regisss/math_qa huggingface dataset:
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a quarter circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 9000 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 90 degrees = 9000 anglets answer - c"
Answer: c
Problem: the product of a and b is equal to 10 more than twice the sum of a and b . if b = 9 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 10 + 2 ( a + b ) 9 a = 10 + 2 a + 18 7 a = 28 a = 4 b - a = 9 - 4 = 5 b is the answer"
Answer: b
Problem: how many times digit 2 is used while writing numbers from 400 to 700 ?
Options: a ) 150 , b ) 190 , c ) 250 , d ) 80 , e ) 130
Rationale: "in 400 to 500 there are 50 two ' s in 500 to 600 there are 50 two ' s in 600 to 700 there are 50 two ' s so total is 150 two ' s correct option : a"
Answer: a
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 28
Rationale: in the first 2 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 2 * 2 = 4 miles . so , the distance between him and walt was 48 - 4 = 44 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 44 / 8 = 5.5 hours . total time that lionel was walking is 2 + 5.5 = 7.5 hours , which means that he covered in that time interval distance = rate * time = 2 * 7.5 = 15 miles . answer : b .
Answer: b
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 15 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 ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 29.1 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 15 = 10 * 4 = 40 time difference = 29.1 ans : c"
Answer: c
Problem: the ratio of the volumes of two cubes is 2744 : 3375 . what is the ratio of their total surface areas ?
Options: a ) 71 : 76 , b ) 71 : 131 , c ) 71 : 145 , d ) 71 : 167 , e ) 71 : 113
Rationale: "ratio of the sides = ³ √ 2744 : ³ √ 3375 = 14 : 15 ratio of surface areas = 142 : 152 = 71 : 76 answer : a"
Answer: a
Problem: a and b started a business investing rs . 90,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 90000 : 20000 = 90 : 20 = 18 : 4 = 9 : 2 answer : b"
Answer: b
Problem: the compound interest on $ 2000 at 10 % per annum is $ 662 . the period ( in years ) is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: a = p ( 1 + r / 100 ) ^ t 2662 = 2000 ( 1 + 10 / 100 ) ^ t ( 11 / 10 ) ^ t = 2662 / 2000 ( 11 / 10 ) ^ t = ( 11 / 10 ) ^ 3 t = 3 years answer is b
Answer: b
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 150 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,350 , d ) $ 1,100 , e ) $ 1,210
Rationale: "10 / 100 p = 150 > > p = 150 * 100 / 10 = 1500 1500 - 150 = 1350 answer : c"
Answer: c
Problem: what is 995 * 995 ?
Options: a ) 974,169 , b ) 974,219 , c ) 974,549 , d ) 985,019 , e ) 990,025
Rationale: "if you take a base of 1000 then 995 is 5 less than 1000 to get the product of 995 x 995 write like this 995 - 5 ( as 5 less than base 1000 ) 995 - 5 now 5 x 5 = 25 and 995 - 5 = 990 so 995 x 995 = 990025 . . . ( bingo the answer is e . you can even have a shortcut . . . . . . 5 x 5 = 25 . . . only answer choice has last three digits as 25 . . so no need to calculate 995 - 5 . after you get 5 x 5 you can straight way pick answer choice e ."
Answer: e
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 15 seconds . the speed of the train is ?
Options: a ) 35 , b ) 50 , c ) 88 , d ) 22 , e ) 12
Rationale: "speed of the train relative to man = ( 125 / 15 ) m / sec = ( 25 / 3 ) m / sec . [ ( 25 / 3 ) * ( 18 / 5 ) ] km / hr = 30 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 30 = = > x = 35 km / hr . answer : a"
Answer: a
Problem: an object thrown directly upward is at a height of h feet after t seconds , where h = - 15 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 90 , b ) 98 , c ) 106 , d ) 120 , e ) 136
Rationale: we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 15 ( 5 - 3 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is a .
Answer: a
Problem: the average of 6 observations is 13 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: let seventh observation = x . then , according to the question we have = > ( 78 + x ) / 7 = 12 = > x = 6 . hence , the seventh observation is 6 . answer : d
Answer: d
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 4 ) and ( 9 , 4 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 4 , b ) 2 , c ) 1 / 4 , d ) 2 / 5 , e ) 5 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 2 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 2 ) is 2 / 5 . the answer is d ."
