regisss/math_qa huggingface dataset:
Problem: nitin ' s age was equal to square of some number last year and the following year it would be cube of a number . if again nitin ' s age has to be equal to the cube of some number , then for how long he will have to wait ?
Options: a ) 10 years
b ) 38 years
c ) 39 years
d ) 64 years
e ) 44 years
Rationale: current age = 26 years because nitin ' s age was equal to square of some number ( 25 = 5 ^ 2 ) last year and the following year it would be cube of a number ( 27 = 3 ^ 3 ) . next cube age will be 64 = 4 ^ 3 which will come after 64 - 26 = 38 years . answer : b
Answer: b
Problem: a family pays $ 900 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 1,700
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 900 + $ 400 = $ 1300 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 700 when the medical expenses are $ 1700 . the answer is e ."
Answer: e
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 13 wins and 7 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 3
Rationale: 13 wins , 7 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 7 games so it can lose another 0 at most . answer ( a )
Answer: a
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 49 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 7 : 2 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 49 : â ˆ š 4 = 7 : 2 . answer d"
Answer: d
Problem: find 62976 ÷ ? = 123
Options: a ) 412 , b ) 502 , c ) 512 , d ) 522 , e ) none
Rationale: "answer let 62976 / n = 123 then n = 62976 / 123 = 512 . option : c"
Answer: c
Problem: x alone can do a piece of work in 15 days and y alone can do it in 10 days . x and y undertook to do it for rs . 720 . with the help of z they finished it in 5 days . how much is paid to z ?
Options: a ) rs . 360 , b ) rs . 120 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: solution : in one day x can finish 1 / 15 th of the work . in one day y can finish 1 / 10 th of the work . let us say that in one day z can finish 1 / zth of the work . when all the three work together in one day they can finish 1 / 15 + 1 / 10 + 1 / z = 1 / 5 th of the work . therefore , 1 / z = 1 / 30 . ratio of their efficiencies = 1 / 15 : 1 / 10 : 1 / 30 = 2 : 3 : 1 . therefore z receives 1 / 6 th of the total money . according to their efficiencies money is divided as 240 : 360 : 120 . hence , the share of z = rs . 120 . answer b
Answer: b
Problem: 4 , 25,49 ,
Options: a ) 149 , b ) 169 , c ) 189 , d ) 209 , e ) 121
Rationale: "11 ^ 2 = 121 because follow sequence of square of the prime numbers answer : e"
Answer: e
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 950 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.64 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 950 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 950 * 3 * ( 4 / 5 ) = 2280 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2280 + 1360 = 3640 solving for units gives us 3.64 so the answer is a"
Answer: a
Problem: a , b , c can complete a piece of work in 24 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 a , b , c together will complete the job in 24 / 7 days answer is e"
Answer: e
Problem: company c sells a line of 25 products with an average retail price of $ 1,000 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 9000 , b ) 8000 , c ) 7000 , d ) 6000 , e ) 5000
Rationale: "the average price of 25 products is $ 1,000 means that the total price of 25 products is 25 * 1,000 = $ 25,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 25,000 - $ 18,200 = $ 7,000 . answer : c ."
Answer: c
Problem: a caterer ordered 200 ice - cream bars and 200 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.40 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 4 $ 200 * . 4 + 200 * s = 200 = > 200 * s = 200 = > s = 0.6 answer a"
Answer: a
Problem: what is the least value of k . so that 123 k 578 is divisible by 11 .
