Datasets:
ericsun153
/
mathqa_shuffle_question_test

Dataset card Data Studio Files
xet
Community
Problem
stringlengths
11
628
Rationale
stringlengths
1
2.74k
options
stringlengths
37
137
correct
stringclasses
5 values
annotated_formula
stringlengths
6
848
linear_formula
stringlengths
7
357
category
stringclasses
6 values
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
"relative speed = ( 126 - 54 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 27 sec = 14 * 20 = 280 m . the length of the faster train = 280 m . answer : a"
a ) 280 , b ) 290 , c ) 300 , d ) 310 , e ) 320
a
multiply(divide(subtract(126, 54), const_3_6), 14)
subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)|
physics
in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters .
"there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 17 , square it and see what would be the remainder upon division of it by 12 . n = 19 - - > n ^ 2 = 361 - - > remainder upon division 361 by 12 is 1 . answer : b ."
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
b
subtract(power(add(17, 2), 2), multiply(12, const_4))
add(n0,n1)|multiply(n2,const_4)|power(#0,n1)|subtract(#2,#1)|
general
a palindrome is a number that reads the same forward and backward , such as 616 . how many even , 4 - digit numbers are palindromes ?
"( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) as 200 is even . = > ( 17 ^ 200 - 1 ) is completely divisible by 18 . hence , when 17 ^ 200 is divided by 18 , we will get 1 as remainder . answer is b"
a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 7
b
subtract(divide(18, const_2), multiply(17, 17))
divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)|
general
p is able to do a piece of work in 10 days and q can do the same work in 12 days . if they can work together for 5 days , what is the fraction of work left ?
"the area of each half is 100 + 4 ( 450 ) + 100 = 2000 the area that is not painted is 100 . the fraction that is not painted is 100 / 2000 = 1 / 20 = 5 % the answer is a ."
a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
a
multiply(divide(const_100, add(add(multiply(multiply(const_4, const_100), const_4), const_100), const_100)), const_100)
multiply(const_100,const_4)|multiply(#0,const_4)|add(#1,const_100)|add(#2,const_100)|divide(const_100,#3)|multiply(#4,const_100)|
geometry
if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 6 x , then f ( - 1 ) =
"( 6 * 75 ) + 47 + x > 500 450 + 47 + x > 500 497 + x > 500 = > x > 3 option d"
a ) 5 , b ) 4 , c ) 7 , d ) 3 , e ) 8
d
subtract(500, add(multiply(6, 75), 47))
multiply(n0,n1)|add(n2,#0)|subtract(n4,#1)|
general
if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is
( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e .
a ) 75 , b ) 125 , c ) 145 , d ) 175 , e ) 225
e
add(add(add(add(add(multiply(multiply(5, 7), 2), multiply(multiply(5, 7), 2)), multiply(multiply(5, 7), 2)), 7), const_4), const_4)
multiply(n0,n7)|multiply(n1,#0)|add(#1,#1)|add(#2,#1)|add(n7,#3)|add(#4,const_4)|add(#5,const_4)
other
let c be defined as the sum of all prime numbers between 0 and 30 . what is c / 3
"b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 36 work is done by a in 1 day 5 / 12 work is done by a in 36 * 5 / 12 = 15 days answer is a"
a ) 15 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
a
multiply(divide(const_1, add(divide(const_1, 9), divide(const_1, 2))), 3)
divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|divide(const_1,#2)|multiply(n3,#3)|
physics
a train passes a station platform in 34 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
"assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 26 seconds 1 pole ( 26 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 26 / 11 ) seconds = 44.9091 seconds answer : b"
a ) 44.4543 , b ) 44.9091 , c ) 44.95128 , d ) 44.91288 , e ) 44.91222
b
multiply(divide(26, 12), 20)
divide(n1,n2)|multiply(n0,#0)|
physics
in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
"p = ( 2 / 5 ) * p + 21 ( 3 / 5 ) * p = 21 p = 35 the answer is a ."
a ) $ 35 , b ) $ 36 , c ) $ 37 , d ) $ 38 , e ) $ 39
a
divide(21, subtract(1, multiply(divide(1, 5), const_2)))
divide(n1,n2)|multiply(#0,const_2)|subtract(n1,#1)|divide(n0,#2)|
general
in a school of 800 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
"the number of chocolate bars is equal to 18 ? 25 = 450 correct answer c"
a ) 350 , b ) 250 , c ) 450 , d ) 550 , e ) 650
c
multiply(18, 25)
multiply(n0,n1)|
general
the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?
"say morks income is - 100 so tax paid will be 40 say mindys income is 5 * 100 = 500 so tax paid is 30 % * 500 = 150 total tax paid = 40 + 150 = 190 . combined tax % will be 190 / 100 + 500 = 31.67 %"
a ) 32.5 % , b ) 34 % , c ) 35 % , d ) 31.67 % , e ) 37.5 %
d
multiply(const_100, divide(add(divide(40, const_100), multiply(5, divide(30, const_100))), add(const_1, 5)))
add(n2,const_1)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#2)|add(#1,#3)|divide(#4,#0)|multiply(#5,const_100)|
gain
the length of minute hand of a clock is 5.6 cm . what is the area covered by this in 10 minutes
"solution : p ( a ∪ b ) = p ( a ) + p ( b ) - p ( a ∩ b ' ) = > 0.8 = 0.4 - p ( a ∩ b ) = > p ( a ∩ b ) = 0.2 p ( a ∩ b ' ) = p ( a ) - p ( a ∩ b ) = 0.4 - 0.2 = 0.2 answer b"
a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) none
b
multiply(multiply(0.4, 0.8), const_10)
multiply(n0,n2)|multiply(#0,const_10)|
general
how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ?
"ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 26000 share of b = 6 / 13 ( 26000 ) = rs . 12000 answer : b"
a ) s . 12028 , b ) s . 12000 , c ) s . 12003 , d ) s . 12029 , e ) s . 24029
b
subtract(26000, multiply(const_60, const_100))
multiply(const_100,const_60)|subtract(n3,#0)|
gain
a can do a work in 8 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ?
"sol . on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . option b"
a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147
b
add(3105, subtract(21, reminder(3105, 21)))
reminder(n0,n1)|subtract(n1,#0)|add(n0,#1)|
general
how many numbers between 100 and 798 are divisible by 2 , 3 , and 7 together ?
"980 x 436 + 980 x 764 = 986 x ( 436 + 664 ) = 986 x 1200 = 117600 . answer is a ."
a ) 1176000 , b ) 968000 , c ) 978000 , d ) 117000 , e ) none of them
a
subtract(980, multiply(multiply(436, 980), 764))
multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|
general
a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 3 kilometer long bridge , at the same speed ?
you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
c
add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1))))
add(const_1,const_4)|divide(n0,#0)|multiply(#0,#0)|divide(n0,#2)|add(#1,#3)|
other
a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 275.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
distance covered in ( 9 × 1000 ) / ( 3600 ) × 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c .
['a ) 430 sq . m', 'b ) 425 sq . m', 'c ) 450 sq . m', 'd ) 475 sq . m', 'e ) 350 sq . m']
c
divide(multiply(multiply(12, divide(multiply(9, const_1000), multiply(const_360, const_10))), multiply(12, divide(multiply(9, const_1000), multiply(const_360, const_10)))), const_2)
multiply(n0,const_1000)|multiply(const_10,const_360)|divide(#0,#1)|multiply(n1,#2)|multiply(#3,#3)|divide(#4,const_2)
geometry
if x and y are integers such that x ^ 2 = 2 y and xy = 32 , then x – y = ?
"p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is d ."
a ) 1 / 5 , b ) 3 / 20 , c ) 2 / 15 , d ) 1 / 12 , e ) 1 / 10
d
multiply(divide(const_1, const_2), divide(const_1, const_4))
divide(const_1,const_2)|divide(const_1,const_4)|multiply(#0,#1)|
probability
the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?
"27 , 36 , 45 , . . . , 90,99 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 99 - 27 ) / ( 9 ) + 1 = 8 + 1 = 9 answer is e"
a ) 5 , b ) 15 , c ) 12 , d ) 7 , e ) 9
e
add(divide(subtract(100, 20), 9), const_1)
subtract(n1,n0)|divide(#0,n2)|add(#1,const_1)|
general
if the sides of a rectangle are increased by 25 % , what is the percentage increase in the area ?
"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : option c"
a ) a ) 72 , b ) b ) 828 , c ) c ) 50 , d ) d ) 34 , e ) e ) 35
c
triangle_area(2.5, 40)
triangle_area(n0,n1)|
geometry
having scored 94 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
answer let original price = rs . 100 . then , new price = rs . 90 . ∴ increased on rs . 90 = rs . 10 required increase % = ( 10 x 100 ) / 90 % = 111 / 9 % correct option : c
a ) 10 % , b ) 9 1 / 11 , c ) 11 1 / 9 , d ) 11 % , e ) none of these
c
add(subtract(const_100, subtract(const_100, 10)), const_2)
subtract(const_100,n0)|subtract(const_100,#0)|add(#1,const_2)
gain
the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 15 % profit ?
p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.4 = 0.6 + p ( a ) - 0.25 p ( a ) = 0.05 ans : a
a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
a
subtract(add(0.25, 0.4), 0.6)
add(n1,n2)|subtract(#0,n0)
other
at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 75 . if the restaurant serves 120 customers today , raising the average to 80 customers per day , what is the value of x ?
since 2 xy prime e factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
d
multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1))
add(const_1,const_1)|multiply(n0,#0)|multiply(#0,#1)|
other
ramesh has solved 108 questions in an examination . if he got only ‘ 0 ’ marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer .
two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a
a ) 100 , b ) 40 , c ) 66 , d ) 80 , e ) 75
a
subtract(divide(factorial(10), multiply(factorial(subtract(10, 3)), factorial(3))), divide(factorial(subtract(10, 4)), multiply(factorial(3), factorial(3))))
factorial(n0)|factorial(n2)|subtract(n0,n2)|subtract(n0,n1)|factorial(#2)|factorial(#3)|multiply(#1,#1)|divide(#5,#6)|multiply(#4,#1)|divide(#0,#8)|subtract(#9,#7)
other
last month , john rejected 0.5 % of the products that he inspected and jane rejected 1.00 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
"his percentage gain is 100 * 80 / 920 as he is gaining 80 units for his purchase of 920 units . so 8.69 % . answer : e"
a ) 5.26 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 8.69 %
e
multiply(subtract(inverse(divide(920, multiply(multiply(add(const_4, const_1), const_2), const_100))), const_1), const_100)
add(const_1,const_4)|multiply(#0,const_2)|multiply(#1,const_100)|divide(n0,#2)|inverse(#3)|subtract(#4,const_1)|multiply(#5,const_100)|
gain
the h . c . f . of two numbers is 18 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
"explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.40 * 100 = 540 answer : option d"
a ) 5.04 % , b ) 50.4 % , c ) 209 % , d ) 540 % , e ) none of these
d
multiply(5.40, const_100)
multiply(n0,const_100)|
general
ratio between rahul and deepak is 4 : 2 , after 6 years rahul age will be 22 years . what is deepak present age
"for retail price = $ 25 first maximum discounted price = 25 - 30 % of 25 = 25 - 7.5 = 17.5 price after additional discount of 20 % = 17.5 - 20 % of 17.5 = 17.5 - 3.5 = 14 answer : option a"
a ) $ 14.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 16.00 , e ) $ 18.00
a
multiply(divide(subtract(const_100, 20), const_100), multiply(divide(subtract(const_100, 30), const_100), 25.00))
subtract(const_100,n2)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(n3,#3)|multiply(#2,#4)|
gain
the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 15 terms of the arithmetic progression ?
