5 m ut / 5 = 5 m ut = 25 m answer is a"
a ) 25 m , b ) 45 m , c ) 32 m , d ) 50 m , e ) 62 m
a
multiply(5, 5)
multiply(n0,n2)|
physics
A
an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 20000 people who applied for the army and 196 were finally selected , what was the value of n ?
"step ( 1 ) 8000 accepted . step ( 2 ) another 40 % of 8000 = 3200 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 3200 = 1600 step ( 4 ) 50 % of 1600 = 800 step ( 5 ) 50 % of 800 = 400 step ( 6 ) 50 % of 400 = 200 70 % of 400 = 280 and last step of accepting 70 % of 280 = 196 ( our target ) total 8 steps required . ans d"
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
d
add(add(const_2, add(const_1, const_4)), const_2)
add(const_1,const_4)|add(#0,const_2)|add(#1,const_2)|
general
D
5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitude test were same as their score in the first test , by approximately what percentage was derek ' s score less than the average score of the 5 people in the second aptitude ?
average score in first test be x so derby score = 0.5 x ( first test ) derby score = 1.5 ( 0.5 x ) ( second test ) = . 75 x so less than x by . 25 answer a 25 %
a ) 25 % , b ) 28 % , c ) 33 % , d ) 40 % , e ) 50 %
a
divide(multiply(50, multiply(5, 5)), 50)
multiply(n0,n0)|multiply(n1,#0)|divide(#1,n1)
general
A
if k is a non - negative integer and 18 ^ k is a divisor of 624,938 then 6 ^ k - k ^ 6 =
"6 + 2 + 4 + 9 + 3 + 8 = 32 , so this number is not divisible by 3 and thus not divisible by 18 . therefore , k = 0 6 ^ k - k ^ 6 = 1 - 0 = 1 the answer is b ."
a ) 0 , b ) 1 , c ) 36 , d ) 118 , e ) 420
b
subtract(power(6, subtract(const_1, const_1)), power(subtract(const_1, const_1), 6))
subtract(const_1,const_1)|power(n2,#0)|power(#0,n2)|subtract(#1,#2)|
general
B
a school has received 40 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
"let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 77.78 e"
a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 77.78
e
divide(multiply(divide(multiply(divide(40, const_100), 400), divide(40, const_100)), divide(40, const_100)), divide(40, const_100))
divide(n2,const_100)|divide(n0,const_100)|multiply(n1,#0)|divide(#2,#1)|multiply(#3,#0)|divide(#4,#1)|
general
E
the ages of 2 persons differ by 38 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
"age of the younger person = x age of the elder person = x + 38 6 ( x - 12 ) = x + 38 - 12 x = 19.6 age of elder person = 19.6 + 38 = 57.6 answer is e"
a ) 30.5 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 57.6
e
subtract(add(divide(multiply(2, 38), subtract(38, const_1)), 38), 2)
multiply(n0,n1)|subtract(n1,const_1)|divide(#0,#1)|add(n1,#2)|subtract(#3,n0)|
general
E
find the average of first 4 multiples of 9 ?
"average = ( 9 + 18 + 27 + 36 ) / 4 = 22.5 answer is c"
a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 40.8
c
divide(add(add(add(4, const_1), add(add(4, const_1), const_2)), add(subtract(9, 4), subtract(9, const_2))), 4)
add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,n0)|
general
C
if a man buys 1 liter of milk for 12 rs . and mixes it with 20 % water and sells it for 15 rs then what is the % age of gain . . .
quantity after adding 20 % water = 1.2 liter sp of 1.2 lit . @ 15 rs . / liter = 15 * 1.2 = 18 rs cp = 12 rs / lit . % profit = 100 * ( 18 - 12 ) / 12 = 50 answer : c
a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
c
multiply(divide(subtract(multiply(add(1, divide(20, const_100)), 15), 12), 12), const_100)
divide(n2,const_100)|add(n0,#0)|multiply(n3,#1)|subtract(#2,n1)|divide(#3,n1)|multiply(#4,const_100)
gain
C
a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
"30 % of 2 litres = 0.6 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 3.0 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 30 % answer : a"
a ) 30 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
a
multiply(divide(add(multiply(divide(30, const_100), 2), multiply(divide(40, const_100), 6)), 10), const_100)
divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(#2,#3)|divide(#4,n5)|multiply(#5,const_100)|
general
A
a is the product of each integer from 1 to 50 , inclusive and b = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of a ?
the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≀ n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10 + 2 = 12 100 ^ k = 10 ^ 2 k β†’ k = 12 / 2 = 6 a
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
a
divide(add(divide(50, divide(const_10, const_2)), const_2), const_2)
divide(const_10,const_2)|divide(n1,#0)|add(#1,const_2)|divide(#2,const_2)
general
A
the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 ?
