regisss/math_qa huggingface dataset:
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 350 , c ) $ 282 , d ) $ 274 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 14 = 16 * 14 = 224 $ total charge = 126 + 224 = 350 $ answer b"
Answer: b
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 125 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 416 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 125 mangoes = 125 * 3.33 = 416 . answer d"
Answer: d
Problem: calculate the time it will take for a full tank of water to become completely empty due to a leak given that the tank could be filled in 10 hours , but due to the leak in its bottom it takes 11 hours to be filled ?
Options: a ) 90 hours , b ) 80 hours , c ) 50 hours , d ) 120 hours , e ) 110 hours
Rationale: part filled without leak in 1 hour = 1 / 10 part filled with leak in 1 hour = 1 / 11 work done by leak in 1 hour = 1 / 10 â ˆ ’ 1 / 11 = 110 hours answer : e
Answer: e
Problem: in the first 25 overs of a cricket game , the run rate was only 5.4 . what should be the run rate in the remaining 25 overs to reach the target of 400 runs ?
Options: a ) 16.5 , b ) 13.2 , c ) 10.6 , d ) 11.2 , e ) 7.25
Rationale: required run rate = 400 - ( 5.4 x 25 ) / 25 = 265 / 25 = 10.6 option c
Answer: c
Problem: if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 279 , what is their sum ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 7 ^ 3 = 343 the two numbers are 4 and 7 . the answer is d ."
Answer: d
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12100 after a year ?
Options: a ) 3630 , b ) 3877 , c ) 2667 , d ) 2977 , e ) 2378
Rationale: "explanation : 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3630 answer : a"
Answer: a
Problem: what is the unit digit in 4 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5
Rationale: unit digit in 4 ^ 100 = unit digit in [ ( 4 ^ 4 ) ^ 25 ] but unit digit in 4 ^ 4 = 6 unit digit 4 ^ 100 = 6 answer is c
Answer: c
Problem: the average age of 37 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 ) 52 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 38 * 15 - 37 * 14 ) years = 52 years . answer : d"
Answer: d
Problem: pipe a can fill a tank in 12 hours . due to a leak at the bottom , it takes 18 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 36 , b ) 87 , c ) 40 , d ) 37 , e ) 86
Rationale: "let the leak can empty the full tank in x hours 1 / 12 - 1 / x = 1 / 18 = > 1 / x = 1 / 12 - 1 / 18 = ( 3 - 2 ) / 36 = 1 / 36 = > x = 36 . answer : a"
Answer: a
Problem: if one and a half women , drink one and a half tea in one and a half minutes . how many tea can 9 women drink in 3 minutes ?
Options: a ) 11 , b ) 8 , c ) 37 , d ) 15 , e ) 18
Rationale: e 18 explanation : more minutes implies more tea . more women implies more tea . the time become twice ( 3 minutes / 1.5 minutes ) . women become six times ( 9 / 1.5 ) . number of tea = 2 * 6 * original ( 1.5 )
Answer: e
Problem: a can run 2 km distance in 2 min 20 seconds , while b can run this distance in 3 min 5 sec . . by how much distance can a beat b ?
Options: a ) 900 m , b ) 500 m , c ) 120 m , d ) 180 m , e ) 190 m
Rationale: a takes time 2.20 minutes = 140 sec b takes time 3 minutes = 185 sec difference = 185 - 140 = 45 sec now we are to find distance covered in 40 sec by b 180 sec = 2000 m 1 sec = 100 / 9 m 45 sec = 45 x 100 / 9 = 500 m answer : b
Answer: b
Problem: the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is :
Options: a ) rs . 3900 , b ) rs . 3990 , c ) rs . 4000 , d ) rs . 4100 , e ) rs . 4200
Rationale: "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a"
Answer: a
Problem: if the remainder is 15 when the integer n is divided by 28 , what is the remainder when 2 n is divided by 14 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 28 k + 15 2 n = 2 ( 28 k + 15 ) = 4 k * 14 + 30 = 4 k * 14 + 2 * 14 + 2 = 14 j + 2 the answer is c ."
Answer: c
Problem: rice weighing 25 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "25 / 2 ÷ 4 = 25 / 8 pounds in each container 25 / 8 pounds * 16 ounces / pound = 50 ounces in each container the answer is b ."
