regisss/math_qa huggingface dataset:
Problem: a sum of money at simple interest amounts to 815 in 3 years and to 854 in 4 years . the sum is :
Options: a ) 698 , b ) 387 , c ) 373 , d ) 593 , e ) 372
Rationale: "a 698 s . i . for 1 year = ( 854 - 815 ) = 39 . s . i . for 3 years = ( 39 x 3 ) = 117 . principal = ( 815 - 117 ) = 698 ."
Answer: a
Problem: a woman spends 15 % of her income in house rent , 15 % of the rest on his children ’ s education , 10 % of the rest miscellaneous causes and 15 % in medical expenses . if she now posses rs . 5548 then her income is ?
Options: a ) 10058 , b ) 10068 , c ) 10078 , d ) 10088 , e ) 10038
Rationale: x * ( 85 / 100 ) * ( 85 / 100 ) * ( 90 / 100 ) * ( 85 / 100 ) = 5548 x * 0.85 * 0.85 * 0.9 * 0.85 = 5548 x = 5548 / 0.5527 x = 10038 answer : e
Answer: e
Problem: a student got twice as many sums wrong as he got right . if he attempted 48 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 48 3 x = 48 x = 16 . answer : b"
Answer: b
Problem: a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 50 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 35 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 570 , b ) 670 , c ) 1070 , d ) 470 , e ) 2070
Rationale: "amount earned by using her cell phone = 35 * 22 = 770 amount earned as usual = 15 * 20 = 300 total = 770 + 300 = 1070 answer : c"
Answer: c
Problem: reeya obtained 50 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 68
Rationale: "explanation : ( 50 + 60 + 70 + 80 + 80 / 5 ) = 68 option e"
Answer: e
Problem: 5 goats ’ s and 10 hens are brought for rs . 2500 . if the average price of a hen be rs . 50 . what is the average price of a goat .
Options: a ) 425 , b ) 375 , c ) 350 , d ) 400 , e ) 500
Rationale: explanation : average price of a hen = rs . 50 total price of 10 hens = 10 * 50 = rs . 500 but total price of 5 goats and 10 hens = rs . 2500 total price of 5 goats is = 2500 - 500 = 2000 average price of a goat = 2000 / 5 = rs . 400 answer : d
Answer: d
Problem: kareena , saif , and a puppy start walking down a road . they start at the same time , from the same point , in the same direction . the saif walks at 5 miles / hour kareena at 6 miles / hour . the puppy runs from saif to kareena and back again with a constant speed of 10 miles / hour . the puppy does not slow down on the turn . how far does the puppy travel in 1 hour ?
Options: a ) 10 miles , b ) 14 miles , c ) 12 miles , d ) 20 miles , e ) 30 miles
Rationale: a 10 miles speed us 10 miles / hour
Answer: a
Problem: if m is a positive integer and m ^ 2 is divisible by 39 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 13
Rationale: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 13 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is e but if m = 39 then answer should be 16 . is the question right ? or am i missing some thing ? e"
Answer: e
Problem: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 7.76 kms , b ) 8.76 kms , c ) 5.76 kms , d ) 3.76 kms , e ) 4.76 kms
Rationale: "explanation : speed in still water = 6 kmph stream speed = 1.2 kmph down stream = 7.2 kmph up stream = 4.8 kmph x / 7.2 + x / 4.8 = 1 x = 2.88 total distance = 2.88 x 2 = 5.76 kms answer : c"
Answer: c
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 315 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: 315 = 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 7 . the answer is b .
Answer: b
Problem: find the value of a from ( 15 ) ^ 2 x 8 ^ 3 ã · 256 = a .
Options: a ) 250 , b ) 420 , c ) 440 , d ) 650 , e ) 450
Rationale: given exp . = ( 15 ) ^ 2 x 8 ^ 3 ã · 256 = a = 225 x 512 ã · 256 = 450 e
Answer: e
Problem: the sum of two prime numbers is 85 . what is the product of these two prime numbers ?