Options: a ) 8 , b ) 7 , c ) 5 , d ) 6 , e ) 4
Rationale: explanation : the difference of the sum of the digits at odd place and the sum of the digits at even place of the number , is either 0 or a number divisible by 11 . ( 1 + 3 + 5 + 8 ) - ( 2 + k + 7 ) = 17 - 9 - k = 8 - k therefore if k = 8 , then the value become zero . k = 8 is the least value so that 123 k 578 is divisible by 11 . answer : option a
Answer: a
Problem: local kennel has cats and dogs in the ratio of 3 : 4 . if there are 8 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 28 , b ) 26 , c ) 24 , d ) 32 , e ) 30
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 3 : 4 or cats 3 dogs 4 we can write number of cats as 3 x and number of dogs as 4 x and we know that 4 x - 3 x = 8 ( therefore x = 8 ) then # of dogs = 4 x 8 = 32 answer is d"
Answer: d
Problem: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 142 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 145 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 142 . so , total number of ducks and frogs in the pond , = 2 * 142 = 284 . therefore , number of frogs , = ( 284 * 39 ) / 76 = 145 . answer : option d"
Answer: d
Problem: john had a stock of 1400 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 ) 71.3 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
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 = 1400 - n = 1400 - 402 = 998 percentage books not sold / total number of books = 998 / 1400 = 0.713 = 71.3 % correct answer b"
Answer: b
Problem: two numbers a and b are such that the sum of 8 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 3 , e ) 3 : 2
Rationale: "explanation : 8 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 8 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 8 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 24 a + 12 b = 12 a + 16 b ⇒ 12 a = 4 b ⇒ ab = 4 / 12 ⇒ a : b = 1 : 3 answer : option d"
Answer: d
Problem: the compound ratio of 5 : 6 , 3 : 4 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 6 * 3 / 4 * 4 / 5 = 1 / 2 1 : 2 answer : e"
Answer: e
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.1 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 6 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.1 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.1 ) < = > k = 0.7 / 0.6 = 7 / 6 . required ratio = 7 / 6 : 1 = 7 : 6 . answer : a
Answer: a
Problem: a man purchased 4 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 = 350 b"
Answer: b
Problem: of 70 players on a football team , 31 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 57 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 31 rest = 70 - 31 = 39 left handed = 39 / 3 = 13 right handed = 26 if all thrower are right handed then total right handed is 31 + 26 = 57 so a . 57 is the right answer"
Answer: a
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 53 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 54
Rationale: "amount earned by james = 40 * x + 13 * 2 x = 66 x therefore , amount earned by harry = 66 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 66 x ] ] so x * ( 1.5 y - 45 + 30 ) = 66 x or x * ( 1.5 y - 15 ) = 66 x so 1.5 y - 15 = 66 so 1.5 y = 81 so y = 54 answer is e"
Answer: e
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 9 , what is the measure of side xy ?
Options: a ) 4 , b ) 4 √ 2 , c ) 8 , d ) 6 , e ) can not be determined from the information provided
Rationale: "ans d . . 6 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 9 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 6"
Answer: d
Problem: yesterday ' s closing prices of 1980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer .
Answer: b
Problem: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is ?
Options: a ) 2267 , b ) 1162 , c ) 2276 , d ) 1250 , e ) 1262
Rationale: "explanation : speed = ( 5 x 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 x 15 x 60 ) m = 1250 m . answer : d"
Answer: d
Problem: a 75 m long train is running at 54 km / hr . in how much time will it cross an electric pole ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: speed of the train = ( 54 * 5 / 18 ) m / sec = 15 m / sec . length of the train = ( speed x time ) time = ( length of the train / speed ) = ( 75 / 15 ) = 5 sec answer : a
Answer: a
Problem: a reduction of 24 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.8 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 3.16
Rationale: "100 * ( 24 / 100 ) = 24 - - - 10 ? - - - 1 = > rs . 2.4 100 - - - 76 ? - - - 2.4 = > rs . 3.16 answer : e"
Answer: e
Problem: what is the least number that should be added to 1077 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1077 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."