Answer: d
Problem: a test has 100 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 100 . thus 5 c < = 260 and so c < = 52 . then 40 < = c < = 52 and c can have 13 possible values . the answer is e ."
Answer: e
Problem: a women in her conversation said ` ` if u reverse my own age , in figures represent my husbands age . he is of course senior to me and difference between our age is one 0 ne - eleventh of their sum . what is the woman ' s and her husbands age ?
Options: a ) 4554 , b ) 4657 , c ) 8457 , d ) 3458 , e ) 5254
Rationale: let man , s age be xy the woman ' s age is yx then 10 x + y - 10 y - x = 1 / 11 ( 10 x + y + 10 y + x ) 9 x - 9 y = x + y 8 x = 10 y x / y = 10 / 8 = 5 / 4 so xy = 54 and yx = 45 answer : a
Answer: a
Problem: if 4 men working 10 hours a day earn rs . 600 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 320 , c ) rs 810 , d ) rs 680 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 600 : x hence 4 * 10 * x = 9 * 6 * 600 or x = 9 * 6 * 600 / 4 * 10 = 810 answer : c"
Answer: c
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability q that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 q = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 20.25 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 45 , d ) 47 , e ) 97
Rationale: "money collected = ( 20.25 x 100 ) paise = 2025 paise numbers of members = 2025 squareroot = 45 answer c"
Answer: c
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 12 sec . what is the length of the platform ?
Options: a ) 187 m , b ) 350 m , c ) 267 m , d ) 287 m , e ) 675 m
Rationale: "speed = 300 / 12 = 25 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 = > x = 675 m . answer : e"
Answer: e
Problem: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8510 / - . find out the amount that he borrowed .
Options: a ) s . 5266 , b ) s . 5269 , c ) s . 5228 , d ) s . 5218 , e ) s . 5526
Rationale: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8510 = p + ( 54 p / 100 ) 8510 = ( 100 p + 54 p ) / 100 8510 = 154 p / 100 p = ( 8510 * 100 ) / 154 = rs . 5525.974 answer : e"
Answer: e
Problem: if the sum of two numbers is 24 and the sum of their squares is 400 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 24 and x ^ 2 + y ^ 2 = 400 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 24 ^ 2 = 400 + 2 xy so xy = 176 / 2 = 88 answer : d"
Answer: d
Problem: if the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 9 , e ) 18
Rationale: "let length of rectangle = l 6 ^ 2 = l * 4 = > l = 36 / 4 = 9 answer d"
Answer: d
Problem: how many integer values t are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: 1 < 3 x + 5 < 17 = > - 4 < 3 x < 12 = > - 4 / 3 < x < 4 x can take integer values t - 10 , 1 , 2 , 3 answer d
Answer: d
Problem: the sum of 3 consecutive multiples of 3 is 117 . what is the largest number ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 42 , e ) 54
Rationale: let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 117 9 x = 108 x = 12 largest number = 3 x + 6 = 42 answer : d
Answer: d
Problem: if the cost price of 81 chocolates is equal to the selling price of 45 chocolates , the gain percent is :
Options: a ) 80 % , b ) 85 % , c ) 82 % , d ) 70 % , e ) 75 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 45 chocolates = rs . 45 ; s . p . of 45 chocolates = rs . 81 . . ' . gain % = 36 * 100 / 45 = 80 % answer : a"
Answer: a
Problem: company z has 50 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 50 . now , plug options for x . only a and e give an integer value for y . but only for e x > y as needed . answer : e ."
Answer: e
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 18 % ?
Options: a ) 37.5 % , b ) 48 % , c ) 50.5 % , d ) 28.125 % , e ) 56 %
Rationale: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 82 gain % = 18 / 64 * 100 = 28.125 % . answer : option d"
Answer: d
Problem: the average age of 39 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 40 * 15 - 39 * 14 ) years = 54 years . answer : d"
Answer: d
Problem: how many times are the hands of a clock at right angle in 2 weeks ?