"5 / 6 * 3 / 2 * 4 / 5 = 1 / 1 1 : 1 answer : d"
a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 2 , d ) 1 : 1 , e ) 1 : 7
d
divide(divide(multiply(5, 3), multiply(6, 2)), divide(multiply(3, 4), multiply(2, 5)))
multiply(n0,n2)|multiply(n1,n3)|multiply(n2,n4)|multiply(n3,n5)|divide(#0,#1)|divide(#2,#3)|divide(#4,#5)|
other
D
if a car had traveled 20 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 60 km , at what speed did it travel ?
"time = distance / speed difference in time = 1 / 2 hrs 60 / x - 60 / ( x + 20 ) = 1 / 2 substitute the value of x from the options . - - > x = 40 - - > 60 / 40 - 60 / 60 = 3 / 2 - 1 = 1 / 2 answer : b"
a ) 35 kmh , b ) 40 kmh , c ) 50 kmh , d ) 60 kmh , e ) 65 kmh
b
divide(subtract(sqrt(add(multiply(multiply(const_2, multiply(60, 20)), const_4), power(20, const_2))), 20), const_2)
multiply(n0,n2)|power(n0,const_2)|multiply(#0,const_2)|multiply(#2,const_4)|add(#3,#1)|sqrt(#4)|subtract(#5,n0)|divide(#6,const_2)|
physics
B
exactly 30 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
let ' s assume there are 100 reporters - - > 30 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 30 ( # of reporters who cover local politics ) : 0.75 x = 30 - - > x = 40 , hence 40 reporters cover politics and the rest 100 - 40 = 60 reporters do not cover politics at all . answer : c .
a ) 20 % , b ) 42 % , c ) 60 % , d ) 80 % , e ) 84 %
c
multiply(subtract(const_1, divide(30, subtract(const_100, 25))), const_100)
subtract(const_100,n1)|divide(n0,#0)|subtract(const_1,#1)|multiply(#2,const_100)
gain
C
employees of a certain company are each to receive a unique 5 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , and 4 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
there are 3 ! ways to make codes starting with 12 . there are 3 ! ways to make codes starting with 24 . the number of codes is 2 * 3 ! = 12 . the answer is b .
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
b
multiply(multiply(const_2, const_3), 2)
multiply(const_2,const_3)|multiply(n3,#0)
general
B
what is 35 % of 4 / 13 of 650 ?
"this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 650 , or 1 / 9 of 650 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 650 is a bit more than 630 , so ( 1 / 9 ) * 630 will be about 70 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the answer is c ."
a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
c
divide(multiply(35, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)
add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)|
gain
C
what is the 4 digit number whose second digit is thrice the first digit and 3 rd digit is sum of 1 st and 2 nd and last digit is thrice the second digit .
let four digits is a , b , c & d . . . so by given b is 3 a c is 4 a d is 9 a so ans is 1349 answer : b
a ) 2674 , b ) 1349 , c ) 3343 , d ) 3678 , e ) 3679
b
add(add(add(multiply(const_100, const_10), multiply(multiply(1, const_3), const_100)), multiply(add(multiply(1, const_3), 1), const_10)), multiply(const_3, multiply(1, const_3)))
multiply(const_10,const_100)|multiply(n2,const_3)|add(n2,#1)|multiply(#1,const_100)|multiply(#1,const_3)|add(#0,#3)|multiply(#2,const_10)|add(#5,#6)|add(#7,#4)
general
B
the unit digit in the product ( 891 * 781 * 912 * 463 ) is :
"explanation : unit digit in the given product = unit digit in ( 1 * 1 * 2 * 3 ) = 6 answer : c"
a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
c
subtract(multiply(multiply(multiply(891, 781), 912), 463), subtract(multiply(multiply(multiply(891, 781), 912), 463), add(const_4, const_4)))
add(const_4,const_4)|multiply(n0,n1)|multiply(n2,#1)|multiply(n3,#2)|subtract(#3,#0)|subtract(#3,#4)|
general
C
an woman swims downstream 45 km and upstream 25 km taking 5 hours each time ; what is the speed of the current ?
"45 - - - 5 ds = 9 ? - - - - 1 25 - - - - 5 us = 5 ? - - - - 1 s = ? s = ( 9 - 5 ) / 2 = 2 answer : a"
a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 2.1
a
divide(subtract(divide(45, 5), divide(25, 5)), const_2)
divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)|
physics
A