Answer: b
Problem: a man sold 18 toys for rs . 21000 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1000
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 21000 . gain = sp â € “ cp 3 x = 21000 â € “ 18 x 21 x = 21000 x = rs . 1000 . answer : option e"
Answer: e
Problem: in a school of 700 students , 45 % wear blue shirts , 23 % wear red shirts , 15 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 109 , b ) 119 , c ) 129 , d ) 139 , e ) 149
Rationale: 45 + 23 + 15 = 83 % 100 – 83 = 17 % 700 * 17 / 100 = 119 the answer is b .
Answer: b
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 9 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 60 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 9 . let c be the event that both are selected . p ( c ) = p ( a ) × p ( b ) as a and b are independent events : = ( 1 / 7 ) × ( 2 / 9 ) = 2 / 63 answer : c ) 2 / 63"
Answer: c
Problem: 150 metres long yard , 11 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 15 , c ) 14 , d ) 16 , e ) 17
Rationale: "11 trees have 10 gaps between them , required distance ( 150 / 10 ) = 15 b"
Answer: b
Problem: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 231 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 120 , c ) 154 , d ) 160 , e ) 210
Rationale: 125 % of 120 % of a = 231 125 / 100 * 120 / 100 * a = 231 a = 231 * 2 / 3 = 154 . answer c
Answer: c
Problem: the length of the bridge , which a train 150 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 377 , b ) 225 , c ) 237 , d ) 245 , e ) 267
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 x = 225 m . answer : b"
Answer: b
Problem: a boat running up stram takes 4 hours to cover a certain distance , while it takes 8 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 3 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 4 ( x + y ) = 8 ( x - y ) 4 x + 4 y = 8 x - 8 y 12 y = 4 x 3 y = x x / y = 3 / 1 3 : 1 answer : option d"
Answer: d
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many w acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn w = 4 * 94 = 376 correct option - c"
Answer: c
Problem: find the l . c . m of 22 , 25 , 44 and 20 .
Options: a ) 1240 , b ) 1600 , c ) 1320 , d ) 1150 , e ) 1100
Rationale: "explanation : 2 x 2 x 11 x 5 x 5 = 1100 answer : option e"
Answer: e
Problem: 3 models ( f , g , and h ) of cars are distributed among 3 showrooms . the number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom . there are 19 cars of model f , 17 cars of model g , and 15 cars of model h . what is the maximum number of cars of model f in any showroom ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: the total number of cars is 51 . so each showroom has 17 cars ( since the number of cars in each showrooms should be equal 51 / 3 = 17 ) . moreover that the number of model f is maximum means that the numbers of model g and h should be minimum . since each model must be represented by at least one car in every showroom that minimum number should be 1 . so maximum number of model f is 17 - 2 = 15 . the answer is ( c )
Answer: c
Problem: the timing of a college is from 12 p . m to 5.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 56 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 5 hours 00 minutes = 300 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 300 â € “ 20 ) / 5 = 56 minutes answer a"
Answer: a
Problem: if q = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
Options: a ) 0 and 3 , b ) 3 and 6 , c ) 6 and 9 , d ) 9 and 12 , e ) 12 and 15
Rationale: my attempt : if q = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 .
Answer: b
Problem: what is the units digit of 29 ! + 50 ! + 3 ! + 3 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 6 = 12 the units digit is 2 . the answer is b ."
Answer: b
Problem: a train 285 m long , running with a speed of 54 km / hr will pass a tree in
Options: a ) 19 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 54 x 5 / 18 ) m / sec . = 15 m / sec . time taken = ( 285 x 1 / 15 ) sec = 19 sec answer a"
Answer: a
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 7 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 81 , d ) 17 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 7 have their meal , the meal left can be catered to 63 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 63 adults = 81 children hence , the meal can be catered to 81 children . answer : c"
Answer: c
Problem: if 42 / 330 = 0.1272 , what is the 32 nd digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 2
Rationale: "we are not concerned what 42 / 330 means . . we have to look at the decimal . . 0 . . 1272 means 0.1272727 . . . so leaving first digit to the right of decimal , all odd numbered are 7 and all even numbered are 2 . here 32 is even , so ans is 2 answer is e"
Answer: e
Problem: a began business with rs . 36000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 2
Rationale: "36 * 12 : 54 * x = 2 : 1 x = 4 12 - 4 = 8 answer : d"
Answer: d
Problem: find the value of √ ( 25 / 16 ) .