Options: a ) 616 , b ) 611 , c ) 661 , d ) 116 , e ) 666
Rationale: "in 1 day , they are at right angles 44 times . in 14 days , they are at right angles 616 times . answer : option a"
Answer: a
Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be maths teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 24 , e ) 1 / 12
Rationale: probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( e )
Answer: e
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 75 questions and secures 125 marks , the number of questions he attempts correctly , is :
Options: a ) 38 , b ) 40 , c ) 26 , d ) 25 , e ) 11
Rationale: "explanation : let the number of correct answers be x . then numbers of incorrect answers will be 75 – x we get 4 x – ( 75 – x ) × 1 = 125 on solving the equation we get x = 40 answer : b"
Answer: b
Problem: the value of x . 320 ã · 2 ã · 3 = x
Options: a ) 53.33 , b ) 46.33 , c ) 15.36 , d ) 15.45 , e ) 15.48
Rationale: 320 ã · 2 ã · 3 = 320 ã — 1 / 2 ã — 1 / 3 = 160 / 3 = 53.33 correct answer : a
Answer: a
Problem: v is the volume of a cylinder ; the radius of the cylinder is 3.5 . the height of the cylinder is 650 % more than the radius . which of the following is true ?
Options: a ) 100 < v < 300
b ) 300 < v < 500
c ) 500 < v < 700
d ) 700 < v < 900
e ) 900 < v < 1100
Rationale: as we see the answers are in form of range we can use approximation volume of cylinder is π r ^ 2 h given π = 22 / 7 and r = 3.5 so r ^ 2 ~ 12 and h = 6.5 * 3.5 ~ 23 so 22 / 7 * 12 * 23 ~ 868 so answer should be d . 700 < v < 900 answer : d
Answer: d
Problem: two employees x and y are paid a total of rs . 580 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 263 , b ) s . 283 , c ) s . 293 , d ) s . 300 , e ) s . 383
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 580 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 580 ⇒ y [ 12 / 10 + 1 ] = 580 ⇒ 22 y / 10 = 580 ⇒ 22 y = 5800 ⇒ y = 5800 / 22 = rs . 263 a )"
Answer: a
Problem: two trains of length 120 m and 300 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 21 sec , b ) 32 sec , c ) 82 sec , d ) 20 sec , e ) 89 sec
Rationale: relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 300 = 420 m . the time required = d / s = 420 / 20 = 21 sec . answer : a
Answer: a
Problem: two trains of length 100 m and 220 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 18 sec , b ) 70 sec , c ) 21 sec , d ) 20 sec , e ) 16 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 220 = 320 m . the time required = d / s = 320 / 20 = 16 sec . answer : e"
Answer: e
Problem: what positive number , when squared , is equal to the cube of the positive square root of 18 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 9
Rationale: "let the positive number be x x ^ 2 = ( ( 18 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 81 = > x = 9 answer e"
Answer: e
Problem: a train 360 m long is running at a speed of 54 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 11 sec , c ) 88 sec , d ) 33.33 sec , e ) 10 sec
Rationale: "speed = 54 * 5 / 18 = 15 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 15 = 33.33 sec answer : d"
Answer: d
Problem: 210 college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: 120 = 60 ( mac ) + x ( window ) + 20 ( both ) = > x = 40 answer : b
Answer: b
Problem: if a truck is traveling at a constant rate of 36 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 18 , b ) 24 , c ) 60 , d ) 36 , e ) 48
Rationale: "speed = 36 km / hr = > 36,000 m / hr in one minute = > 36000 / 60 = 600 meters in one sec = > 600 / 60 = 10 meters time = total distance need to be covered / avg . speed = > 600 / 10 = 60 and hence the answer : c"
Answer: c
Problem: solve this 6 + 7 = 12 8 + 9 = 16 5 + 6 = 10 7 + 8 = 14 then , 3 + 3 = ? ?
Options: a ) 11 , b ) 12 , c ) 5 , d ) 14 , e ) 18
Rationale: 5 answer : c
Answer: c
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many solutions zwill this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "z = | x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 1.26 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 1.26 - - > 15 p - 13.5 p = 126 - - > p = 84 . answer : e .
Answer: e
Problem: if 3 / p = 8 & 3 / q = 18 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 3 / 8 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 8 ) - ( 1 / 6 ) = 5 / 24 answer : a"
Answer: a
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 147 , d ) 165 , e ) 315
Rationale: "ans : 147 7 c 1 * 7 c 2 answer c )"
Answer: c
Problem: mohit sold an article for $ 18000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 25000 , c ) 15000 , d ) 18000 , e ) 17000
Rationale: "c 15000 let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 18000 - 10 / 100 ( 18000 ) = 18000 - 1800 = $ 16200 = > 1.08 x = 16200 = > x = 15000"
Answer: c
Problem: a is twice as fast as b . if b alone can do a piece of work in 30 days , in what time can a and b together complete the work ?