lets take a number 20 20 / 5 = 4 20 * 5 = 100 diff = 100 - 4 = 96 % answer : a
a ) 96 % , b ) 95 % , c ) 2400 % , d ) 200 % , e ) 400 %
a
multiply(subtract(multiply(5, 5), const_1), divide(const_100, multiply(5, 5)))
multiply(n0,n0)|divide(const_100,#0)|subtract(#0,const_1)|multiply(#1,#2)
general
a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is .
explanation : let the fourth term be x . thus 56 , 16 , 49 , x are in proportion . product of extreme terms = 56 x product of mean terms = 16 x 49 since , the numbers make up a proportion therefore , 56 x = 16 49 or , x = ( 16 49 ) / 56 or , x = 14 therefore , the fourth term of the proportion is 14 . answer : b
a ) 10 , b ) 14 , c ) 40 , d ) 50 , e ) 60
b
divide(multiply(49, 16), 56)
multiply(n1,n2)|divide(#0,n0)
physics
weights of two friends ram and shyam are in the ratio 3 : 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 ?
"assume the price = 100 price during sale = 90 price after sale = 100 percent increase = 10 / 90 * 100 = 11 % approx . correct option : c"
a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 90 %
c
divide(multiply(10, const_100), subtract(const_100, 10))
multiply(n0,const_100)|subtract(const_100,n0)|divide(#0,#1)|
gain
a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 4 students left over . what is the sum of the two smallest possible values of n ?
"explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 324 . hourly wage = 324 / 36 = 9 answer : c ) 9"
a ) 2 , b ) 8 , c ) 9 , d ) 1 , e ) 2
c
divide(324, add(multiply(8, const_3), multiply(6, const_2)))
multiply(n0,const_3)|multiply(n1,const_2)|add(#0,#1)|divide(n2,#2)|
physics
3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a ’ s present age is :
solution : both fractions should be reduced before performing arithmetic operations . we get 3 * 27 / 31 + 3.27 / 3.31 = 3 * 27 / 31 + 27 / 31 = 4 * 27 / 31 = 151 / 31 answer d
a ) 0 , b ) 156 / 31 , c ) 123 / 31 , d ) 151 / 31 , e ) none
d
divide(add(subtract(add(81, multiply(27, 3)), subtract(93, 81)), const_1), 31)
multiply(n0,n1)|subtract(n4,n3)|add(n3,#0)|subtract(#2,#1)|add(#3,const_1)|divide(#4,n2)
general
there are 20 poles with a constant distance between each pole . a car takes 26 second to reach the 12 th pole . how much will it take to reach the last pole .
"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out e : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
b
add(const_10, divide(add(25, 25), const_2))
add(n2,n2)|divide(#0,const_2)|add(#1,const_10)|
general
two trains are moving in opposite directions with speed of 60 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder t as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 6,8 and 10 is 121 . c
a ) 21 , b ) 41 , c ) t = 121 , d ) 241 , e ) 481
c
add(lcm(lcm(6, 8), 10), 1)
lcm(n2,n3)|lcm(n4,#0)|add(n0,#1)
general
the l . c . m of 22 , 54 , 108 , 135 and 198 is
"e 250 e = 72 * 5 / 18 = 20 = 400 â € “ 150 = 250"
a ) 443 m , b ) 354 m , c ) 450 m , d ) 350 m , e ) 250 m
e
subtract(multiply(20, multiply(72, const_0_2778)), 150)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
physics
1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = ?
e their ages were respectively 58 and 28
a ) 60 and 23 , b ) 66 and 25 , c ) 29 and 56 , d ) 71 and 43 , e ) 58 and 28
e
divide(divide(multiply(1624, 30), const_4), const_2)
multiply(n0,n1)|divide(#0,const_4)|divide(#1,const_2)
general
a sum of money deposited at c . i . amounts to rs . 500 in 3 years and to rs . 650 in 4 years . find the rate percent ?
lcm = 72 72 - 1 = 71 answer : a
a ) 71 , b ) 70 , c ) 72 , d ) 73 , e ) 36
a
subtract(lcm(24, 36), 1)
lcm(n3,n4)|subtract(#0,n0)
general
for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score w for the exam ?
"cp = 135 * 15 = 2025 and sp = 115 * 18 = 2070 gain % = 100 * ( 2070 - 2025 ) / 2025 = 20 / 9 answer : c"
a ) 40 , b ) 30 / 11 , c ) 20 / 9 , d ) 27 / 11 , e ) 29 / 8
c
multiply(divide(subtract(multiply(115, 18), multiply(135, 15)), multiply(135, 15)), const_100)
multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)|
gain
in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
"let initial price be 100 price in day 1 after 3 % discount = 97 price in day 2 after 3 % discount = 94.09 price in day 3 after 10 % discount = 84.68 so , price in day 3 as percentage of the sale price on day 1 will be = 84.68 / 97 * 100 = > 87.3 % answer will definitely be ( c )"
a ) 85.1 % , b ) 86.9 % , c ) 87.3 % , d ) 88.8 % , e ) 89.5 %
c
add(multiply(divide(divide(10, const_100), subtract(1, divide(1, 3))), const_100), 2)
divide(n5,const_100)|divide(n1,n0)|subtract(n1,#1)|divide(#0,#2)|multiply(#3,const_100)|add(n2,#4)|
gain
in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
"number of pens = 1200 number of pencils = 820 required number of students = h . c . f . of 1200 and 820 = 20 answer is b"
a ) 40 , b ) 20 , c ) 60 , d ) 80 , e ) 65
b
gcd(1200, 820)
gcd(n0,n1)|
general
sum of 36 odd numbers is ?
this is a rather straight forward ratio problem . 1 . 80 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 80 / x thus , x = 2000 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . d
a ) 400 , b ) 625 , c ) 1,250 , d ) 2,000 , e ) 10,000
d
divide(80, divide(2, 50))
divide(n2,n1)|divide(n0,#0)
gain
in a class of 50 students , 20 play baseball , 15 play cricket and 11 play football . 7 play both baseball and cricket , 4 play cricket and football and 5 play baseball and football . if 18 students do not play any of these given sports , how many students play exactly two of these sports ?
