regisss/math_qa huggingface dataset:
Problem: 10 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 75
Rationale: "there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake . total = 45 + 30 = 75 ans : e"
Answer: e
Problem: a goods train runs at a speed of 72 kmph and crosses a 280 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 280 + x / t 72 * 5 / 18 = 280 + x / 26 x = 240 answer : b"
Answer: b
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 100 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 18 , b ) 16 , c ) 17 , d ) 15 , e ) 19
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 100 5 x - 10 = 100 5 x = 90 x = 18 answer : a"
Answer: a
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 3 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 19.5
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 3 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 3 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 3 x = 4.5 since you need a 15 l solution , you must evaporate 19.5 of the original 50 l solution to get a 3 % solution . answer is e ."
Answer: e
Problem: average age of 7 members of a family is 29 years . if present age of the youngest member is 5 year , find average age of the remaining members at the time of birth of the youngest member .
Options: a ) 28 , b ) 37 , c ) 29 , d ) 237 , e ) 212
Rationale: average age ( present ) of 7 members = 29 years 5 years ago , average age of 7 members was 29 - 5 = 24 years . since , the youngest member was not born 5 years ago . therefore , average age of remaining 6 members is increased by 246246 = 4 years . therefore , 5 years ago , average age of 6 members was 24 + 4 = 28 years . answer : a
Answer: a
Problem: there is a 50 % chance jen will visit chile this year , while there is a 25 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? [ / b ]
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 63.5 % , e ) 75 %
Rationale: "the thing to note in the question is she would not be visiting both . thus p ( chile ) * ( 1 - p ( madagascar ) ) + p ( madagascar ) * ( 1 - p ( chile ) ) which is ( 1 / 2 * 3 / 4 ) + ( 1 / 4 * 1 / 2 ) , 3 / 8 * 1 / 8 = 1 / 2 = 50 % answer : b"
Answer: b
Problem: thabo owns exactly 200 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 35 , d ) 45 , e ) 50
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 200 3 x + 60 + x = 200 x = 35 answer ( c . )"
Answer: c
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 14 - > t = 20 . c = 6 . mo drinks 4 cups of tea a day then number of days that are not rainy = 20 / 4 = 5 so number of rainy days = 7 - 5 = 2 a is the answer ."
Answer: a
Problem: the market value of a certain machine decreased by 25 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 4,000 , e ) $ 800
Rationale: "d . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 25 / 100 ) = 8000 - 2000 = $ 6000 market value in 1984 = market value in 1983 - ( 25 % of $ 8000 ) = 6000 - 2000 = $ 4000"
Answer: d
Problem: if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 12 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 12 is 1 . answer : b"
Answer: b
Problem: in the manufacture of a certain product , 10 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.25 % , b ) 0.5 % , c ) 0.75 % , d ) 1.25 % , e ) 2.5 %
Rationale: "0.1 * 0.05 = 0.005 = 0.5 % the answer is b ."
Answer: b
Problem: convert 300 inches into centimeter ?
Options: a ) 762 cm , b ) 750 cm , c ) 650 cm , d ) 710 cm , e ) 754 cm
Rationale: "1 inch = 2.54 cm 300 inches = 300 * 2.54 = 762 cm answer is e"
Answer: e
Problem: a boat goes 130 km downstream in 10 hours , and 75 km upstream in 15 hours . the speed of the stream is ?
Options: a ) 3.5 , b ) 3 , c ) 5 , d ) 4 , e ) 8
Rationale: "125 - - - 10 ds = 130 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 13 - 5 ) / 2 = 4 kmph . answer : d"
Answer: d
Problem: pat , kate , and mark charged a total of 135 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 75 , d ) 90 , e ) 108
Rationale: 75 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 135 = > x = 15 30 : 15 : 90 90 - 15 = 75 answer c
Answer: c
Problem: sum of the squares of 3 no . is 52 and the sum of their products taken two at a time is 72 . find the sum ?