Options: a ) 85 , b ) 91 , c ) 115 , d ) 133 , e ) 166
Rationale: since there is only one even prime number ( 2 ) , and the sum of two odd numbers is even , the product of these two numbers must be even . correct answer e
Answer: e
Problem: a and b can do a work in 15 days , b and c in 30 days , c and a in 45 days . if a , b and c work together , they will complete the work in ?
Options: a ) 10 days , b ) 16 days , c ) 20 days , d ) 25 days , e ) 22 days
Rationale: "a + b 1 day work = 1 / 15 b + c 1 day work = 1 / 30 c + a 1 day work = 1 / 45 adding we get 2 ( a + b + c ) = 1 / 15 + 1 / 30 + 1 / 45 = 11 / 90 a + b + c 1 day work = 11 / 180 a , b , c can finish the work in 180 / 11 days = 16 days approximately answer is b"
Answer: b
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,053 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1053 / 1000 ) - 1 = 0.053 = 5.3 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.053 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.053 - 0.01 x = - 0.007 x = - 0.007 / - 0.01 = 7 / 10 = 70 % so x = 70 % of the 1000 which is 700 answer : c"
Answer: c
Problem: 6 ! / ( 6 - 3 ) ! = ?
Options: a ) 120 , b ) 346 , c ) 356 , d ) 366 , e ) 396
Rationale: 6 ! / 6 - 3 ) ! = 6 ! / 3 ! = 6 * 5 * 4 = 120 . hence , the correct answer is a .
Answer: a
Problem: x is a positive integer less than 500 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "when x divided by 7 and leave reminder 1 . x could be 1 , 8,15 , . . . . when divided by 3 and leave reminder 2 - x could be 2 , 5,8 , . . . . so x must be of the form 21 m + 8 where m = 0 , 1,2 , . . . . . first no will be 8 and last no will be 491 . so total no . less than 500 will be 24 . answer : d"
Answer: d
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 27 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "first , let ' s translate the expression 21 # 27 , using the definition given : 21 # 27 = 21 × 24 × 27 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 27 = 3 ^ 3 ( 7 × 8 × 9 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 27 = 3 ^ 3 ( 7 × 2 ^ 3 × 3 ^ 2 ) let ' s group the prime bases : 21 # 27 = 2 ^ 3 × 3 ^ 5 × 7 the sum of the exponents is 3 + 5 + 1 = 9 the answer is d ."
Answer: d
Problem: the average age of the boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
Options: a ) 27 , b ) 29 , c ) 11 , d ) data inadequate , e ) 28
Rationale: clearly , to find the average , we ought to know the number of boys , girls or students in the class , neither of which has been given . so , the data provided is inadequate answer : d
Answer: d
Problem: the length of the bridge , which a train 170 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 239 , b ) 277 , c ) 205 , d ) 88 , e ) 232
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 170 + x ) / 30 = 25 / 2 = = > 2 ( 170 + x ) = 750 = = > x = 205 m . answer : c"
Answer: c
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 3 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 216 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 3 ) or $ 216 . the best answer is therefore a . answer : a ."
Answer: a
Problem: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 9 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 23 years , b ) 24 years , c ) 25 years , d ) 26 years , e ) 27 years
Rationale: "explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 38 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer d"
Answer: d
Problem: if ( 2 ^ 12 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 12 , b ) 8 , c ) 15 , d ) 16 , e ) 23
Rationale: "given 2 ^ 12 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 12 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans a on comparing the power of 2 = > m = 12"
Answer: a
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 125 resolutions ?
Options: a ) 794 m , b ) 704 m , c ) 454 m , d ) 186 m , e ) 176 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 125 resolutions . = 125 * 2 * 22 / 7 * 22.4 = 17600 cm = 176 m answer : e"
Answer: e
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 160 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 160 and so k = 160 - l l + 10 = 1.5 k = 1.5 ( 160 - l ) 2.5 l = 230 l = 92 the answer is c ."
Answer: c
Problem: if 40 % of a certain number is 160 , then what is 60 % of that number ?