"r is the set of positive odd integers less than 100 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 1,3 , 5,7 , 9,11 , 13,15 . . . s = 1 , 9,25 , 49,81 . . . numbers : 1 , 9 , 25 , 49 , and 81 are odd integers ( less than 100 ) that are in both sets . solution : five answer : d"
a ) none , b ) two , c ) four , d ) five , e ) seven
d
subtract(subtract(100, const_4), const_4)
subtract(n0,const_4)|subtract(#0,const_4)|
physics
a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :
"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which w is 40 % of 80 hence , d is the answer"
a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
d
divide(80, const_2)
divide(n3,const_2)|
general
the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ?
"28 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 28 = 1 / 100 * x = > x = 28000 answer : a"
a ) 28000 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27991
a
divide(divide(divide(multiply(multiply(multiply(28, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)
multiply(n3,const_100)|multiply(n4,const_100)|multiply(n5,const_100)|multiply(#0,#1)|multiply(#3,#2)|divide(#4,n0)|divide(#5,n1)|divide(#6,n2)|
physics
if 12 men and 16 boys can do a piece of work in 7 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .
"explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 20286 / - - 17640 / - = rs . 2646 / - rate of interest = ( 2646 / 17640 ) × ( 100 / 1 ) = > 15 % answer : option d"
a ) 5 % , b ) 7 % , c ) 9 % , d ) 15 % , e ) 12 %
d
multiply(divide(subtract(20286, 17640), 17640), const_100)
subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)|
general
gary ’ s gas station serves an average of 15 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
let the rate be x , then population of the bacteria after each hour can be given as 600,600 x , 600 ( x ^ 2 ) , 600 ( x ^ 3 ) now population at 4 pm = 4800 thus we have 600 ( x ^ 3 ) = 4800 = 8 thus x = 2 therefore population at 3 pm = 600 ( 4 ) = 2400 answer : a
a ) 2400 , b ) 3600 , c ) 3000 , d ) 2800 , e ) 2500
a
multiply(multiply(power(divide(multiply(multiply(2, 4), 600), 600), const_0_33), 600), power(divide(multiply(multiply(2, 4), 600), 600), const_0_33))
multiply(n2,n4)|multiply(n1,#0)|divide(#1,n1)|power(#2,const_0_33)|multiply(n1,#3)|multiply(#4,#3)
physics
a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ?
solution 5 years ago average age of a , b , c , d = 45 years = > 5 years ago total age of a , b , c , d = 45 x 4 = 180 years = > total present age of a , b , c , d = 180 + 5 x 4 = 200 years if e ' s present age is x years = 200 + x / 5 = 50 x = 50 years . answer a
a ) 50 , b ) 47 , c ) 48 , d ) 49 , e ) 46
a
subtract(multiply(50, 5), add(multiply(45, multiply(const_2, const_2)), multiply(5, const_4)))
multiply(n0,n3)|multiply(const_2,const_2)|multiply(n0,const_4)|multiply(n1,#1)|add(#3,#2)|subtract(#0,#4)
general
in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ?
"average price per book = ( 1180 + 860 ) / ( 65 + 55 ) = 2040 / 120 = $ 17 the answer is c ."
a ) $ 13 , b ) $ 15 , c ) $ 17 , d ) $ 19 , e ) $ 21
c
divide(add(1180, 860), add(65, 55))
add(n1,n3)|add(n0,n2)|divide(#0,#1)|
general
a man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 3 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
"total no of rocks = 45 probability of choosing 1 st slate rock = 15 / 45 probability of choosing 2 nd slate rock = 14 / 44 ( without replacement ) so combined probability = 15 / 45 * 14 / 44 = 7 / 66 so , answer d ."
a ) 1 / 3 , b ) 7 / 22 , c ) 1 / 9 , d ) 7 / 66 , e ) 2 / 45
d
multiply(divide(15, add(add(15, 20), 10)), divide(subtract(15, const_1), subtract(add(add(15, 20), 10), const_1)))
add(n0,n1)|subtract(n0,const_1)|add(n2,#0)|divide(n0,#2)|subtract(#2,const_1)|divide(#1,#4)|multiply(#3,#5)|
other
the sum of 55 consecutive integers is 5555 . what is the greatest integer in the set ?
"net part filled in 1 hour 1 / 4 - 1 / 9 = 5 / 36 the cistern will be filled in 36 / 5 hr = 7.2 hr answer is d"
a ) 6 hr , b ) 5.6 hr , c ) 9.5 hr , d ) 7.2 hr , e ) 4 hr
d
divide(const_1, subtract(divide(const_1, 4), divide(const_1, 9)))
divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)|
physics
today is thursday . i came home from a trip 3 days before the day after last monday . how many days have i been home ?
"answer should be e . v = \ pir ^ 2 h = \ pi * 20 ^ 2 * 7 = approximately 9000"
a ) 700 , b ) 1500 , c ) 3000 , d ) 5000 , e ) 9000
e
volume_cylinder(divide(40, const_2), 7)
divide(n0,const_2)|volume_cylinder(#0,n1)|
geometry
if there are thrice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ?