Options: a ) 18 , b ) 21 , c ) 13 , d ) 16 , e ) 14
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 52 + 2 * 72 a + b + c = â ˆ š 196 = 14 answer e"
Answer: e
Problem: a bag contains 3 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 3 + 2 + 4 = 9 n ( s ) = 9 c 3 = 84 n ( e ) = 3 c 1 * 2 c 1 * 4 c 1 = 3 * 2 * 4 = 24 probability = 24 / 84 = 2 / 7 answer is a"
Answer: a
Problem: how many seconds will a 650 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 48 km / hr ?
Options: a ) 25 , b ) 45 , c ) 54 , d ) 44 , e ) 48
Rationale: "speed of train relative to man = 48 - 3 = 45 km / hr . = 45 * 5 / 18 = 25 / 2 m / sec . time taken to pass the man = 650 * 2 / 25 = 54 sec . answer : c"
Answer: c
Problem: when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 7 , the remainder is 6 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 6 . . d"
Answer: d
Problem: what is the unit digit in [ ( 6273 ) ^ 1793 x ( 625 ) ^ 317 x ( 341 ) ^ 491 ] ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 5 , e ) none of them
Rationale: unit digit in ( 6374 ) ^ 1793 = unit digit in ( 4 ) ^ 1793 = unit digit in [ ( 4 ^ 2 ) ^ 896 x 4 ] = unit digit in ( 6 x 4 ) = 4 unit digit in ( 625 ) ^ 317 = unit digit in ( 5 ) ^ 317 = 5 unit digit in ( 341 ) ^ 491 = unit digit in ( 1 ) ^ 491 = 1 required digit = unit digit in ( 4 x 5 x 1 ) = 0 answer is 0
Answer: a
Problem: what is the rate percent when the simple interest on rs . 780 amount to rs . 130 in 4 years ?
Options: a ) 4.16 , b ) 5.16 , c ) 6.16 , d ) 7.16 , e ) 8.16
Rationale: "130 = ( 780 * 4 * r ) / 100 r = 4.16 % answer : a"
Answer: a
Problem: the cross - section of a river bank is a trapezium in shape . if the river bank is 12 m wide at the top and 8 m wide at the bottom and the area of cross - section is 500 sq m , the depth of river bank is ?
Options: a ) 20 m , b ) 60 m , c ) 40 m , d ) 50 m , e ) 90 m
Rationale: 1 / 2 * d ( 12 + 8 ) = 500 d = 50 answer : d
Answer: d
Problem: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 2 : 1 , d ) 13 : 11 , e ) 14 : 8
Rationale: correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 6 : 3 = 2 : 1
Answer: c
Problem: x can do a piece of work in 20 days . he works at it for 10 days and then y finished it in 12 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 29 , e ) 30
Rationale: "work done by x in 10 days = 10 * 1 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by y in 12 days whole work will be done by y in 12 * 2 = 24 days answer is c"
Answer: c
Problem: a man can row upstream at 27 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 31 , b ) 92 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 27 ds = 35 m = ( 35 + 27 ) / 2 = 31 answer : a"
Answer: a
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum m of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum m = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Problem: by how much does the larger root of the equation 2 a ^ 2 + 5 a = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: for 2 a ^ 2 + 5 a = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .
Answer: e
Problem: if x + 1 / x = 2 then find x 2 + 1 / x 2
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: if x + 1 / x = p = = > x ^ 2 + 1 / x ^ 2 = p ^ 2 - 2 ans = 2 ^ 2 - 2 = 2 answer : b
Answer: b
Problem: the faces of a triangular prism are to be painted by 5 different colors . in how many ways can be this be done ?
Options: a ) a . 720
b ) b . 256
c ) c . 1
d ) d . 120
e ) e . 36
Rationale: if i have to paint 5 sides with 5 different colour . . . first face can have 5 c 1 options , 2 nd would have 4 c 1 , and subsequent ones would have 3 c 1 , 2 c 1 and 1 options respectively . total options = 5 c 1 x 4 c 1 x 3 c 1 x 2 c 1 x 1 = 120 distinct ways correct answer - d
Answer: d
Problem: three interviewers , a , b , and c are interviewing 30 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 10 applicants , b admitted 12 applicants , and c admitted 15 applicants , at least how many applicants get the admission ?