Options: a ) 5 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 3 , e ) 5 / 4
Rationale: "√ ( 25 / 16 ) = √ 25 / √ 16 = 5 / 4 answer is e ."
Answer: e
Problem: how many of the positive factors of 24 are not factors of 25
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 25 - 1,5 , 25 comparing both , we have 1 factor of 24 which are not factors of 25 - 1 answer : d"
Answer: d
Problem: a man can do a piece of work in 4 days , but with the help of his daughter , he can do it in 3 days . in what time can his daughter do it alone ?
Options: a ) 12 , b ) 28 , c ) 26 , d ) 19 , e ) 112
Rationale: explanation : daughter ’ s 1 day ’ s work = ( 1 / 3 – 1 / 4 ) = 1 / 12 daughter alone can do the work in 12 / 1 = 12 days answer : a
Answer: a
Problem: john had a stock of 900 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 55.3 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 900 - n = 900 - 402 = 498 percentage books not sold / total number of books = 498 / 900 = 0.553 = 55.3 % correct answer e"
Answer: e
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 738 , c ) 654 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 825 ) = rs . 29 . s . i . for 3 years = rs . ( 29 x 3 ) = rs . 87 . principal = rs . ( 825 - 87 ) = rs . 738 answer : b"
Answer: b
Problem: the age of father 7 years ago was 5 times the age of his son . 5 years hence , father ' s age will be thrice that of his son . the ratio of their present ages is :
Options: a ) 67 : 19 , b ) 65 : 17 , c ) 61 : 19 , d ) 63 : 15 , e ) 67 : 17
Rationale: let the ages of father and son 7 years ago be 5 x and x years respectively . then , ( 5 x + 7 ) + 5 = 3 [ ( x + 7 ) + 5 ] 5 x + 12 = 3 x + 36 x = 12 . required ratio = ( 5 x + 7 ) : ( x + 7 ) = 67 : 19 . answer : option a
Answer: a
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 14 inches on a side and costs $ 10 , and a large pizza that measures 21 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 10 square inches , c ) 49 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 14 * 14 = 196 ) for the small pizza and ( 21 * 21 = 441 ) for the large pizza . in total sq inches that would be ( 196 + 441 ) * 2 = 1274 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 441 = 1323 sq inches . hence , the difference is 49 square inches more ( 1323 - 1274 ) . the correct answer is c"
Answer: c
Problem: if the lcm of a and b is 72 and their hcf is 6 , what is the product of a & b ?
Options: a ) 432 , b ) 433 , c ) 434 , d ) 435 , e ) 436
Rationale: the most important property of lcm ( the least common multiple ) and gcd ( the greatest common divisors ) is : for any positive integers x and y , x ∗ y = gcd ( x , y ) ∗ lcm ( x , y ) so ab = 72 * 6 = 432 . answer : a
Answer: a
Problem: in a 120 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 8 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 120 m in 7 / 56 * 120 = 15 seconds since a beats b by 7 seconds , a runs 120 m in ( 15 - 7 ) = 8 seconds hence , a ' s time over the course = 8 seconds answer : d"
Answer: d
Problem: if x is a randomly chosen integer between 1 and 20 , inclusive , and y is a randomly chosen integer between 21 and 40 , inclusive , what is the probability that xy is a multiple of 4 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 7 / 16 , e ) ½
Rationale: there are two ways that i see of getting a multiple of 4 1 ) x and / or y is a multiple of 4 2 ) x is a multiple of 2 and y is a multiple of 2 for 1 we have p ( option 1 ) = ( 5 / 20 ) ( 20 / 20 ) + ( 5 / 20 ) ( 20 / 20 ) - ( 5 / 20 ) ( 5 / 20 ) = 1 / 2 - 1 / 16 since 5 of the numbers in each range are divisible by 4 , and if either x or y is selected to be divisible by 4 the selection of the other variable does not matter . notice the last subtraction term which corrects the fact that we have counted the possibility of both being divisible by 4 twice ( e . g . p ( a union b ) = p ( a ) + p ( b ) - p ( a and b ) ) . notice at this point that the probability of option one is already 7 / 16 , the second largest available option . if we can come up with any other possibilities for getting xy divisble by 4 we must go with option e . of course this is the case because if we select a multiple of 2 that is not a multiple of 4 from both ranges of numbers , the product is divisible by 4 . we can formally compute this as : p ( option 2 ) = ( 5 / 20 ) * ( 5 / 20 ) = 1 / 16 since we do not wish to double count possibilities that fall into category 1 , we only count the probability of selecting even numbers from each set that are not divisible by 4 ( e . g . the other 5 even integers in each set ) . total probability is then p ( option 1 ) + p ( option 2 ) = 1 / 2
Answer: e
Problem: the average of 20 number is zero of them at the most , how many may be greater than zero ?