Options: a ) 270 , b ) 380 , c ) 260 , d ) 360 , e ) 240
Rationale: "explanation : 40 % = 40 * 4 = 160 60 % = 60 * 4 = 240 answer : option e"
Answer: e
Problem: if 22 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 88 , d ) 80 , e ) 75
Rationale: "let x be the number of students in the school . 0.22 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.22 x / 0.25 = 0.88 x students went to the camping which is 88 % . the answer is c"
Answer: c
Problem: if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to
Options: a ) 2 : 1 , b ) 14 : 3 , c ) 7 : 2 , d ) 1 : 2 , e ) none
Rationale: solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a
Answer: a
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.05 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: 1 st day fine - 0.05 2 nd day fine - 0.05 * 2 = 0.1 ( as doubling gives lower value ) 3 rd day fine - 0.1 * 2 = 0.2 ( as doubling gives lower value ) 4 th day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value we add 0.3 this time ) 5 th day fine - 0.4 + 0.3 = 0.7 ( as doubling gives higher value we add 0.3 this time ) answer : b .
Answer: b
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d"
Answer: d
Problem: 45 x ? = 10 % of 900
Options: a ) 2 , b ) 4 , c ) 5 , d ) 500 , e ) none
Rationale: answer let 45 x a = ( 10 x 900 ) / 100 ∴ a = ( 10 x 9 ) / 45 = 2 correct option : a
Answer: a
Problem: a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?
Options: a ) 90 °
b ) 135 °
c ) 216 °
d ) 240 °
e ) 270 °
Rationale: the percent of the budget for salaries is 100 - ( 20 + 9 + 5 + 4 + 2 ) = 60 % 100 % of the circle is 360 degrees . then ( 60 % / 100 % ) * 360 = 216 degrees the answer is c .
Answer: c
Problem: sales price is $ 44 , gross profit is 120 % of cost , what is the value of gross profit ?
Options: a ) 24 , b ) 33 , c ) 39 , d ) 40 , e ) 42
Rationale: cost + profit = sales cost + ( 120 / 100 ) cost = 44 cost = 20 profit = 44 - 20 = 24 answer ( a )
Answer: a
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.67 %
Rationale: "x - wt of mix x added y - wt of mix y added 0.4 x + 0.25 y = 0.3 ( x + y ) 0.1 x = 0.05 y x / y = 5 / 10 = 1 / 2 y / x = 2 ( y + x ) / x = 3 = > x / ( y + x ) * 100 = 100 / 3 = 33.33 % answer : b"
Answer: b
Problem: a circular road runs around a circular garden . if the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one - third of the outer circle , then the width of the road is :
Options: a ) 4 metres , b ) 5 metres , c ) 7 metres , d ) 6 metres , e ) 8 metres
Rationale: let radius of inner circle = r 1 radius of outer circle = r 2 also r 1 = 1 / 3 * r 2 3 * r 1 = r 2 circumference of inner circle = 2 * pi * r 1 circumference of outer circle = 2 * pi * r 2 = 6 * pi * r 1 ( since r 2 = 3 * r 1 ) 2 * pi * r 1 + 6 * pi * r 1 = 88 ( as per question ) r 1 = 3.5 m r 2 = 3 * 3.5 = 10.5 m width of road = 10.5 - 3.5 = 7 m ans . answer : c
Answer: c
Problem: in a multiple choice test comprising 5 questions , each with 4 choices , what is the probability of a student getting 3 or more questions correct ? each question has only one correct answer and the student is equally likely to choose any of the 4 choices .