"let assume there are 100 students of which 70 are male and 30 are females if 40 are married then 60 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 40 is the total number of students who are married and out of that 20 are males then the remaining 20 will be females who are married . total females = 30 married females = 20 then single females = 30 - 20 = 10 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ e ]"
a ) 2 / 7 , b ) 5 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 / 3
e
divide(const_10, 40)
divide(const_10,n1)|
gain
find the average of all prime numbers between 1 and 5 .
"expanding we have 6 x ^ 2 - 3 x + 4 x - 2 6 x ^ 2 + x - 2 taking coefficients , a = 6 , k = 1 , n = - 2 therefore a - n + k = 6 - ( - 2 ) + 1 = 8 + 1 = 9 the answer is c ."
a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 11
c
add(add(multiply(3, 2), multiply(1, 2)), subtract(multiply(2, 2), multiply(1, 3)))
multiply(n0,n1)|multiply(n1,n3)|multiply(n1,n1)|multiply(n0,n3)|add(#0,#1)|subtract(#2,#3)|add(#4,#5)|
general
if taxi fares were $ 3.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was
"60 % of oranges = 600 100 % of oranges = ( 600 × 100 ) / 6 = 1000 total oranges = 1000 answer : c"
a ) 700 , b ) 710 , c ) 1000 , d ) 730 , e ) 740
c
add(600, multiply(600, divide(40, const_100)))
divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)|
gain
what will be the difference between simple and compound interest at 14 % per annum on a sum of rs . 1000 after 4 years ?
"the triangle with sides 196 cm , 81 cm and 277 cm is right angled , where the hypotenuse is 277 cm . area of the triangle = 1 / 2 * 81 * 196 = 7938 cm 2 answer : option e"
a ) 5000 , b ) 5656 , c ) 7878 , d ) 7900 , e ) 7938
e
divide(multiply(81, 277), const_2)
multiply(n1,n2)|divide(#0,const_2)|
geometry
the average age of a group of 10 students is 20 years . if 2 more students join the group , the average age increases by 1 year . the average age of the new students is
so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e .
a ) 90 , b ) 95 , c ) 70 , d ) 85 , e ) 50
e
subtract(divide(add(add(add(add(10, 2030), 4050), 6070), 8090), add(const_4, const_1)), multiply(multiply(const_100, const_10), const_4))
add(n0,n1)|add(const_1,const_4)|multiply(const_10,const_100)|add(n2,#0)|multiply(#2,const_4)|add(n3,#3)|add(n4,#5)|divide(#6,#1)|subtract(#7,#4)
general
a , b and c start a business each investing 20,000 . after 10 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 71400 was recorded . find the share of b .
"100 - - - 10 ds = 10 ? - - - - 1 30 - - - - 10 us = 3 ? - - - - 1 s = ? s = ( 10 - 3 ) / 2 = 3.5 answer : b"
a ) 2.5 , b ) 3.5 , c ) 4.5 , d ) 5.3 , e ) 3.4
b
divide(add(divide(30, 10), divide(100, 10)), const_2)
divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)|
physics
there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 27 , then find the smaller number ?
"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 1323 3 b 2 = 1323 b 2 = 441 = 21 ( b > 0 ) b = 21 m . answer : d"
a ) 11 , b ) 17 , c ) 18 , d ) 21 , e ) 1322
d
sqrt(divide(1323, const_3))
divide(n0,const_3)|sqrt(#0)|
geometry
in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 12 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
"let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.3 x = 4.8 alternate solution : try to backsolve . initial volume = 4.8 after one hour - - > ( 1 / 4 ) 4.8 = 1.2 after two hours - - > ( 1 / 4 ) 1.2 = 0.3 answer : c"
a ) 2.5 , b ) 3.0 , c ) 4.8 , d ) 6.5 , e ) 8.0
c
divide(divide(0.3, const_0_25), const_0_25)
divide(n4,const_0_25)|divide(#0,const_0_25)|
physics
√ ( 21 ) ^ 2
"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3.5 * 22 / 2 = 38.5 cm 2 answer : e"
a ) 22 , b ) 35 , c ) 77 , d ) 54 , e ) 38
e
triangle_area(3.5, 22)
triangle_area(n0,n1)|
geometry
6 ^ 4 − 4 ^ 4 = ?
"index for females = ( 20 - 6 ) / 20 = 7 / 10 = 0.7 index for males = ( 20 - 14 / 20 = 3 / 10 = 0.3 index for females exceeds males by 0.7 - 0.3 = 0.4 answer : a"
a ) 0.4 , b ) 0.0625 , c ) 0.2 , d ) 0.25 , e ) 0.6
a
subtract(divide(subtract(20, 6), 20), divide(6, 20))
divide(n1,n0)|subtract(n0,n1)|divide(#1,n0)|subtract(#2,#0)|
general
a 6 % stock yields 8 % . the market value of the stock is :
"x ' s 1 day ' s work = 1 / 40 y ' s 1 day ' s work = 1 / 60 ( x + y ) ' s 1 day ' s work = ( 1 / 40 + 1 / 60 ) = 1 / 24 both together will finish the work in 24 days . correct option is c"
a ) 10 , b ) 12 , c ) 24 , d ) 30 , e ) 15
c
inverse(add(divide(const_1, 40), divide(const_1, 60)))
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2)|
physics
if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ?