Options: a ) 0 , b ) 1 , c ) 10 , d ) 19 , e ) 20
Rationale: solution average of 20 numbers = 0 . ∴ sum of 20 numbers = ( 0 × 20 ) = 0 . it is quite possible that 19 of these number may be positive and if their sum is a , then 20 th number is ( - a ) . answer d
Answer: d
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1792 ?
Options: a ) 1600 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771
Rationale: "1792 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1600 . answer : a"
Answer: a
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,800 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,800 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.8 so , answer is d ."
Answer: d
Problem: there are 200 female managers in a certain company . find the total number r of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) r = 300 , b ) r = 400 , c ) r = 500 , d ) 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 49 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 49 , so 0.14 * { total } = 49 - - > { total } = 350 . answer : e ."
Answer: e
Problem: how many litres of pure acid are there in 8 litres of a 20 % solution ?
Options: a ) 2 litres , b ) 1.4 litres , c ) 1 litres , d ) 1.6 litres , e ) none of these
Rationale: "explanation : quantity of pure acid = 8 × ( 20 / 100 ) = 1.6 answer : option d"
Answer: d
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 500 m long ?
Options: a ) 266 sec , b ) 170 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1700 m t = d / s t = 1700 / 10 t = 170 sec answer : b"
Answer: b
Problem: what is the least number which when divided by 6 , 7 , 9 and 18 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 136 , d ) 156 , e ) 166
Rationale: "explanation : lcm of 6 , 7 , 9 and 18 is 126 required number = 126 + 4 = 130 answer : option a"
Answer: a
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 50 % profit ?
Options: a ) 277 , b ) 960 , c ) 277 , d ) 266 , e ) 121
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 150 % of rs . 640 = 150 / 100 * 640 = rs . 960 . answer : b"
Answer: b
Problem: a room 14 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 22636 , b ) 22640 , c ) 22647 , d ) 22533 , e ) 22675
Rationale: "explanation : area of the room = ( 1421 x 777 ) cm 2 . size of largest square tile = h . c . f . of 1421 cm and 777 cm = 7 cm . area of 1 tile = ( 7 x 7 ) cm 2 . number of tiles required = ( 1147 × 777 ) / ( 7 × 7 ) = 22533 answer : option d"
Answer: d
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 5 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 32 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 5 + 3 ) * 4 = 32 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : a"
Answer: a
Problem: the number which exceeds 16 % of it by 105 is :
Options: a ) 125 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: solution solution let the number be x . x - 16 % of x = 105 x - 16 / 100 x = 105 x - 4 / 25 x = 105 21 / 25 x = 105 x = ( 105 x 25 / 21 ) = 125 answer a
Answer: a
Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 6 : 9 , find the age of sachin
Options: a ) 24.5 , b ) 14 , c ) 24.21 , d ) 27 , e ) 25
Rationale: "explanation : if rahul age is x , then sachin age is x - 7 , so , 9 x - 63 = 6 x 3 x = 63 x = 21 so sachin age is 21 - 7 = 14 answer : b ) 14"
Answer: b
Problem: a man has some hens and cows . if the number of heads be 44 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 18 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 44 implies , 2 x + 4 y = 140 and x + y = 44 solving these two equations , we get x = 18 and y = 26 therefore , hens are 26 . answer : c"
Answer: c
Problem: in the x - y plane , there are 4 points ( 00 ) , ( 04 ) , ( 54 ) , and ( 50 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8
Rationale: the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b .