Options: a ) 6 , b ) 2 , c ) 0 , d ) 8 , e ) 12
Rationale: "if a admitted 10 are overlapping with b admission of 12 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : c"
Answer: c
Problem: during a sale of 30 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 12 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . b"
Answer: b
Problem: there are two cubes with ratio between volume is 125 : 64 . then what is the value of length of each cube ?
Options: a ) 25 : 16
b ) 16 : 25
c ) 4 : 5
d ) 5 : 4
e ) 150 : 96
Rationale: given 6 a 12 : a 22 = 150 : 96 then a 12 : a 22 = 25 : 16 a 1 : a 2 = 5 : 4 so the answer is d
Answer: d
Problem: how many positive integers less than 247 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 41 , as all the other choices are very far away . the numbers 244 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice b is correct here .
Answer: b
Problem: ram , who is half as efficient as krish , will take 36 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 36 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 36 days is 36 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 36 w / 3 w = 12 days answer b"
Answer: b
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 24 different signs . if the company used 22 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 24 signs ?
Options: a ) 246 , b ) 248 , c ) 92 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 24 different signs = 24 * 24 . # of 2 - letter codes possible from 22 different signs = 22 * 22 . the difference = 24 ^ 2 - 22 ^ 2 = ( 24 - 22 ) ( 24 + 22 ) = 92 . answer : c ."
Answer: c
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 5 as remainder
Options: a ) 1637 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1635
Rationale: let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 5 5 x = 1360 x = 272 large number = 272 + 1365 = 1637 a
Answer: a
Problem: the sum of ages of 10 children born at the intervals of 1 years each is 105 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 2 , d ) 7 , e ) 6
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 , ( x + 3 ) , ( x + 4 ) , ( x + 5 ) , ( x + 6 ) , ( x + 7 ) , ( x + 8 ) , and ( x + 9 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) + ( x + 7 ) + ( x + 8 ) + ( x + 9 ) = 105 10 x = 60 x = 6 age of the youngest child = x = 6 years . answer : e"
Answer: e
Problem: a pipe can fill a cistern in 33 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 33 minutes 1 / 11 part filled in = 33 * 1 / 11 = 3 minutes answer is c"
Answer: c
Problem: a wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %
Rationale: "there are a total of 8 * 8 * 8 = 512 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 6 * 6 * 6 = 216 cubes . the number of cubes with at least one side painted red is 512 - 216 = 296 cubes the probability that a cube has at least one side painted red is 296 / 512 which is about 57.8 % the answer is d ."
Answer: d
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 36 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 36 days whole work will be done by y in 36 * 5 / 4 = 45 days answer is a
Answer: a
Problem: mr . hanson has a pool of money from which to give out christmas bonuses to his 5 employees . he wants all his employees to have identical bonuses , but when he divides them out , he finds he has 2 dollars left over , as the payroll system will only accept whole dollar amounts . the next christmas , mr . hanson discovers the pool for the bonuses is 3 times the size . this time , how much money will be left over ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: set x = to amount of money for bonuses , and y to be the amount of each individual bonus . x = 5 * y + 2 . 3 x = 15 * y + 6 3 x = 3 * 5 * y + 6 3 x = 5 ( 3 ( y + 1 ) ) + 1 remainder is then 1 , so option b .
Answer: b
Problem: calculate 469138 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4690910862 , d ) 4586870843 , e ) none
Rationale: "answer 469138 x 9999 = 469138 x ( 10000 - 1 ) = 4691380000 - 469138 = 4690910862 . option : c"
Answer: c
Problem: the cash difference between the selling prices of an book at a profit of 8 % and 16 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 27 : 29 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 108 % of x / 116 % of x = 108 / 116 = 27 / 29 = 27 : 29 d"
Answer: d
Problem: if a rectangular billboard has an area of 117 square feet and a perimeter of 44 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 117 and a perimeter of 44 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 117 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 117 , so the correct answer is let ' s test answer d : 9 if . . . the shorter side = 9 . . . the area = 117 . . . . 117 / 9 = 13 = the longer side perimeter = 9 + 9 + 13 + 13 = 44 d"
Answer: d
Problem: bird is flying 120 km / hr between b to r . two trains at b to r at 60 kmph . the distance traveled by the bird before it is killed ?