"let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b"
a ) 6 , b ) 8 , c ) 10 , d ) 14 , e ) 15
b
multiply(divide(36, subtract(multiply(subtract(const_10, 1), multiply(2, 1)), subtract(const_10, 1))), 2)
multiply(n0,n2)|subtract(const_10,n2)|multiply(#0,#1)|subtract(#2,#1)|divide(n1,#3)|multiply(#4,n0)|
general
3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
explanation : solution : let the required number of carpets be x . more weavers , more carpets ( direct proportion ) more days , more carpets ( direct proportion ) weavers 7 : 14 } : : 7 : x days 7 : 14 . ' . 7 * 7 * x = 14 * 14 * 7 < = > x = 14 * 14 * 7 / 7 * 7 = 28 . answer : b
a ) 14 , b ) 28 , c ) 21 , d ) 35 , e ) none of these
b
add(14, add(7, 7))
add(n0,n0)|add(n3,#0)
gain
the denominator of a fraction is 6 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 4 ⠁ „ 5 . what is the value of the original fraction ?
"sol . speed of stream = 1 / 2 ( 12 - 6 ) kmph = 3 kmph . answer c"
a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph
c
divide(subtract(12, 6), const_2)
subtract(n1,n0)|divide(#0,const_2)|
physics
the current in a river is 5 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
i year best is to give a number to his income , say 100 . . and let saving be x . . so expenditure = 100 - x next year - income = 140 savings = 2 x expenditure = 140 - 2 x . . now 140 - 2 x + 100 - x = 2 ( 100 - x ) . . . 240 - 3 x = 200 - 2 x . . . . . . . . . . . . . . . . x = 40 . . . saving % = 40 / 100 * 100 = 40 % answer : b
a ) 45 % , b ) 40 % , c ) 25 % , d ) 28 % , e ) 33.33 %
b
multiply(divide(subtract(add(add(100, 40), 100), multiply(2, 100)), const_100), const_100)
add(n0,n1)|multiply(n1,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,const_100)|multiply(#4,const_100)
general
the cross - section of a cannel is a trapezium in shape . if the cannel is 14 m wide at the top and 4 m wide at the bottom and the area of cross - section is 380 sq m , the depth of cannel is ?
"speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 40 = 15 = > x = 180 m answer : c"
a ) 615 m , b ) 240 m , c ) 180 m , d ) 197 m , e ) 691 m
c
multiply(20, multiply(54, const_0_2778))
multiply(n2,const_0_2778)|multiply(n1,#0)|
physics
in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
"speed upstream = 8.5 kmph speed downstream = 11.5 kmph total time taken = 105 / 8.5 + 105 / 11.5 = 21.48 hours answer is b"
a ) 20.48 hours , b ) 21.48 hours , c ) 22.48 hours , d ) 23.48 hours , e ) 24.48 hours
b
add(multiply(add(add(10, 1.5), subtract(10, 1.5)), 105), multiply(subtract(add(divide(105, add(10, 1.5)), divide(105, subtract(10, 1.5))), add(add(10, 1.5), subtract(10, 1.5))), const_60))
add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(n2,#0)|divide(n2,#1)|add(#3,#4)|multiply(n2,#2)|subtract(#5,#2)|multiply(#7,const_60)|add(#6,#8)|
physics
the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ?
"let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1587.75 = > x = 787 e"
a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 787
e
divide(add(const_1000, 587.75), const_2)
add(n4,const_1000)|divide(#0,const_2)|
other
1 / 0.05 is equal to
"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 a"
a ) 1636 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489
a
multiply(divide(subtract(1365, 10), subtract(6, const_1)), 6)
subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)|
general
if a and b are positive integers , and a = 20 b - 15 , the greatest common divisor of a and b can not be
widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 4 ) / 4 ) + 1 = 23 + 1 = 24 widgets inspected by both : ( ( 96 / 12 ) + 1 = 9 total : 19 + 24 - 9 = 34 hence , widgets not inspected : 98 - 34 = 64 option d
a ) 66 , b ) 68 , c ) 70 , d ) 64 , e ) 72
d
subtract(98, subtract(add(floor(divide(98, add(const_4, const_1))), floor(divide(98, const_4))), floor(divide(98, add(const_10, add(const_4, const_1))))))
add(const_1,const_4)|divide(n0,const_4)|add(#0,const_10)|divide(n0,#0)|floor(#1)|divide(n0,#2)|floor(#3)|add(#6,#4)|floor(#5)|subtract(#7,#8)|subtract(n0,#9)
other
a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?
"on dividing 3000 by 19 , we get 17 as remainder .  number to be added = ( 19 - 17 ) = 2 . answer a 2"
a ) 2 , b ) 1 , c ) 4 , d ) 18 , e ) 17
a
subtract(multiply(add(multiply(const_4, const_10), const_2), 19), 3000)
multiply(const_10,const_4)|add(#0,const_2)|multiply(n1,#1)|subtract(#2,n0)|
general
in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.35 $ . assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty . how much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75 % bigger ?
"p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( b ) - 0.45 p ( b ) = 0.55 ans : e"
a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
e
subtract(add(0.6, 0.45), 0.4)
add(n1,n2)|subtract(#0,n0)|
other
each month a retailer sells 100 identical items . on each item he makes a profit of $ 40 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
"speed = [ 36 x 5 / 18 ] m / sec = 10 m / sec time = 45 sec let the length of bridge be x metres . then , ( 130 + x ) / 45 = 10 = > 130 + x = 450 = > x = 320 m . answer : a"
a ) 320 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) 240 m
a
subtract(multiply(divide(multiply(36, speed(const_1000, const_1)), speed(const_3600, const_1)), 45), 130)
speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)|
physics
the average of 30 numbers is 25 . if each number is multiplied by 5 , find the new average ?
"total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . upto 12 terms ) . this is an a . p . with first term , a = 35 , number of terms , n = 12 , common difference d = 2 required distance = 12 / 2 ( 2 * 35 + ( 12 - 1 ) * 2 ) = 6 ( 70 + 22 ) = 552 km . correct option : c"
a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these
c
multiply(add(multiply(2, 35), multiply(subtract(12, const_1), 2)), divide(12, 2))
divide(n2,n0)|multiply(n0,n1)|subtract(n2,const_1)|multiply(n0,#2)|add(#1,#3)|multiply(#4,#0)|
physics
how many four - digit numbers that do not contain the digits 3 or 6 are there ?