Answer: b
Problem: the probability of two events a and b are 0.25 and 0.35 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.55 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 35 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : a"
Answer: a
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 8 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 17 , e ) 50
Rationale: "his height was = 5 feet 8 inch = 8 + 60 = 68 inch . required % correction = 68 * ( 1.25 - 1 ) = 17 d"
Answer: d
Problem: the tens digit of a two digit number is 4 times of its unit digit and the sum of the digits be 10 . then the first number is
Options: a ) 67 , b ) 73 , c ) 53 , d ) 82 , e ) 89
Rationale: let the number be 10 x + y according to the question x = 4 y x + y = 10 4 y + y = 10 or y = 2 and x = 8 so required number is = 10 * 8 + 2 = 82 answer : d
Answer: d
Problem: a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 180 - 50 ) m = 130 m . answer : c
Answer: c
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 40 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 333 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 40 ) = 21 + 312 = > 333 hence answer will be ( a ) 333"
Answer: a
Problem: in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is
Options: a ) 50 liters , b ) 55 liters , c ) 60 liters , d ) 70 liters , e ) 75 liters
Rationale: "quantity of milk = 60 x 2 litres = 40 litres . 3 quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = 40 . 20 + x now , 40 = 1 20 + x 2 20 + x = 80 x = 60 . quantity of water to be added = 60 liters . c"
Answer: c
Problem: a 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 280 / 9 = 500 / 9 x = 220 ans is 220 m answer : b"
Answer: b
Problem: find the average of all the numbers between 11 and 34 which are divisible by 5 ?
Options: a ) 10 , b ) 20 , c ) 22 , d ) 30 , e ) 15
Rationale: "average = ( 15 + 20 + 25 + 30 ) 4 = 90 / 4 = 22 answer is c"
Answer: c
Problem: x and y can do a piece of work in 20 days and 12 days respectively . x started the work alone and then after 4 days y joined him till the completion of work . how long did the work last ?
Options: a ) 8 days , b ) 10 days , c ) 12 days , d ) 13 days , e ) 14 days
Rationale: "let the total units of work to be completed be 60 . units of work completed by x in a single day = 60 / 20 = 3 units . units of work completed by y in a single day = 60 / 12 = 5 units . thus , 8 units of work can be done by them in a single day working together . x works for 4 days alone = 12 units of work . remaining work = ( 60 - 12 ) = 48 units . now , x and y works together to complete the remaining work = 48 / 8 = 6 days hence , total days taken to complete the work = ( 6 + 4 ) = 10 days . answer : b"
Answer: b
Problem: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 1 * 1 / 4 = 1 / 4 answer : a"
Answer: a
Problem: find the curved surface area , if the radius of a cone is 7 m and slant height is 14 m ?
Options: a ) 308 , b ) 369 , c ) 434 , d ) 476 , e ) 513
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 7 ã — 14 = 22 ã — 14 = 308 m ( power 2 ) answer is a ."
Answer: a
Problem: if | x | = 9 x - 16 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 2 , d ) 4 , e ) - 1 / 2
Rationale: substituted option c i . e x = 2 . inequality satisfied . this eliminates all options except answer is c
Answer: c
Problem: sonika deposited rs . 8000 which amounted to rs . 10200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 10680 , c ) 2999 , d ) 2774 , e ) 1212
Rationale: "( 8000 * 3 * 2 ) / 100 = 480 10200 - - - - - - - - 10680 answer : b"
Answer: b
Problem: the average monthly salary of 24 employees in an organisation is rs . 2400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4900 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 2500 * 25 - 2400 * 24 ) = rs . 4900 answer : c"
Answer: c
Problem: the s . i . on a certain sum of money for 6 years at 16 % per annum is half the c . i . on rs . 8000 for 2 years at 20 % per annum . the sum placed on s . i . is ?
Options: a ) 3000.33 , b ) 2802.33 , c ) 1833.33 , d ) 2990.33 , e ) 2982.33
Rationale: c . i . = [ 8000 * ( 1 + 20 / 100 ) 2 - 8000 ] = ( 8000 * 6 / 5 * 6 / 5 - 8000 ) = rs . 3520 . sum = ( 3520 * 100 ) / ( 6 * 16 ) = rs . 1833.33 answer : c
Answer: c
Problem: a farmer wishes to start a 100 square metres rectangular vegetable garden . since he has only 30 m barbed wire , he fences three sides of the garden letting his house compound wall act as the fourth side fencing . the dimension of the garden is :
Options: a ) 15 m × 6.67 m
b ) 20 m × 5 m
c ) 30 m × 3.33 m
d ) 40 m × 2.5 m
e ) none of these
Rationale: we have : 2 b + l = 30 ⇒ l = 30 – 2 b . area = 100 m 2 ⇒ l × b = 100 ⇒ b ( 30 – 2 b ) = 100 ⇒ b 2 – 15 b + 50 = 0 ⇒ ( b – 10 ) ( b – 5 ) = 0 ⇒ b = 10 or b = 5 . when b = 10 , l = 10 and when b = 5 , l = 20 . since the garden is rectangular , so its dimension is 20 m × 5 m . answer b
Answer: b
Problem: if z is a multiple of 9402 , what is the remainder when z ^ 2 is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the sum of the digits is 9 + 4 + 2 = 15 . thus 3 is a factor of 9402 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a ."