Options: a ) 13 , b ) 10 , c ) 16 , d ) 50 , e ) 23
Rationale: "option b explanation : a can do the work in 30 / 2 i . e . , 15 days . a and b ' s one day ' s work = 1 / 15 + 1 / 30 = ( 2 + 1 ) / 30 = 1 / 10 so a and b together can do the work in 10 days ."
Answer: b
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability c that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability c = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Problem: the total cost of a vacation was divided among 4 people . if the total cost of the vacation had been divided equally among 5 people , the cost per person would have been $ 50 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 400 , d ) $ 500 , e ) $ 1000
Rationale: "c for cost . p price per person . c = 4 * p c = 5 * p - 250 substituting the value of p from the first equation onto the second we get p = 250 . plugging in the value of p in the first equation , we get c = 1000 . which leads us to answer choice e"
Answer: e
Problem: by mixing two brands of coffee and selling the mixture at the rate of $ 177 per kg . a shopkeeper makes a profit of 18 % . if to every 2 kg of one brand costing $ 200 per kg , 3 kg of the other brand is added , then how much per kg does the other brand cost ?
Options: a ) $ 110.66 , b ) $ 132.66 , c ) $ 116.66 , d ) $ 126.66 , e ) $ 118.66
Rationale: c $ 116.66 let the cost of the brand be $ x per kg . c . p . of 5 kg = ( 2 * 200 + 3 * x ) = $ ( 400 + 3 x ) s . p of 5 kg = $ ( 5 * 177 ) = $ 885 [ 885 - ( 400 + 3 x ) ] / ( 400 + 3 x ) * 100 = 18 24250 - 150 x = 3600 + 27 x 177 x = 20650 = > x = 116 2 / 3 so , cost of the other brand = $ 116.66 .
Answer: c
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.75 ?
Options: a ) 1280 , b ) 1145 , c ) 1040 , d ) 950 , e ) 260
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.75 - $ 0.65 = $ 1.10 the charge for the next 1000 grams is $ 1.00 which leaves a charge of $ 0.10 the weight is somewhere between 1250 and 1350 . the answer is a ."
Answer: a
Problem: johnny makes $ 6.75 per hour at his work . if he works 10 hours , how much money will he earn ?
Options: a ) $ 67.50 , b ) $ 54 , c ) $ 28.50 , d ) $ 12.50 , e ) $ 9.60
Rationale: 6.75 * 10 = 67.50 . answer is a .
Answer: a
Problem: machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 6 hours and machine y produces k bottles in 3 hours . how many hours does it take machines x and y , working simultaneously , to produce 12 k bottles ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 18 , e ) 24
Rationale: "x rate = k / 6 y rate = k / 3 k / 6 + k / 3 = 12 k / t solving t = 24 answer e"
Answer: e
Problem: 34 , 45 , 56 , 67,78 , _ ?
Options: a ) 33 , b ) 82 , c ) 99 , d ) 89 , e ) 27
Rationale: answer : d
Answer: d
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 4 days . b can do the work alone in ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 24 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 4 6 / x = 1 / 4 = > x = 24 so , b takes 12 hours to finish the work . answer : d"
Answer: d
Problem: a man purchased 3 blankets @ rs . 100 each , 3 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 750 , b ) 277 , c ) 878 , d ) 450 , e ) 272
Rationale: "10 * 150 = 1500 3 * 100 + 3 * 150 = 750 1500 – 750 = 750 answer : a"
Answer: a
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 18522 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 18522 / - - 17640 / - = rs . 882 / - rate of interest = ( 882 / 17640 ) × ( 100 / 1 ) = > 8820 / 1764 = 5 % principal = amount / ( 1 + r / 100 ) n = 17640 / ( 1 + 5 / 100 ) 2 = 17640 / ( 21 / 20 × 21 / 20 ) = 17640 / ( 1.05 × 1.05 ) = 17640 / 1.1025 = 16000 thus the principal is rs . 16000 / - and the rate of interest is 5 % a"
Answer: a
Problem: how many integers from 101 to 1000 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 9 = 9 second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 9 * 10 = 90 answer is e ."