"according to order of operations , 24 ? 3 ? 10 ( division and multiplication ) is done first from left to right 24 / 2 = 8 * 10 = 80 hence 11110 + 24 * 3 * 10 = 11110 + 80 = 11190 correct answer c"
a ) 90111 , b ) 52631 , c ) 11190 , d ) 65321 , e ) 11133
c
subtract(11110, multiply(multiply(24, 3), 10))
multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|
general
5 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
"360 . answer d"
a ) 720 , b ) 120 , c ) 300 , d ) 360 , e ) 333
d
subtract(subtract(subtract(divide(divide(divide(factorial(15), factorial(subtract(15, 3))), factorial(3)), const_2), 15), 15), const_10)
factorial(n0)|factorial(n1)|subtract(n0,n1)|factorial(#2)|divide(#0,#3)|divide(#4,#1)|divide(#5,const_2)|subtract(#6,n0)|subtract(#7,n0)|subtract(#8,const_10)|
physics
darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
"explanation : 2356 6532 - - - - - - - - - - - - 4176 answer : b"
a ) 6084 , b ) 4176 , c ) 2077 , d ) 2721 , e ) 1812
b
subtract(add(add(add(multiply(multiply(6, const_100), const_10), multiply(5, const_100)), multiply(3, const_10)), 2), add(add(add(const_1000, multiply(3, const_100)), multiply(5, const_10)), 6))
multiply(n0,const_100)|multiply(n3,const_100)|multiply(n1,const_10)|multiply(n1,const_100)|multiply(n3,const_10)|add(#3,const_1000)|multiply(#0,const_10)|add(#6,#1)|add(#5,#4)|add(#7,#2)|add(n0,#8)|add(n2,#9)|subtract(#11,#10)|
general
a lady starts from p towards q and realizes that at a point r , if he walks 50 km further he will be at a point s , which is as far away from r as it is from q . what is the distance between p and q if the distance between p and r is half the distance from r to q ? ( assume that p , q , r and s are all on the same straight line )
( 1000 xtx 4 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 â † ’ t = 3.2 answer a
a ) 3.2 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.5
a
divide(350, add(divide(multiply(4, 1000), const_100), divide(multiply(1400, 5), const_100)))
multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)|divide(n4,#4)|
gain
a batsman scored 120 runs which included 5 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
"n = 4 k + 1 = 5 j + 4 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 5 j + 4 . 1 , 5 , 9 = 5 ( 1 ) + 4 the next such number is 9 + 4 * 5 = 29 . 9 + 29 = 38 the answer is c ."
a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 46
c
add(add(multiply(5, const_2), 4), add(multiply(5, multiply(const_2, 4)), 4))
multiply(n2,const_2)|multiply(const_2,n3)|add(n3,#0)|multiply(n2,#1)|add(n3,#3)|add(#2,#4)|
general
a palindrome is a number that reads the same forward and backward , such as 120 . how many odd , 4 - digit numbers are palindromes ?
divisor = ( 6 * 3 ) + 7 = 25 5 * quotient = 25 quotient = 5 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 5 ) + 6 = 106 . e )
a ) 74 , b ) 78 , c ) 86 , d ) 92 , e ) 106
e
add(multiply(add(multiply(6, const_3), 7), divide(add(multiply(6, const_3), 7), 5)), 6)
multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)
general
a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , which a and b together can do it in 2 hours . how long will c alone take to do it ?
"b = 1 / 8 – 1 / 22 = 0.075 days answer : a"
a ) 0.075 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
a
inverse(subtract(inverse(8), inverse(20)))
inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)|
physics
redo ’ s manufacturing costs for sets of horseshoes include a $ 10,500 initial outlay , and $ 30 per set . they can sell the sets $ 60 . if profit is revenue from sales minus manufacturing costs , and the company producessells 1000 sets of horseshoes , what was their profit ?
"gear l - - 20 rotations per 60 seconds - - 2 rotation per 6 seconds . gear r - - 60 rotations per 60 seconds - - 6 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 4 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 4 units . required net difference should be 8 rotations = > 2 ( 6 seconds later ) = = > 12 seconds . answer : e"
a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 14 , e ) e ) 12
e
divide(divide(8, subtract(divide(60, const_60), divide(20, const_60))), const_3)
divide(n1,const_60)|divide(n0,const_60)|subtract(#0,#1)|divide(n2,#2)|divide(#3,const_3)|
physics
due to construction , the speed limit along an 5 - mile section of highway is reduced from 60 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
( ( 90 θ 33 ) θ 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 97 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 97 divided by 16 is 1 . 7 - 1 = 6 . answer : d .
a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
d
subtract(reminder(reminder(90, 33), 17), reminder(97, reminder(33, 17)))
reminder(n0,n1)|reminder(n1,n2)|reminder(#0,n2)|reminder(n3,#1)|subtract(#2,#3)
general
to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 760 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
"we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 3 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 3 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 3 or x = 1 i guess range is 3 - 1 = 2 c"
a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
c
sqrt(3)
sqrt(n1)|
general
if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value q of z - x ?
"given that 1,000 microns = 1 decimeter = 1,000 , 000,000 angstroms so , 1 micron = 1,000 , 000,000 / 1,000 = 1 , 000,000 answer : c"
a ) 1,000 , b ) 100 , c ) 1 , 000,000 , d ) 10 , e ) 10,000
c
multiply(divide(1, multiply(const_100, const_100)), multiply(const_100, const_100))
multiply(const_100,const_100)|divide(n1,#0)|multiply(#1,#0)|
general
anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?