Answer: a
Problem: a techno company has 14 machines of equal efficiency in its factory . the annual manufacturing costs are rs 42000 and establishment charges are rs 12000 . the annual output of the company is rs 70000 . the annual output and manufacturing costs are directly proportional to the number of machines . the shareholders get 12.5 profit , which is directly proportional to the annual output of the company . if 7.14 machines remain closed throughout the year , then the percentage decrease in the amount of profit of the shareholders would be :
Options: a ) 12 % , b ) 12.5 % , c ) 13.5 % , d ) 13 % , e ) 14 %
Rationale: explanation : the original profit is : - = > 70000 − 42000 − 12000 = 16000 . if 7.14 % of 14 i . e . one of the machines closed throughout the year , then the change in profit will be : - = > ( 13 / 14 ) × [ 70000 − 42000 ] . = > 14000 . thus , decrease in the profit % is : - = > ( 2000 / 16000 ) × 100 . = > 12.5 % . answer : b
Answer: b
Problem: p and q can complete a work in 80 days and 48 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?
Options: a ) 35 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 8 days = 8 ã — ( 1 / 80 ) = 1 / 10 remaining work = 1 â € “ 1 / 10 = 9 / 10 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 9 / 10 ) / ( 1 / 30 ) = 27 total days = 8 + 27 = 35 answer : option a"
Answer: a
Problem: a and b together can complete work in 6 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 3 , b ) 8 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 6 - 1 / 6 = 1 / 6 b alone can complete the work in 6 days so half of the work in 3 days answer : option a
Answer: a
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 4 ) = 0 and f ( - 3 ) = 0 , then b + c =
Options: a ) 18 , b ) 15 , c ) - 13 , d ) - 21 , e ) - 24
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 4 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 4 ) = 0 = 16 + 4 b + c - - - taking 16 to the other side - > 4 b + c = - 16 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 7 b = - 7 - - - > b = - 1 and while substituting b = - 1 we get c = - 12 . b + c = - 13 - - - answer c"
Answer: c
Problem: how many even number in the range between 25 to 100 inclusive are not divisible by 3
Options: a ) 27 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 26 , 28,30 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 38 . for 6 , 36 , 42 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 11 . hence , only divisible by 2 but not 3 = 38 - 11 = 27 . hence , answer a"
Answer: a
Problem: sum of two numbers is 30 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 30 2 x – 3 y = 5 x = 19 y = 11 c )"
Answer: c
Problem: the sum of three consecutive multiples of 3 is 72 . what is the larget number ?
Options: a ) 26 , b ) 27 , c ) 46 , d ) 57 , e ) none
Rationale: "sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 ⇔ 9 x = 63 ⇔ x = 7 . ∴ largest number = 3 x + 6 = 27 . answer b"
Answer: b
Problem: 9 log 9 ( 6 ) = ?
Options: a ) 1 , b ) 6 , c ) 3 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 6 ) = 6 correct answer b"
Answer: b
Problem: two mixtures of a and b have a and b in the ratio 3 : 2 and 3 : 4 . in what proportion should these two mixtures be mixed to get a new mixture in which the ration of a to b is 5 : 4 ?