Answer: e
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 37 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 6 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 37 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 6 more to make it 37 m + 36 answer - d"
Answer: d
Problem: a train covers a distance of 12 km in 10 min . if it takes 2 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 40 , b ) 80 , c ) 20 , d ) 100 , e ) 60
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 2 = 40 m . answer : option a"
Answer: a
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 49 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 7 , b ) 7 : 3 , c ) 4 : 9 , d ) 4 : 4 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 49 : â ˆ š 9 = 7 : 3 . answer : b"
Answer: b
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 65.9 , b ) 62.3 , c ) 62.7 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 90 / 100 ) = 59.375 mp = 65.9 answer : a"
Answer: a
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 1 : 1 , b ) 2 : 1 , c ) 3 : 1 , d ) 5 : 1 , e ) 6 : 1
Rationale: "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 400 , water 400 the ratio = 400 / 400 - - > 1 : 1 answer : a"
Answer: a
Problem: the price of a jacket is reduced by 10 % . during a special sale the price of the jacket is reduced another 30 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 58.7 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 10 % , therefore bringing down the price to $ 90 . 3 ) again it is further discounted by 30 % , therefore bringing down the price to $ 63 . 4 ) now 67.5 has to be added byx % in order to equal the original price . 63 + ( x % ) 63 = 100 . solving this eq for x , we get x = 58.7 ans is b"
Answer: b
Problem: the ratio between the sale price and the cost price of an article is 7 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 8 , b ) 2 : 1 , c ) 2 : 2 , d ) 2 : 4 , e ) 2 : 5
Rationale: "explanation : let c . p . = rs . 5 x and s . p . = rs . 7 x . then , gain = rs . 2 x required ratio = 2 x : 5 x = 2 : 5 answer : e"
Answer: e
Problem: two trains 110 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 ?
Options: a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.8 , e ) 9.72
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 110 + 160 = 270 m . required time = 270 * 9 / 250 = 243 / 25 = 9.72 sec . ' answer : e"
Answer: e
Problem: thomas ' s age and matt ' s age are in the ratio 3 : 5 . two years ago the ratio of their ages was 5 : 9 . find the ratio of their ages 4 years hence ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: let ages of thomas and matt be x and y respectively . x / y = 3 / 5 = > x = 3 / 5 y ( x - 2 ) / ( y - 2 ) = 5 / 9 = > 9 x - 18 = 5 y - 10 = > 9 x = 5 y + 8 but x = 3 / 5 y 9 * 3 / 5 y = 5 y + 8 27 y = 25 y + 40 = > y = 20 years = > x = 3 * 20 / 5 = > 12 years ratio of their ages four years hence , ( 12 + 4 ) / ( 20 + 4 ) = 16 / 24 . = > 2 : 3 answer : b
Answer: b
Problem: dan ' s age after 16 years will be 4 times his age 8 years ago . what is the present age of dan ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: let dan ' s present age be x . x + 16 = 4 ( x - 8 ) 3 x = 48 x = 16 the answer is b .
Answer: b
Problem: a certain cube floating in a bucket of water has between 75 and 85 percent of its volume below the surface of the water . if between 9 and 16 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4
b ) 5
c ) 7
d ) 8
e ) 9
Rationale: if sides are 7 , vol = 7 ^ 3 = 343 75 % = 257.25 , 85 % = 291.55 so vol above water , between 85.75 and 51.45 - - > too big if side are 4 , vol = 64 75 % = 48 , 85 % = 54.4 vol above water between 16 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 75 % = 93.75 , . 85 % = 106.25 vol above water between 18.75 - 31.25 ( sides are 4 cubic centimeters ) a
Answer: a
Problem: how much space , in cubic units , is left vacant when maximum number of 6 x 6 x 6 cubes are fitted in a rectangular box measuring 12 x 18 x 14 ?