Answer: d
Problem: how many pieces of 0.63 meteres can be cut from a rod 32.5 meteres long
Options: a ) 30 , b ) 40 , c ) 51 , d ) 60 , e ) 70
Rationale: "explanation : we need so simple divide 32.5 / 0.63 , = ( 3250 / 63 ) = 51 option c"
Answer: c
Problem: how many terminating zeroes q does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 17 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 17 w 19 + 9 x = 17 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c"
Answer: c
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 2 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 218 , c ) 400 , d ) 388 , e ) 211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 2 = > x = 400 answer : c ) rs 400"
Answer: c
Problem: a city with a population of 218,000 is to be divided into 10 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 19,920 , b ) 19,940 , c ) 19,960 , d ) 19,980 , e ) 20,000
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 218,000 = p + 9 ( 1.1 ) p 10.9 p = 218,000 p = 20,000 the answer is e ."
Answer: e
Problem: two trains of equal are running on parallel lines in the same direction at 47 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 , b ) 88 , c ) 66 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 47 - 36 = 11 km / hr . = 11 * 5 / 18 = 55 / 18 m / sec . 2 x / 36 = 55 / 18 = > x = 55 . answer : d"
Answer: d
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 30 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 450 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: pastry is divided in 30 customers equally . so , total number of pastry must be a multiple of 30 only option a satisfies the condition , and hence is the answer
Answer: a
Problem: if x and y are positive integers and x = 5 y + 7 , what is the remainder when x is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 7 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 12 12 / 5 = 2 remainder 2 final answer : c"
Answer: c
Problem: on a certain road 14 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 17.5 % , d ) 22 % , e ) 30 %
Rationale: "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 14 % + 0,2 x id est x = 17,5 %"
Answer: c
Problem: the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 90 , b ) 93 , c ) 56 , d ) 80.5 , e ) 78
Rationale: "total increase in weight = 8 × 6 = 48 if x is the weight of the new person , total increase in weight = x − 45 = > 48 = x - 45 = > x = 48 + 45 = 93 answer : b"
Answer: b
Problem: how many digits 2 ^ 300 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 91 , e ) 101
Rationale: 2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 90 therefore 91 digits would be my best guess d
Answer: d
Problem: after distributing the sweets equally among 25 children , 8 sweets remain . had the number of children been 28 , 22 sweets would have been left after equal distribution . what was the total number of sweets ?
Options: a ) 328 , b ) 348 , c ) 358 , d ) 362 , e ) data inadequate
Rationale: explanation : let the total number of sweets be ( 25 x + 8 ) . then , ( 25 x + 8 ) - 22 is divisible by 28 ( 25 x - 14 ) is divisible by 28 28 x - ( 3 x + 14 ) is divisible by 28 ( 3 x + 14 ) is divisible by 28 x = 14 . therefore total number of sweets = ( 25 x 14 + 8 ) = 358 . answer : c
Answer: c
Problem: a batsman scored 150 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 60 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 150 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 150 - 60 = 90 required % = ( 90 / 150 ) × 100 = 60 % answer : option b"
Answer: b
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 120 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 3000 , d ) 1000 , e ) 2871
Rationale: ( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 120 x = 3000 answer : c
Answer: c
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.000168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 7 digits after decimal total no . of decimals = 9 req . no . of digits = ( n - 1 ) = ( 9 - 1 ) = 8 answer : e
Answer: e
Problem: the average age of a class of 23 students is 22 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 46 , d ) 42 , e ) 49
Rationale: "total age of all students = 23 ã — 22 total age of all students + age of the teacher = 24 ã — 23 age of the teacher = 24 ã — 23 â ˆ ’ 23 ã — 22 = 23 ( 24 â ˆ ’ 22 ) = 23 ã — 2 = 46 answer is c ."