Options: a ) 90 kms . , b ) 100 kms . , c ) 110 kms . , d ) 120 kms . , e ) 130 kms .
Rationale: it will depend on the distance between b and r . if distance between b and r is 120 kms , time taken by trains before collision = 120 / ( 60 + 60 ) = 1 hr distance traveled by bird in 1 hr = 120 kms . so the distance traveled by the bird before it is killed = 120 kms . answer : d
Answer: d
Problem: a = 5 ^ 15 - 125 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get none different values and answer is a . . . ."
Answer: a
Problem: in a 600 m race , the ratio of the speeds of two contestants a and b is 5 : 4 . a has a start of 100 m . then , a wins by :
Options: a ) 200 m , b ) 20 m , c ) 403 m , d ) 20 m , e ) 23 m
Rationale: to reach the winning post a will have to cover a distance of ( 600 - 100 ) m , i . e . , 500 m . while a covers 5 m , b covers 4 m . while a covers 500 m , b covers 4 x 500 / 5 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 200 m behind . a wins by 200 m . answer : a
Answer: a
Problem: at present the ratio between the ages of arun and deepak is 2 : 3 . after 5 years , arun ' s age will be 25 years . what is the age of deepak at present ?
Options: a ) 20 years , b ) 30 years , c ) 15 years , d ) 25 years , e ) 28 years
Rationale: "let the present ages of arun and deepak be 2 x years and 3 x years respectively 2 x + 5 = 25 2 x = 20 x = 10 deepak ' s age = 3 x = 30 years answer is b"
Answer: b
Problem: the length of the bridge is 200 m , which a 100 m long train cross in 60 sec . then what is the speed of train ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 10 , e ) 8
Rationale: speed = length / time length = ( 200 + 100 ) = 300 m time = 60 sec speed = 300 / 60 = 5 m / sec answer b
Answer: b
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × e , what is the value of e ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × e = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x e = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e e = 7 ^ 2 = 49 answer d"
Answer: d
Problem: if i earn a profit 50 $ in a day and i have 9 employees . after keeping 10 percent profit for me , and distribute remianing money equally among my employees then how much each employee would get ?
Options: a ) $ 3 , b ) $ 7 , c ) $ 1 , d ) $ 5 , e ) $ 9
Rationale: since i earned $ 50 sp 10 percent would be 5 $ and 45 $ would remain . dividing 45 by 9 , each employee would get 5 $ each and hince option d is correct .
Answer: d
Problem: a 14 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 175 , b ) rs . 92 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 14 , investment = rs . ( 100 / 8 x 14 ) = rs . 175 ∴ market value of rs . 100 stock = rs . 175 answer a"
Answer: a
Problem: in the third grade of windblown school there are 84 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 84 failed in math = 84 / 3 = 28 failed in literature = 84 / 6 = 14 the least failed in both can be 0 while max can be 14 answer a"
Answer: a
Problem: the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their volumes ?
Options: a ) 1 : 9 , b ) 1 : 2 , c ) 1 : 8 , d ) 1 : 1 , e ) 1 : 6
Rationale: "1 : 8 answer : c"
Answer: c
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 25 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 320 , c ) 177 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 25 + 2.5 % of 25 ) = rs . 25.625 therefore , number of shares = 8200 / 25.625 = 320 answer : b"
Answer: b
Problem: find the distance covered by a man walking for 30 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 20 / 60 = 5 km answer is d"
Answer: d
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 7 / 5 , d ) 5 / 7 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were right - handed - - > 6 * 1 / 3 = 2 were right - handed and 4 left - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : c ."