Options: a ) 428 , b ) 429 , c ) 430 , d ) 431 , e ) 432
Rationale: "no of cubes that can be accommodated in box = ( 12 * 18 * 14 ) / ( 6 * 6 * 6 ) 12 * 16 in numerator can be perfectly divided by 6 * 6 in denominator . side with length 14 ca n ' t be perfectly divided by 6 and hence is the limiting factor . closet multiple of 6 less that 14 is 12 . so vacant area in cube = = 18 * 12 * ( 14 - 12 ) = 18 * 12 * 2 = 432 ans - e"
Answer: e
Problem: a work as fast as b . if b can complete a work in 16 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 1 / 3 days , e ) 6 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 8 b ' s 1 day work = 1 / 16 a + b 1 day work = 1 / 8 + 1 / 16 = 3 / 16 = > 16 / 3 = 5 1 / 3 a and b can finish the work in 5 1 / 3 days answer is d"
Answer: d
Problem: the sum of 11 consecutive integers is 1111 . what is the greatest integer in the set ?
Options: a ) 100 , b ) 102 , c ) 104 , d ) 106 , e ) 108
Rationale: "let x be the first integer in the set , then x + 10 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 10 ) = 11 x + 10 * 11 / 2 = 11 ( x + 5 ) then x + 5 = 101 x = 96 the largest integer in the set is 96 + 10 = 106 the answer is d ."
Answer: d
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers q are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes q in this range . answer : a .
Answer: a
Problem: 5020 − ( 1004 ÷ 20.08 ) = ?
Options: a ) 4520 , b ) 4350 , c ) 4210 , d ) 4100 , e ) 4970
Rationale: "explanation : = 5020 − ( 1004 / 2008 × 100 ) = 5020 − 50 = 4970 option e"
Answer: e
Problem: it takes 60 identical printing machines 2 hours to print 300 cards . how much more time would it take 50 of these machines to print the same total ?
Options: a ) 20 min , b ) 25 min , c ) 26 min , d ) 36 min , e ) 30 min
Rationale: 50 % of 60 = 30 % or 0.30 2 hr x 60 min = 120 min 120 min x 0.30 = 36 min it will take 36 min longer to print them with only 50 printers . answer is d
Answer: d
Problem: a 18 % stock yielding 12 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 120 , e ) s . 150
Rationale: "income of rs 12 on investment of rs 100 income of rs 18 on investment of ? = ( 18 * 100 ) / 12 = 150 answer : e"
Answer: e
Problem: ( 23341379 × 72 ) = ?
Options: a ) 1223441288 , b ) 2142579288 , c ) 2142339288 , d ) 2142339277 , e ) 1680579288
Rationale: "23341379 × 72 = 23341379 ( 70 + 2 ) = ( 23341379 × 70 ) + ( 23341379 × 2 ) = 1633896530 + 46682758 = 1680579288 answer is e ."
Answer: e
Problem: the maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 1 , b ) 10 , c ) 11 , d ) 19 , e ) none of these
Rationale: solution required number of student = h . c . f of 1802 and 1203 = 1 . answer a
Answer: a
Problem: how many of the positive factors of 25 , 150 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 25 - 1 , 5 , 25 factors of 150 - 1 , 2 , 3 , 5 , 6 , 10 , 15 , 25 , 30 , 50 , 75 , 150 comparing both , we have three common factors of 25 and 150 - 1 , 5,25 answer ( c )"
Answer: c
Problem: if the cost price of 35 chocolates is equal to the selling price of 21 chocolates , the gain percent is :
Options: a ) 66.55 % , b ) 66.66 % , c ) 66 % , d ) 55 % , e ) 66.33 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 21 chocolates = rs . 21 ; s . p . of 21 chocolates = rs . 35 . . ' . gain % = 14 * 100 / 21 = 66.66 % answer : b"
Answer: b
Problem: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm ?
Options: a ) 766 cm 2
b ) 535 cm 2
c ) 285 cm 2
d ) 324 cm 2
e ) 235 cm 2
Rationale: area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c
Answer: c
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 11 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 12 , b ) 18 , c ) 22 , d ) 28 , e ) 36
Rationale: "3.456789 ^ 11 has 6 * 11 = 66 decimal places . 10 ^ 44 moves the decimal place to the right 44 places . ( 10 ^ 4 * 3.456789 ) ^ 11 has 66 - 44 = 22 digits after the decimal point . the answer is c ."