Options: a ) 24 / 256 , b ) 53 / 512 , c ) 105 / 512 , d ) 459 / 512 , e ) 47 / 256
Rationale: probability for choosing correct answer is 1 / 4 and incorrect answer is 3 / 4 for 3 correct answers , c ( 5,3 ) * ( 1 / 4 ) ^ 3 * ( 3 / 4 ) ^ 2 = 90 / ( 4 ^ 5 ) for 4 correct answers , c ( 5,4 ) * ( 1 / 4 ) ^ 4 * ( 3 / 4 ) ^ 1 = 15 / ( 4 ^ 5 ) for 5 correct answers , c ( 5,5 ) * ( 1 / 4 ) ^ 5 * ( 3 / 4 ) ^ 0 = 1 / ( 4 ^ 5 ) so total probability = 106 / 1024 = 53 / 512 ans b
Answer: b
Problem: p and q together can do a work in 6 days . if p alone can do it in 15 days . in how many days can q alone do it ?
Options: a ) 5 , b ) 4 , c ) 10 , d ) 11 , e ) 12
Rationale: 1 / 6 - 1 / 15 = = > 1 / 10 = = > 10 answer c
Answer: c
Problem: in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 12 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
Options: a ) 15 , b ) 45 , c ) 30 , d ) 45 , e ) 60
Rationale: this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 12 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 12 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 12 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 12 ) ( 1 ) 11 x = 7 x + 12 4 x = 12 x = 3 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 3 ) = 45 final answer : b
Answer: b
Problem: the ratio between the sale price and the cost price of an article is 9 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 4 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 5 x and s . p . = rs . 9 x . then , gain = rs . 4 x required ratio = 4 x : 5 x = 4 : 5 c"
Answer: c
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 300 , find the original price per kg ?
Options: a ) s . 7.7 , b ) s . 7.4 , c ) s . 7.5 , d ) s . 7.1 , e ) s . 7.9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 300 - - - 80 ? - - - 2 = > rs . 7.5 answer : c"
Answer: c
Problem: 8 is 6 % of a , and 6 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 3 / 8 , b ) 8 / 15 , c ) 9 / 16 , d ) 12 / 25 , e ) 16 / 27
Rationale: "6 a / 100 = 8 a = 400 / 3 8 b / 100 = 6 b = 75 c = b / a = 75 * 3 / 400 = 9 / 16 the answer is c ."
Answer: c
Problem: of the 65 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: neither car nor garage = total - garage - ( swim - common ) = 65 - 50 - ( 40 - 35 ) = 65 - 55 = 10 answer a
Answer: a
Problem: exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ."
Answer: b
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 10 , and the difference between the total number of strawberries and the total number of blueberries would increase by 50 . each blue box contains how many blueberries ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "let x be the number of blueberries in each blue box . then there are x + 10 strawberries in each red box . x + ( x + 10 ) = 50 x = 20 the answer is c ."
Answer: c
Problem: if x / y = 3 and ( 2 a - x ) / ( 3 b - y ) = 3 , then the value of a / b is ?
Options: a ) – 3 , b ) 9 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: x = 3 y 2 a - 3 y = 3 ( 3 b - y ) 2 a - 3 y = 9 b - 3 y 2 a = 9 b a / b = 9 / 2 answer : b
Answer: b
Problem: if z is a multiple of 9702 , what is the remainder when z ^ 2 is divided by 4 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it depends on z .
Rationale: "2 is a factor of 9702 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ."
Answer: a
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) rs . 1200 , b ) rs . 890 , c ) rs . 600 , d ) rs . 1190 , e ) rs . 450
Rationale: "explanation : s . p . = 85 % of rs . 1400 = rs . ( 85 / 100 * 1400 ) = rs . 1190 answer : d"
Answer: d
Problem: a and b can finish a work in 12 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 24 days
Rationale: "b = 1 / 12 – 1 / 24 = 1 / 24 = > 24 days answer : e"
Answer: e
Problem: when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 2 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 2 ) ^ 2 = ( 5 x + 5 ) ^ 2 = 5 y , for some integer y when we divide this by 5 , the remainder is 0 . the answer is a ."
Answer: a
Problem: if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 3072 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536
Rationale: "0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a ."
Answer: a
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 250 resolutions ?