Answer: c
Problem: x is a positive integer less than 600 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 600 n = 25.42 or n = 25 answer : - e"
Answer: e
Problem: if the radius of a circle is increased by 30 % then the area is increased by :
Options: a ) 44 % , b ) 69 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 130 / 100 r then area = pi * ( 130 r / 100 ) 2 area = 169 r / 100 that is area increases from 100 to 169 = increase in area = 69 % answer : b"
Answer: b
Problem: the length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is :
Options: a ) 15 m
b ) 22.5 m
c ) 25 m
d ) 30 m
e ) none of these
Rationale: solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 ⇔ x 2 + 5 x − 750 = 0 ⇔ ( x + 30 ) ( x + 25 ) = 0 ⇔ x = 25 . ∴ length = ( x + 5 ) = 30 m . answer d
Answer: d
Problem: what is the perimeter of a square with area p ^ 2 / 16 ?
Options: a ) 3 p / 4
b ) 3 p ^ 2 / 4
c ) p
d ) 3 p ^ 2
e ) 4 p / 3
Rationale: area of square , ( side ) ^ 2 = ( p / 4 ) ^ 2 therefore side of the square = p / 4 perimeter of square = 4 * side = 4 * ( p / 4 ) = p answer is c .
Answer: c
Problem: 65 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64
b ) 128
c ) 151
d ) 216
e ) 256
Rationale: 65 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 65 = 151 hence , c is the answer .
Answer: c
Problem: how long does a train 100 m long traveling at 60 kmph takes to cross another train of 170 m in length has a speed of 40 kmph ?
Options: a ) 1.42 sec , b ) 16.8 sec , c ) 5 sec , d ) 1.68 sec , e ) 3.6 sec
Rationale: "d = 100 m s = ( 60 + 40 ) * 5 / 18 = 250 / 3 t = 100 * 9 / 250 = 3.6 sec answer : e"
Answer: e
Problem: a student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let the number of people to choose from = n no of people to be chosen = 2 the number of ways 2 people can be chosen from n people = nc 2 now , the two people selected can be arranged in 2 ! ways hence nc 2 * 2 ! = 90 which gives n = 10 answer : d"
Answer: d
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 2 . line b has a slope of 5 and a y - intercept of - 10 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation of line a is y = - x + 2 the equation of line b is y = 5 x - 10 5 x - 10 = - x + 2 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c .
Answer: c
Problem: if 9 is added to thrice a number and this sum is multiplied by 6 , the result is the same as if the number is multiplied by 7 and 10 is added to the product . what is the number ?
Options: a ) - 7 , b ) - 8 , c ) - 9 , d ) - 10 , e ) - 11
Rationale: let the number be x ; 6 ( 9 + 3 x ) = 7 x + 10 ; x = - 11 answer : e
Answer: e
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 20 + 29 + 8 ) = 5 % basic astrophysics . 5 % of 360 ° is 18 ° . answer : c ."
Answer: c
Problem: by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 q ^ 2 + 5 q = 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: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is b ."
Answer: b
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 27 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d"
Answer: d
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d"
Answer: d
Problem: pradeep has to obtain 35 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 800 , d ) 1000 , e ) 900
Rationale: explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b
Answer: b
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 64 , d ) 76 , e ) 88
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.22 ( 800 ) = 264 the answer is c ."
Answer: c
Problem: a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 120 = 10 * 12 x = 22 the answer is b ."
Answer: b
Problem: find the area of a parallelogram with base 14 cm and height 24 cm .
Options: a ) 336 , b ) 384 , c ) 345 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a"
Answer: a
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 35 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 25 % , b ) 28 % , c ) 30 % , d ) 32.5 % , e ) 35 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.35 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 35 % income the savings increased by 100 % . or s = . 35 i or s = 35 % of income e is the answer"
Answer: e
Problem: how is 5 % expressed as a decimal fraction ?
Options: a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5
Rationale: "5 / 100 = 0.05 answer : b"
Answer: b
Problem: 34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 6 feet , and the diagonal of the rectangular plate was 10 ft . what is height of the of the cylinder ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 8 . correct answer c .
Answer: c
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these
Rationale: train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer .
Answer: d
Problem: how many three digit numbers q are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples q - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Problem: how many numbers from 2 to 9 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 4 , e ) e ) 8
Rationale: "2 / 2 = 1 and 9 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : d"
Answer: d
Problem: p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is q ' s share ?
Options: a ) 114 , b ) 120 , c ) 134 , d ) 144 , e ) none of these
Rationale: explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 b ' s share = 378 * ( 8 / 21 ) = 18 * 8 = 144 . answer : option d
Answer: d
Problem: if a ( a + 5 ) = 36 and b ( b + 5 ) = 36 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 5 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 4 then b = - 9 or if a = - 9 then b = 4 but in each case a + b = - 9 + 4 = - 5 answer : option b"
Answer: b
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 2013 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 672
Rationale: "same logic but with application of factorials . 2 * 4 * 6 * 8 * . . . * n = 2 ( 1 * 2 * 3 * 4 * . . . n / 2 ) = 2 * ( n / 2 ) ! now we have : 2 * ( n / 2 ) ! / 2013 = 2 * ( n / 2 ) ! / ( 3 × 11 × 61 ) for the expression 2 * ( n / 2 ) ! to be divisible by 2013 min value of n / 2 should be 61 . so n / 2 = 61 = > n = 122 answer d ."
Answer: d
Problem: billy worked for 3 straight hours on his homework questions . if he solved 132 questions in the third hour , which was twice as many as he solved in the second hour , and 3 times as many questions as he solved in the first hour , how many questions did he solve total ?
Options: a ) 242 , b ) 312 , c ) 424 , d ) 525 , e ) 622
Rationale: total questions solved = questions solved in 3 rd hr + in 2 nd hr + in 1 st hr 132 + 132 / 2 + 132 / 3 = 242 a is the answer
Answer: a
Problem: if e = 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 e = 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: a man buys an item at rs . 750 and sells it at the loss of 10 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 675 , c ) rs . 860 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 90 % of 750 = 90 / 100 * 750 = 675 option b"
Answer: b
Problem: what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 2 ?
Options: a ) 5 , b ) 1 , c ) 2 , d ) 3 , e ) none of these
Rationale: "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : e"
Answer: e
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 55 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 32 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 55 = 385 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 385 - 780 = 32 . answer : a"
Answer: a
Problem: how many two - digit numbers yield a remainder of 1 when divided by both 6 and 15 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "easier to start with numbers that are of the form 15 p + 1 - - - > 16,31 , 46,61 , 76,91 . out of these 2 ( 31,61 ) are also of the form 6 q + 1 . thus 2 is the answer . c is the correct answer ."
Answer: c
Problem: for what value of â € œ k â €  will the equation ( 2 kx 2 + 3 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 16 / 9
Rationale: for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 3 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 9 answer : e
Answer: e
Problem: if 9 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 80 , b ) 63 , c ) 120 , d ) 1008 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 9 c 2 for vertical 8 c 2 total parallelogram is 9 c 2 * 8 c 2 = 36 * 28 = 1008 answer : d"
Answer: d
Problem: entry fee in an examination was re . 1 . later , this was reduced by 25 % which increased the sale by 20 % . the percentage increase in the number of visitors is
Options: a ) 60 , b ) 50 , c ) 66 , d ) 54 , e ) none
Rationale: sol . let the total original sale be rs . 100 . then , original number of visitors = 100 . new number of visitors = 120 / 0.75 = 160 . ∴ increase % = 60 % . answer a
Answer: a
Problem: a , b and c can do a piece of work in 7 days , 21 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 8 / 19 , c ) 5 , d ) 67 , e ) 9
Rationale: "1 / 7 + 1 / 21 + 1 / 28 = 19 / 84 = > 84 / 19 = > 4 8 / 19 days answer : b"
Answer: b
Problem: a retailer bought a machine at a wholesale price of $ 126 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 168
Rationale: my solution : wholesale price = 126 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 126 + 1 / 5 ( 126 ) x = 168 ; answer : e
Answer: e
Problem: if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is
Options: a ) 18.20 , b ) 18.33 , c ) 18 , d ) 18.3 , e ) none of these
Rationale: "explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = ( 110 x 20 / 120 ) = rs . 18.33 answer : b"
Answer: b
Problem: the grade point average of the entire class is 85 . if the average of one third of the class is 97 , what is the average of the rest of the class ?