Answer: c
Problem: a 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 300 , c ) 889 , d ) 276 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 36 = 50 / 3 3 x + 900 = 1800 = > x = 300 m . answer : b"
Answer: b
Problem: the average expenditure of a labourer for 3 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 70.2 , b ) 50.1 , c ) 75.2 , d ) 78.4 , e ) 52.5
Rationale: "income of 3 months = ( 3 × 85 ) – debt = 255 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 525 average monthly income = 525 ÷ 10 = 52.5 answer e"
Answer: e
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 63.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 63 = 945 so , the score of the person who left is 55 ( 1000 - 945 ) answer will be ( d )
Answer: d
Problem: how many positive integers w between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 25 % ?
Options: a ) 37.5 % , b ) 37.6 % , c ) 38.5 % , d ) 17.1 % , e ) 37.2 %
Rationale: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 75 gain % = 11 / 64 * 100 = 17.1 % . answer : d"
Answer: d
Problem: one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 40 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 3 , b ) 2 , c ) 9 , d ) 8 , e ) 7
Rationale: there are total 40 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 10 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 40 = 25 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 10 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 40 = 10 + 25 - b + ( 10 - b - 1 ) b = 2 answer ( b )
Answer: b
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 60
Rationale: "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 57 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 18 - - > { loaned out } = 60 . answer : e ."
Answer: e
Problem: a train 330 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 18 sec , b ) 15 sec , c ) 4 sec , d ) 16 sec , e ) 12 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 330 * 3 / 55 ] sec = 18 sec answer : a"
Answer: a
Problem: if the selling price of 50 articles is equal to the cost price of 40 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 56 %
Rationale: "c c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 40 . loss % = 10 / 50 * 100 = 20 %"
Answer: c
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 136 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 147 , b ) s . 148 , c ) s . 144 , d ) s . 189 , e ) s . 192
Rationale: "given that sp = rs . 136 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 136 ) / 85 = rs . 160 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 160 * 120 ) / 100 = rs . 192 answer : e"
Answer: e
Problem: what two - digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 15 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 15 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 73 thus the answer is d"
Answer: d
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 47 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 296 , e ) 282.4
Rationale: 1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 47 cm . : 47 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 47 / ( 4.81 ) = 296 answer will be d .
Answer: d
Problem: a train 800 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 87 kmph , b ) 97 kmph , c ) 72 kmph , d ) 144 kmph , e ) 120 kmph
Rationale: "length = speed * time speed = l / t s = 800 / 20 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"
Answer: d
Problem: if it is 5 : 14 in the evening on a certain day , what time in the morning was it exactly 2 , 880,702 minutes earlier ? ( assume standard time in one location . )
Options: a ) 5 : 32 , b ) 5 : 36 , c ) 5 : 48 , d ) 5 : 54 , e ) 5 : 58
Rationale: 5 : 14 minus 2 , 880,702 must end with 2 , the only answer choice which ends with 2 is a . answer : a .
Answer: a
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 14 weavers in 14 days ?
Options: a ) 40 , b ) 45 , c ) 49 , d ) 53 , e ) 58
Rationale: "1 weaver can weave 1 mat in 4 days . 14 weavers can weave 14 mats in 4 days . 14 weavers can weave 49 mats in 14 days . the answer is c ."
Answer: c
Problem: diana is painting statues . she has 7 / 8 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?
Options: a ) 10 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: number of statues = all the paint ÷ amount used per statue = 7 / 8 ÷ 1 / 16 = 7 / 8 * 16 / 1 = 112 / 8 = 14 . answer is d .
Answer: d
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.4 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 200 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 × $ 0.4 = $ 200 the answer is a ."
Answer: a
Problem: if pintu is coded as 79523 in a certain code language , how would you code jumbo in the same language ?
Options: a ) 13426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . jumbo is 13426 . . . answer : a
Answer: a
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 10 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 ⁄ 15 = 3 ⁄ 5 remaining job = 1 - 3 ⁄ 5 = 2 ⁄ 5 remaining job can be done by ashutosh in 2 ⁄ 5 × 10 = 4 hours answer a"
Answer: a
Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 3 ohms and y is 5 ohms ?
Options: a ) 15 / 8 , b ) 3 / 8 , c ) 5 / 8 , d ) 7 / 15 , e ) 8 / 15
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 3 + 1 / 5 = 8 / 15 r = 15 / 8 the answer is a ."
Answer: a
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.12510168 ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 9 digits after decimal total no . of decimals = 11 req . no . of digits = ( n - 1 ) = ( 11 - 1 ) = 10 answer : c"
Answer: c