Options: a ) 6 : 1 , b ) 5 : 4 , c ) 20 : 7 , d ) 10 : 9 , e ) 14 : 11
Rationale: i got c but with a different , yet slightly longer approach , which i constantly use for proportion problems such as this one . usually , this approach is very efficient when used with slightly difficult questions , but this problem is quite hard so i had to slightly tweak it . i will show you how i usually use the approach and later show you how to use it with this specific problem . example . 1 liter of solution a contains 45 % alcohol , while 1 liter of solution b contains 20 % alcohol . in what ratio must the two solutions be used to get a solution with 30 % alcohol solution : 1 . 45 / 100 * [ a / ( a + b ) ] + 20 / 100 * [ b / ( a + b ) ] = 30 / 100 2 . multiply 100 to both sides to arrive at 45 a / ( a + b ) + 20 b / ( a + b ) = 30 3 . multiply ( a + b ) to both sides to arrive at 45 a + 20 b = 30 a + 30 b 4 . distribute to arrive at 15 a = 10 b 5 . thus the ratio is a / b = 10 / 15 = 2 / 3 now using this same approach , we tackle gopu 106 ’ s question . it is important to first think of x in the mixture as the alcohol in the problem above ; hence , a mixture of x and y in the ratio of 3 : 2 translates to x is 3 / 5 of the solution . applying this concept to all three equations , we write : 1 . 3 / 5 * [ a / ( a + b ) ] + 3 / 7 * [ b / ( a + b ) ] = 5 / 9 2 . now here is the tweak that must be made to continue with this approach . you must find the common denominator for all three numbers and organize the fractions accordingly . by finding the common denominator of 5 , 79 ( or 315 ) we re - write the equations as follows 3 . 189 / 315 * [ a / ( a + b ) ] + 135 / 315 * [ b / ( a + b ) ] = 175 / 315 4 . multiply 315 to both sides to arrive at 189 a / ( a + b ) + 135 b / ( a + b ) = 175 5 . multiply ( a + b ) to both sides to arrive at 189 a + 135 b = 175 a + 175 b 6 . distribute to arrive at 14 a = 40 b 7 . thus the ratio is a / b = 40 / 14 = 20 / 7 or answer c
Answer: c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 60 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 80 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 60 % is one st . dev , then on either side of m we have 60 / 2 = 30 % . so , 30 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 30 = 80 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 80 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it a"
Answer: a
Problem: 8 kilograms of rice costing rs . 16 per kg is mixed with 4 kilograms of rice costing rs . 22 per kg . what is the average price of the mixture ?
Options: a ) 20 , b ) 18 , c ) 16 , d ) 19 , e ) 17
Rationale: p 1 = rs . 16 per kg , p 2 = rs . 22 per kg , q 1 = 8 kg , q 2 = 4 kg now , p = ( p 1 q 1 + p 2 q 2 ) / ( q 1 + q 2 ) average price of the mixture = 8 * 16 + 4 * 22 / 12 = 128 + 88 / 12 = 216 / 12 = 18 answer : b
Answer: b
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 70 metres ?
Options: a ) 22 seconds , b ) 65 seconds , c ) 78 seconds , d ) 12 seconds , e ) 14 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 70 / 5 = 14 seconds . answer : e"
Answer: e
Problem: if the numbers 1 to 99 are written on 99 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 99 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 73 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 99 . answer : c"
Answer: c
Problem: a trader purchased two colour televisions for a total of rs . 35000 . he sold one colour television at 30 % profit and the other 40 % profit . find the difference in the cost prices of the two televisions if he made an overall profit of 32 % ?
Options: a ) 21000 , b ) 21009 , c ) 21029 , d ) 21298 , e ) 21098
Rationale: let the cost prices of the colour television sold at 30 % profit and 40 % profit be rs . x and rs . ( 35000 - x ) respectively . total selling price of televisions = x + 30 / 100 x + ( 35000 - x ) + 40 / 100 ( 35000 - x ) = > 130 / 100 x + 140 / 100 ( 35000 - x ) = 35000 + 32 / 100 ( 35000 ) x = 28000 35000 - x = 7000 difference in the cost prices of televisions = rs . 21000 answer : a
Answer: a
Problem: an article is bought for rs . 775 and sold for rs . 900 , find the gain percent ?
Options: a ) 11.1 % , b ) 12.1 % , c ) 13.1 % , d ) 15.1 % , e ) 16.1 %
Rationale: "775 - - - - 125 100 - - - - ? = > 16.1 % answer : e"
Answer: e
Problem: 9 ! / ( 9 - 3 ) ! = ?
Options: a ) 336 , b ) 346 , c ) 356 , d ) 366 , e ) 504
Rationale: 9 ! / ( 9 - 3 ) ! = 9 ! / 6 ! = 9 * 8 * 7 = 504 . hence , the correct answer is e .