Options: a ) 277 m , b ) 704 m , c ) 352 m , d ) 288 m , e ) 378 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 250 resolutions . = 250 * 2 * 22 / 7 * 22.4 = 35200 cm = 352 m answer : c"
Answer: c
Problem: if grapes are 93 % water and raisins are 16 % water , then how many kilograms did a quantity of raisins , which currently weighs 8 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108
Rationale: let x be the original weight . the weight of the grape pulp was 0.07 x . since the grape pulp is 84 % of the raisins , 0.07 x = 0.84 ( 8 ) . then x = 12 * 8 = 96 kg . the answer is b .
Answer: b
Problem: find the slope of the line perpendicular to the line y = x - 7
Options: a ) 1 , b ) 2 , c ) - 1 , d ) 4 , e ) 5
Rationale: two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 . if m is the slope of the line perpendicular to the given line , then m × 1 = - 1 solve for m m = - 1 correct answer c ) - 1
Answer: c
Problem: set a consists of all the prime numbers between 10 and 25 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 23 lowest number = 11 range = highest - lowest = 23 - 11 = 12 option a"
Answer: a
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 370 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 47 , e ) 49
Rationale: let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 370 ) / 36 * 5 / 18 = 49 min . answer : e
Answer: e
Problem: a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 2.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = 25 * 60 + 2500 = 4000 m t = 4000 / 60 * 18 / 5 = 240 sec = 4 mins answer : a"
Answer: a
Problem: the length of a rectangle is halved , while its breadth is tripled . what is the % change in area ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Problem: there were two candidates in an election . winner candidate received 60 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 864 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 288 60 % - - - - - - - - ? = > 864 answer : b"
Answer: b
Problem: in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 2 , − 3 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 6 / 12 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c"
Answer: c
Problem: a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of b .
Options: a ) 225 , b ) 500 , c ) 75 , d ) 800 , e ) none 0 of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a"
Answer: a
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions
Options: a ) 700 , b ) 704 , c ) 704 , d ) 706 , e ) 707
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : option b"
Answer: b
Problem: a 220 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 280 , b ) 270 , c ) 260 , d ) 250 , e ) 240
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 220 ) / 9 = 500 / 9 = > x = 280 . answer : option a"
Answer: a
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 402 to 500 inclusive ?
Options: a ) 14,550 , b ) 18,550 , c ) 22,550 , d ) 26,550 , e ) 30,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 402 + 404 + . . . + 500 = 50 ( 400 ) + ( 2 + 4 + . . . + 100 ) = 20,000 + 2550 = 22,550 the answer is c ."
Answer: c
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 7 , e ) 6
Rationale: "let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e ."
Answer: e
Problem: ramu bought an old car for rs . 48000 . he spent rs . 14000 on repairs and sold it for rs . 72900 . what is his profit percent ?
Options: a ) 16 % , b ) 17.5 % , c ) 18.2 % , d ) 58.5 % , e ) 13 %
Rationale: "total cp = rs . 48000 + rs . 14000 = rs . 62000 and sp = rs . 72900 profit ( % ) = ( 72900 - 62000 ) / 62000 * 100 = 17.5 % answer : b"
Answer: b
Problem: rs . 2600 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2600 - x ) * 6 * 1 ] / 100 = 140 x = 1600 answer : a"
Answer: a
Problem: a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252
Rationale: "first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d"
Answer: d
Problem: the average weight of 7 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 74 kg , b ) 78.5 kg , c ) 99.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 7 x 3.5 ) kg = 24.5 kg . weight of new person = ( 75 + 24.5 ) kg = 99.5 kg . answer : option c"
Answer: c
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 32 people were made to stand in a column , how many columns could be formed ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "16 * 30 = 32 * n n = 15 the answer is a ."