"required difference = [ 3 1 / 2 % of $ 8400 ] – [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a ."
a ) 14 , b ) 24 , c ) 34 , d ) 12 , e ) 13
a
divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 8400), const_100)
divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)|
general
an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
"let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 63 3 x = 60 x = 20 greatest number , ( x + 2 ) = 22 . answer : d"
a ) 26 , b ) 28 , c ) 29 , d ) 22 , e ) 31
d
divide(add(63, const_1), const_2)
add(n0,const_1)|divide(#0,const_2)|
physics
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 15.00 / day for each additional week , how much does it cost to stay for 23 days ?
"p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 770 / x = 770 / 1.1 x + 10 1.1 ( 770 ) = 770 + 11 x 11 x = 77 x = 7 the answer is c ."
a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
c
divide(subtract(770, divide(770, add(divide(10, const_100), const_1))), 10)
divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)|divide(#3,n1)|
gain
a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 24.00 , how much did he pay for it ?
explanation : 20 cp = 30 sp 30 - - - 10 cp loss 100 - - - ? = > 33.33 % loss answer : c
a ) 63.33 % , b ) 34.33 % , c ) 33.33 % , d ) 31.33 % , e ) 36.33 %
c
multiply(subtract(const_1, divide(20, 30)), const_100)
divide(n0,n1)|subtract(const_1,#0)|multiply(#1,const_100)
gain
a , band c can do a piece of work in 11 days , 20 days and 20 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
"solution : given ratio of ram and shayam ' s weight = 3 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 3 / 5 or , x = 18 % . answer : option a"
a ) 18 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
a
add(15, multiply(subtract(15, 10), divide(3, 5)))
divide(n0,n1)|subtract(n4,n2)|multiply(#0,#1)|add(n4,#2)|
gain
the radius of a cone is 49 m , slant height is 35 m . find the curved surface area ?
"percent of defective produced = 7 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 7 / 100 ) * 100 % = ( 28 / 10000 ) * 100 % = ( 28 / 100 ) % = . 28 % answer b"
a ) 0.125 % , b ) 0.28 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
b
multiply(7, divide(4, const_100))
divide(n1,const_100)|multiply(n0,#0)|
gain
let c be defined as the sum of all prime numbers between 0 and 38 . what is c / 3
"solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 7 = 38 years . answer d"
a ) 14 years , b ) 17 years , c ) 19 years , d ) 38 years , e ) none
d
subtract(add(add(multiply(35, 16), 21), 35), multiply(35, 16))
multiply(n0,n1)|add(n2,#0)|add(n0,#1)|subtract(#2,#0)|
general
city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 40 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
"original price = 100 cp = 70 s = 70 * ( 180 / 100 ) = 126 100 - 126 = 26 % answer : b"
a ) 18 % , b ) 26 % , c ) 12 % , d ) 32 % , e ) 15 %
b
multiply(subtract(divide(divide(multiply(subtract(const_100, 30), add(const_100, 80)), const_100), const_100), const_1), const_100)
add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,const_1)|multiply(#5,const_100)|
gain
if 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x , then what is the value of x ?
average speed = 2 * 3 * 2 / 3 + 2 = 12 / 5 km / hr distance traveled = 12 / 5 * 5 = 12 km distance between house and school = 12 / 2 = 6 km answer is b
a ) 5 km , b ) 6 km , c ) 10 km , d ) 12 km , e ) 8 km
b
multiply(divide(5, add(divide(3, 2), const_1)), 3)
divide(n0,n1)|add(#0,const_1)|divide(n2,#1)|multiply(n0,#2)
physics
a sum of rs . 1360 has been divided among a , b and c such that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets . b ' s share is :
let length of tunnel is x meter distance = 600 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 600 + x = ( 65 / 3 ) * 60 600 + x = 20 * 65 = 1300 x = 1300 - 600 = 700 meters answer : a
a ) 700 , b ) 288 , c ) 500 , d ) 277 , e ) 121
a
multiply(multiply(subtract(divide(600, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2)
subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)|subtract(#2,const_1)|multiply(#3,const_10)|multiply(#4,const_2)
physics
two trains 160 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + b ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 c ' s 1 hour work = ( 7 / 12 - 1 / 2 ) = 1 / 12 c alone will take 12 hours to do the work . answer : a
a ) 12 hours , b ) 10 hours , c ) 6 hours , d ) 8 hours , e ) 4 hours
a
divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4))))
divide(const_1,n1)|divide(const_1,n2)|divide(const_1,n0)|subtract(#1,#2)|subtract(#0,#3)|divide(const_1,#4)
physics
a number increased by 25 % gives 520 . the number is ?
"total = 75 books . 60 % of books that were loaned out are returned - - > 100 % - 60 % = 40 % of books that were loaned out are not returned . now , there are 68 books , thus 75 - 65 = 10 books are not returned . { loaned out } * 0.4 = 10 - - > { loaned out } = 25 . answer : b ."
a ) 20 , b ) 25 , c ) 35 , d ) 40 , e ) 55
b
divide(subtract(75, 65), subtract(const_1, divide(60, const_100)))
divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2)|
gain
$ 350 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
"original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
a ) q = 200 , b ) q = 600 , c ) q = 800 , d ) q = 1600 , e ) q = 50
d
multiply(power(const_2, 4), const_100)
power(const_2,n0)|multiply(#0,const_100)|
general
the maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
"a = 2 m = m + 12 m = 12 a = 24 a = 4 b , and so b = 6 the answer is a ."
a ) 6 , b ) 12 , c ) 10 , d ) 15 , e ) 18
a
divide(multiply(2, 12), 4)
multiply(n0,n2)|divide(#0,n1)|
general