Answer: c
Problem: a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 4 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 5 : 11 , e ) 7 : 3
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 4 ounces in the ratio 1 : 3 or , x + 3 x = 4 gives x ( alcohol ) = 1 and remaining water = 3 mixing both we have alcohol = 4 + 1 and water = 8 + 3 ratio thus alcohol / water = 5 / 11 answer d"
Answer: d
Problem: the number which exceeds 16 % of it by 84 is :
Options: a ) 100 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 84 x - 16 / 100 x = 84 x - 4 / 25 x = 84 21 / 25 x = 84 x = ( 84 x 25 / 21 ) = 100 answer a"
Answer: a
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 21 in two years , at the same percent rate per annum ?
Options: a ) rs . 520 , b ) rs . 480 , c ) rs . 420 , d ) rs . 200 , e ) rs . 600
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 21 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 21 – 20 ) / 20 ] * 100 = 5 % p . a . let the principal be rs . x time = t = 2 years % rate = 5 % p . a . si = ( prt / 100 ) 20 = ( x * 5 * 2 ) / 100 x = rs . 200 answer : d"
Answer: d
Problem: ratio between rahul and deepak is 4 : 3 , after 4 years rahul age will be 32 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 21 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 4 = 32 = > x = 7 so deepak age is = 3 ( 7 ) = 21 option d"
Answer: d
Problem: a train 850 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 450 , c ) 500 , d ) 520 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 850 + x ) / 60 = 65 / 3 x = 450 m . answer : option b"
Answer: b
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 140 of the workers of that company are men , how many of the workers are women ?
Options: a ) 85 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 80 * 1 + 40 * 2 ) / 3 = 160 / 3 % are men total = 120 * 300 / 160 = 225 no . of women = 225 - 140 = 85 a"
Answer: a
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a ∪ b ) = 6 / 15 find p ( a | b )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a ∪ b ) / p ( b ) p ( a | b ) = ( 6 / 15 ) / ( 4 / 15 ) = 3 / 2 . c"
Answer: c
Problem: worker a takes 8 hours to do a job . worker b takes 6 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 24 / 7 , e ) 80 / 9
Rationale: "one day work of a = 1 / 8 one day work of b = 1 / 6 so one day work of a and b together = 1 / 8 + 1 / 6 = 7 / 24 so total days required = 24 / 7 answer : d"
Answer: d
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 7 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 7 * 7 = > a = 7 * 7 * 8 x * 2 x = 7 * 7 * 8 x = 14 = > 2 x = 28 answer : d"
Answer: d
Problem: how many numbers from 32 to 97 are exactly divisible by 9 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' b ' 32 / 9 = 3 and 97 / 9 = 10 = = > 10 - 3 = 7 numbers"
Answer: b
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 4 ) , how many units is p from the y - axis ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "the x - axis is 4 units from the point p . thus the y - axis is 8 units from the point p . the answer is c ."
Answer: c
Problem: if 20 men can build a wall 66 metres long in 4 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 278.4 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 567.6 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 4 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 4 * 20 ) = 567.6 mtrs answer : e"
Answer: e
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 250 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 50 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 250 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 250 ) * 100 / 500 = 50 % answer : option c"
Answer: c
Problem: a train , 800 meter long is running with a speed of 78 km / hr . it crosses a tunnel in 1 minute . what is the length of the tunnel ( in meters ) ?
Options: a ) 440 m , b ) 500 m , c ) 260 m , d ) 430 m , e ) 450 m
Rationale: "explanation : distance = 800 + x meter where x is the length of the tunnel time = 1 minute = 60 seconds speed = 78 km / hr = 78 × 10 / 36 m / s = 130 / 6 = 65 / 3 m / s distance / time = speed ( 800 + x ) / 60 = 65 / 3 = > 800 + x = 20 × 65 = 1300 = > x = 1300 - 800 = 500 meter answer : option b"
Answer: b
Problem: a library has an average of 150 visitors on sundays and 120 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 50 , b ) 75 , c ) 150 , d ) 125 , e ) 100
Rationale: "since the month begin with sunday , so there will be five sundays in the month required average = ( 150 * 5 + 120 * 25 ) / 30 = 3750 / 30 = 125 answer is d"
Answer: d
Problem: find the smallest number which should be multiplied with 520 to make it a perfect square .