Answer: a
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 10
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted answer : option e"
Answer: e
Problem: the average age of applicants for a new job is 10 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34
Rationale: minimum age = average - 1 standard deviation = 10 - 8 = 2 maximum age = average + 1 standard deviation = 10 + 8 = 18 maximum number of different ages of the applicants = 18 - 2 + 1 = 17 answer c
Answer: c
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 900 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: 1 hour he ride 50 km he ride 900 km in = 900 / 50 * 1 = 18 hours answer is e
Answer: e
Problem: a and b invests rs . 6000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 8 : 21 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 48000 : 126000 8 : 21 answer : b"
Answer: b
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 7 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 56 , d ) 70 , e ) 60
Rationale: "c 56 sum = ( n x n ) + n hence , 7 x 7 = 49 + 7 = 56"
Answer: c
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 80 m = 80 / 5 = 16 seconds . answer : a"
Answer: a
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 92 , d ) d . 46 , e ) e . 44
Rationale: at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c
Answer: c
Problem: each week , harry is paid x dollars per hour for the first 21 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 21 x + 1.5 x ( h - 21 ) = = > 42 = 21 + 1.5 ( h - 21 ) = = > h - 21 = 21 / 1.5 = 14 = > h = 35 answer is a"
Answer: a
Problem: the volume of a cube is 729 cc . find its surface .
Options: a ) 486 , b ) 556 , c ) 255 , d ) 287 , e ) 267
Rationale: "a 3 = 729 = > a = 9 6 a 2 = 6 * 9 * 9 = 486 answer : a"
Answer: a
Problem: a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30
Rationale: "first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of ways in which 4 girls can select 4 black balls = 4 c 4 = 1 therefore , total favorable outcomes / total outcomes = 2 / 70 = 1 / 35 a"
Answer: a
Problem: a can knit a pair of socks in 3 days . b can knit the same thing in 6 days . if they are knitting together , in how many days will they knit two pairs of socks ?
Options: a ) 4 days , b ) 2 days , c ) 4 1 ⁄ 2 days , d ) 3 days , e ) none of these
Rationale: explanationa ’ s one day ’ s work = 1 ⁄ 3 rd work . b ’ s one day ’ s work = 1 ⁄ 6 rd work . ( a + b ) ’ s one day ’ s work = 1 ⁄ 3 + 1 ⁄ 6 = 1 ⁄ 2 nd work . ∴ a and b together can complete the work ( knit a pair of socks ) in 2 days . ∴ they together knit two pair of socks in 4 days . answer a
Answer: a
Problem: the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 72 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 72 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 72 x = 0.06 the answer is b ."
Answer: b
Problem: running at their respective constant rates , machine x takes 6 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 10 , e ) 12
Rationale: "together they make 5 / 4 w widgets in 3 days . so they make w widgets in 3 * 4 / 5 = 12 / 5 days . 1 / ( t + 2 ) + 1 / t = 5 / 12 now , calculating this is really cumbersome so try to plug in options to get to the answer . if machine x takes 12 days to produce 2 w widgets , it would take 6 days to make w widgets , t would be 4 . 1 / 6 + 1 / 4 = 5 / 12 it works so t = 4 . answer : a"
Answer: a
Problem: find the ones digit of 73 ^ 353
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 353 will be the same as the units digit of 3 ^ 353 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 353 = 352 + 1 = ( multiple of 4 ) + 1 , then the units digit of 3 ^ 353 will be the first number in the pattern thus 3 . answer : a ."
Answer: a
Problem: if 2 x + y = 26 and x + 2 y = 10 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 26 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 36 divide both sides by 3 to get : x + y = 12 so , ( x + y ) / 3 = 12 / 3 = 4 answer : e"
Answer: e
Problem: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 16 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 1584
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 16 = 1584 answer : e"
Answer: e
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1015 . find the cost of each ice - cream cup ?
Options: a ) 34 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1015 96 + 225 + 490 + 6 x = 1015 6 x = 204 = > x = 34 . answer : a"
Answer: a
Problem: a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more thanc . out of a total profit of rs . 35000 , a receives :
Options: a ) 14700 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 * 21 / 50 ) = rs . 14,700 . answer : a ) 14700
Answer: a
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,700 , e ) $ 21,100
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 2000 = $ 20700 correct option : d"
Answer: d
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 6 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11.5 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 6 days = 6 * ( 1 / 24 + 1 / 30 ) = 9 / 20 remaining work = 11 / 20 the number of days required for this initial work = 5.5 days . the total number of days required = 6 + 5.5 = 11.5 days . answer : d"
Answer: d
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?