Answer: e
Problem: if 213 × 16 = 3408 , then 1.6 × 21.3 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 1.6 × 21.3 = ( 16 / 10 x 213 / 10 ) = ( 16 x 213 / 100 ) = 3408 / 100 = 34.08 . answer c"
Answer: c
Problem: if the simple interest on a sum of money for 5 years at 18 % per annum is rs . 900 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 1287.76 , b ) rs . 1284.76 , c ) rs . 1587.76 , d ) rs . 1266.76 , e ) rs . 1283.76
Rationale: "sum = ( 900 * 100 ) / ( 5 * 18 ) = rs . 1 , 000.00 c . i . on rs . rs . 1 , 000.00 for 5 years at 18 % = rs . 2 , 287.76 . = rs . 2 , 287.76 - 1 , 000.00 = rs . 1287.76 answer : a"
Answer: a
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 150 . the amount of the bill is
Options: a ) 1200 , b ) 1764 , c ) 1400 , d ) 1354 , e ) none of these
Rationale: explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 150 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 150 or x = 1250 . p . w . = rs . 1250 sum due = p . w . + t . d . = rs . ( 1250 150 ) = rs . 1400 answer : c
Answer: c
Problem: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.81 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.81 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.81 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.81 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Problem: a freight elevator can carry a maximum load of 1100 pounds . sean , who weighs 200 pounds , is in the elevator with two packages weighing 150 pounds and 280 pounds . if he needs to fit 3 more packages in the elevator that weigh as much as possible without exceeding the elevator limit , what is the difference between their average and the average of the two packages already in the elevator ?
Options: a ) 59 , b ) 85 , c ) 190 , d ) 215 , e ) 210
Rationale: the average of existing 2 package is 150 + 280 / 2 = 430 / 2 = 215 remaining allowed weight = 1100 - 200 - 430 = 470 . allowed per package = 470 / 3 = 156 so difference in average of existing and allowable = 215 - 156 = 59 hence a
Answer: a
Problem: power windows : 60 % anti - lock brakes : 25 % cd player : 75 % the table above shows the number of vehicles at bill ' s car dealership that have certain features . no vehicle has all 3 features , but 10 % have power windows and anti - lock brakes , 15 % have anti - lock brakes and a cd player , and 22 % have power windows and a cd player . what percent of the vehicles at bill ' s car dealership have a cd player but no power windows or anti - lock brakes ?
Options: a ) 25 , b ) 18 , c ) 11 , d ) 38 , e ) 0
Rationale: answer : d were looking for the number of cars with a cd player but no other features . we know that 40 % of the cars have a cd player , 15 % have a cd player and anti - lock brakes , while 22 % have a cd player and power windows . since no car has all three features , those account for all of the possibilities except for what were looking for . if a car has a cd player , it must either have anti - lock brakes , power windows , or no other features . since the total of cars with a cd player is 75 % , we can set up the following equation : 75 = 15 + 22 + x x = 38 , choiced .
Answer: d
Problem: a train 360 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 30 sec , c ) 26 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 50 = 30 sec answer : b"
Answer: b
Problem: the value of ( log 9 27 + log 8 32 ) is :
Options: a ) 7 / 2 , b ) 19 / 6 , c ) 5 / 3 , d ) 7 , e ) 8
Rationale: let log 9 27 = x . then , 9 x = 27 = > ( 32 ) x = 33 = > 2 x = 3 = > x = 3 / 2 let log 8 32 = y . then 8 y = 32 = > ( 23 ) y = 25 = > 3 y = 5 = > y = 5 / 3 answer : c
Answer: c
Problem: a meal cost $ 37.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 41 - 43 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 37.5 ) = 3.75 15 % ( 37.5 ) = 5.625 total amount could have been 37.5 + 3.75 and 37.5 + 5.625 = > could have been between 41.25 and 43.125 = > approximately between 41 and 43 answer is a ."
Answer: a
Problem: find the slope of the line perpendicular to the line y = ( 1 / 4 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 4 , 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 / 4 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 4 ) = - 1 solve for m m = - 4 correct answer c ) - 4"
Answer: c
Problem: a person can row at 9 kmph and still water . he takes 7 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 60 km , b ) 87 km , c ) 33 km , d ) 67 km , e ) 20 km
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 7.5 = > x / 10 + x / 8 = 15 / 2 = > ( 4 x + 5 x ) / 40 = 15 / 2 = > x = 33 km . answer : c"
Answer: c
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 4 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 4 4 - - - - - - - - - ? è 16 answer : a"
Answer: a