Options: a ) 30 , b ) 120 , c ) 55 , d ) 35 , e ) none of these
Rationale: "520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square . answer : e"
Answer: e
Problem: in a company of 200 employees , 120 are females . a total of 100 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with a college degree only , how many employees are females with advanced degrees ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "the number of males is 200 - 120 = 80 . the number of males with advanced degrees is 80 - 40 = 40 . the number of females with advanced degrees is 100 - 40 = 60 . the answer is a ."
Answer: a
Problem: in what ratio should a variety of rice costing rs . 4.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 12
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 4.5 ) = 5 / 12 answer : e"
Answer: e
Problem: in a certain pond , 60 fish were caught , tagged , and returned to the pond . a few days later , 60 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1818 , d ) 2500 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 60 * 100 = 3.33 % . we are told that 3.33 % approximates the percent of tagged fish in the pond . since there are 60 tagged fish , then we have 0.033 x = 60 - - > x = 1,818 . answer : c ."
Answer: c
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 10 minutes . the length of the bridge is ?
Options: a ) 500 m , b ) 1110 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 10 minutes = 15 / 18 * 10 * 60 = 500 m answer is a"
Answer: a
Problem: 12 + 13 + 14 + . . . 61 + 62 + 63 = ?
Options: a ) 1361 , b ) 1362 , c ) 1950 , d ) 1364 , e ) 1365
Rationale: "sum = 12 + 13 + 14 + . . . 61 + 62 + 63 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 63 positive integers = 63 * 64 / 2 sum of first 11 positive integers = 11 * 12 / 2 sum = 12 + 13 + 14 + . . . 61 + 62 + 63 = 63 * 64 / 2 - 11 * 12 / 2 = 1950 answer : c"
Answer: c
Problem: tickets numbered from 1 to 21 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 21 = 1 / 3 the answer is a ."
Answer: a
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 63 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 63 1 percent for 1 year = 21 = > 100 percent = 2100 answer : b"
Answer: b
Problem: ( 128.5 x 64 ) + ( 13.8 x 465 ) = ? x 25
Options: a ) 524.48 , b ) 556.02 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 64 ) + ( 13.8 x 465 ) / 25 = 8224 + 6417 / 25 = 585.64 answer : option d"
Answer: d
Problem: 128 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 160 , b ) 190 , c ) 225 , d ) 250 , e ) 500
Rationale: let b be the number of boys in the school . 128 = xb / 100 b = 0.5 x 12800 = 0.5 x ^ 2 x ^ 2 = 25600 x = 160 the answer is a .
Answer: a
Problem: a basket contains 5 apples , of which 1 is spoiled and the rest are good . if henry is to select 2 apples from the basket simultaneously and at random , what is the possibility that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 5 , b ) 3 / 10 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: "p ( both apples are not spoiled ) = 4 c 2 / 5 c 2 = 4 * 3 / 5 * 4 = 3 / 5 p ( one of the apple spoiled ) = 1 - 3 / 5 = 2 / 5 answer is c ."
Answer: c
Problem: the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference w would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference w = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 7500 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 87.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 7500 ⇔ 12 x 2 = 7500 ⇔ x 2 = 625 ⇔ x = 25 . so , length = 75 m and breadth = 100 m . perimeter = [ 2 ( 75 + 100 ) ] m = 350 m . ∴ cost of fencing = rs . ( 0.25 × 350 ) = rs . 87.50 . answer d"
Answer: d
Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is
Options: a ) 38 % , b ) 40 % , c ) 44 % , d ) 48 % , e ) 50 %
Rationale: let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy c )
Answer: c
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 5 ?
Options: a ) 4 / 3 , b ) 3 / 2 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 5 + 1 ) / ( 5 - 1 ) = 6 / 4 = 3 / 2 answer : b"
Answer: b
Problem: find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm ?