Options: a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1800 , e ) $ 1900
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a"
Answer: a
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 6 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 42 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 6 - - - - - - - - - ? = 42 m answer : d"
Answer: d
Problem: a jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 35 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 230 + 120 ) m = 350 m . ∴ time taken = ( 350 ⁄ 10 ) sec = 35 sec . answer c"
Answer: c
Problem: a train covers a distance of 36 km in 12 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 300 m , b ) 1000 m , c ) 120 m , d ) 200 m , e ) 500 m
Rationale: "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 10 = 500 m . answer : e"
Answer: e
Problem: 8 people decided to split the restaurant bill evenly . if the bill was $ 214.18 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.24
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 418 not divisible by a hence , we need to add 6 to this number for it to be divisible by 8 correct option : e"
Answer: e
Problem: if 4 women can color 48 m long cloth in 2 days , then 6 women can color 36 m long cloth in
Options: a ) 2 days , b ) 3 days , c ) 1 day , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 women = 36 / 6 × 6 = 1 day . c"
Answer: c
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 4 cubic feet . if a large block has twice the width , twice the depth , and twice the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 16
b ) 20
c ) 36
d ) 32
e ) 28
Rationale: volume of cube = lbh = 4 new cube l , b , h are increases of 2 l , 2 b , 2 h new volume of cube = 2 l * 2 b * 2 h = 8 * lbh = 8 * 4 = 32 answer : d
Answer: d
Problem: a man is 32 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is
Options: a ) 26 years , b ) 27 years , c ) 28 years , d ) 29 years , e ) 30 years
Rationale: "explanation : let ' s son age is x , then father age is x + 32 . = > 2 ( x + 6 ) = ( x + 32 + 6 ) = > 2 x + 12 = x + 38 = > x = 26 years answer : option a"
Answer: a
Problem: the monthly rent of a shop of dimension 20 feet × 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ?
Options: a ) 48
b ) 56
c ) 68
d ) 87
e ) 92
Rationale: sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a
Answer: a
Problem: ashley and betty start a business with $ 9000 each , and after 3 months , betty adds another $ 5000 . how should they share the profits at the end of the 24 months ?
Options: a ) 72 : 107 , b ) 4 : 5 , c ) 17 : 23 , d ) 3 : 4 , e ) 68 : 95
Rationale: ashley invests $ 9000 for 24 months , but betty invests $ 9000 for the first 3 months and then adds $ 5000 . so , the investment of betty for remaining 21 months is $ 14000 . ashley : betty 9000 * 24 : ( 9000 * 3 ) + ( 14000 * 21 ) 216000 : 321000 a : b = 72 : 107 answer : a
Answer: a
Problem: in an examination , 25 % of total students failed in hindi , 50 % failed in english and 25 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 37 , c ) 28 , d ) 40 , e ) 50
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 50 â € “ 25 = 50 therefore students who passed = 100 â € “ 50 = 50 . answer : e"
Answer: e
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 12 units ?
Options: a ) 140 sq . units , b ) 170 sq . units , c ) 190 sq . units , d ) 168 sq . units , e ) 149 sq . units
Rationale: "explanation : given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 12 units area of the rectangle = lb = 14 * 12 = 168 sq . units answer : option d"
Answer: d
Problem: a pineapple costs rs 9 each and a watermelon costs rs . 6 each . if i spend rs 51 on total what is the number of pineapple i purchased ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 3 , e ) 2
Rationale: "5 * 9 + 6 = 51 5 pineapples answer : c"
Answer: c
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a"
Answer: a
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : b"
Answer: b
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability j that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability j of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e .
Answer: e
Problem: how many multiples of 7 are there between 14 and 343 , exclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44
Rationale: "7 * 2 = 14 7 * 49 = 343 total multiples = ( 49 - 2 ) + 1 = 48 exclude 7 343 = 48 - 2 = 46 answer is ( c )"
Answer: c