Options: a ) 140 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 182 cm 2 , e ) 200 cm 2
Rationale: "1 / 2 * 28 ( 8 + 2 ) = 140 cm 2 answer : a"
Answer: a
Problem: 3 machines operating independently , simultaneously , and at the same constant rate can fill a certain production order in 44 hours . if one additional machine were used under the same operating conditions , in how manyfewerhours of simultaneous operation could the production order be fulfilled ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 11 , e ) 48
Rationale: if 3 machines can do the work in 44 hr then 4 machines can do the work in 3 / 4 * 44 = 33 hrs . hence time saved will be 11 hr option d is the correct answer
Answer: d
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are accounting majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are accounting majors is p = 3 . the answer is a .
Answer: a
Problem: a train 250 m long is running at a speed of 58 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : d . speed of the train relative to man = ( 58 - 8 ) kmph = ( 50 * 5 / 18 ) m / sec = ( 125 / 9 ) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 125 / 9 m / sec = 250 * 9 / 125 sec = 18 sec"
Answer: d
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 10 ) . what is the slope of line m ?
Options: a ) - 3 , b ) 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : b solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 10 ) . midpoint is ( 4 , - 3 ) as we can see that the y axis of intercept point is ( 0 , - 2 ) means line m is parallel to x axis slope m = 1 ans : b"
Answer: b
Problem: on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: "0.20 p = rt + c 0.5 ( rt ) = no c = > 0.50 ( rt ) had c 0.20 p = 0.50 ( rt ) rt / p = 40 % answer - b"
Answer: b
Problem: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108
Rationale: total students = 420 boys = 312 , girls = 108 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 108 - 35 = 73 . correct option : b
Answer: b
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 60 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 180 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 60 percent 180 min . answer : d
Answer: d
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 14 . what is the value of f ( 6 ) ?
Options: a ) 3 , b ) 0 , c ) 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 14 then f ( 5 ) = 14 - 5 = 9 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 9 - 6 = 3 . answer : a . questions on funtions to practice :"
Answer: a
Problem: the banker â € ™ s discount of a certain sum of money is rs . 80 and the true discount on the same sum for the same time is rs . 70 . the sum due is
Options: a ) 210 , b ) 280 , c ) 560 , d ) 450 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 80 * 70 / 80 - 70 ] = rs . [ 80 * 70 / 10 ] = rs . 560 answer c"
Answer: c
Problem: in what time will a train 150 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 3.8 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 150 / 40 = 3.8 sec . answer : c"
Answer: c
Problem: from a container having pure milk , 10 % is replaced by water and the process is repeated twice . at the end of the second operation , the milk is ?
Options: a ) 50 % , b ) 60 % , c ) 55 % , d ) 75 % , e ) 81 %
Rationale: "let the total quantity of original milk = 1000 gm milk after 1 st operation = 90 % of 1000 = 900 gm milk after second operation = 90 % of 900 = 810 gm strength of final mixture = 81 % answer is e"
Answer: e
Problem: what is the smallest number which , when increased by 9 , is divisible by 8 , 11 , and 24 ?
Options: a ) 237 , b ) 246 , c ) 255 , d ) 264 , e ) 273
Rationale: lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 9 = 255 . the answer is c .
Answer: c
Problem: on an order of 19 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 0.05 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %
Rationale: "clearly , the retailer gets 1 dozen out of 20 dozens free . equivalent discount = 1 / 20 * 100 = 5 % . answer d ) 5 %"
Answer: d
Problem: a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.02 % , c ) 0.2 % , d ) 4 % , e ) 40 %
Rationale: we are given that 0.02 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.02 by 20 . this gives us : 0.02 x 20 = 0.4 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.4 / 10 ) x 100 % ( 4 / 100 ) x 100 % = 4 % answer d
Answer: d
Problem: i sold a book at a profit of 10 % . had i sold it for $ 140 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 2800 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 140 5 % of cost = $ 140 cost = 140 * 100 / 5 = $ 2800 answer is d"
Answer: d
Problem: a glass was filled with 15 ounces of water , and 0.05 ounce of the water evaporated each day during a 15 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.005 % , b ) 0.05 % , c ) 0.5 % , d ) 5 % , e ) 25 %
Rationale: "in 15 days 15 * 0.05 = 0.75 ounces of water evaporated , which is 0.75 / 15 â ˆ — 100 = 5 of the original amount of water . answer : d ."
Answer: d