Options: a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 85 x = ( 1 / 3 ) 97 x + ( 2 / 3 ) ( p ) x 255 = 97 + 2 p 2 p = 158 p = 79 . the answer is d ."
Answer: d
Problem: the diameter of a wheel is 0.7 m . how far will it travel in 200 revolutions
Options: a ) 4.4 m , b ) 220 m , c ) 440 m , d ) 560 , e ) 650
Rationale: diameter ( d ) = 0.7 m circumference of the wheel , = 2 * pi * r = d * pi = 0.7 * 3.14 = 2.198 m . in one revolution , wheel will covered = 2.198 m , so , in 200 revolution , it will cover = 200 * 2.198 = 4.396 m = 440 m ( approx ) . answer : option c
Answer: c
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 35 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 45 % , b ) 65 % , c ) 85 % , d ) 115 % , e ) 125 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.35 ( 5 b + x ) = b + x 0.75 b = 0.65 x x = 1.15 b the answer is d ."
Answer: d
Problem: two 6 faced dice are thrown together . the probability that both show the same number on them is ?
Options: a ) 1 / 6 , b ) 1 / 12 , c ) 1 / 18 , d ) 1 / 2 , e ) 1 / 4
Rationale: "it all 3 numbers have to be same basically we want doublets . 11 , 22 , 33 , 44 , 55 and 66 . those are six in number . further the three dice can fall in 6 * 6 = 36 ways . hence the probability is 6 / 36 = 1 / 6 answer : a"
Answer: a
Problem: what is the area of square field whose side of length 16 m ?
Options: a ) 225 , b ) 777 , c ) 256 , d ) 288 , e ) 261
Rationale: "16 * 16 = 256 sq m answer : c"
Answer: c
Problem: if the average marks of 3 batches of 40 , 50 and 60 students respectively is 45 , 55 , 65 , what is the average marks of all the students ?
Options: a ) 56.33 , b ) 34.89 , c ) 23.67 , d ) 54.65 , e ) 43.98
Rationale: average marks of batch 1 = 45 students in batch 1 = 40 total marks of batch 1 = 40 * 45 average marks of batch 2 = 55 students in batch 2 = 50 total marks of batch 2 = 50 × 55 average marks of batch 3 = 65 students in batch 3 = 60 total marks of batch 3 = 65 × 60 total students = 40 + 60 + 50 = 150 average marks of all the students = ( ( 40 * 45 ) + ( 50 × 55 ) + ( 65 × 60 ) ) / 150 = 169 / 3 = 56.333 answer is a .
Answer: a
Problem: in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 10 per kg so that cost of mixture is rs . 12 per kg ?
Options: a ) 2 : 3 , b ) 5 : 8 , c ) 5 : 6 , d ) 3 : 4 , e ) 1 : 2
Rationale: "( 12 - 10 ) / ( 16 - 12 ) = 2 / 4 = 1 : 2 answer : e"
Answer: e
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 10 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 91 , d ) 88 , e ) 66
Rationale: right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 10 total people can seat = 81 + 10 = 91 answer : c
Answer: c
Problem: if 4 < x < 8 < y < 12 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x = 4.1 and y = 11.1 greatest possible difference = 11.1 - 4.1 = 7 answer e"
Answer: e
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 70 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 10 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 70 ) = 90 ( x - 5 ) 100 = 10 x = > x = 10 . answer : b"
Answer: b
Problem: what annual payment will discharge a debt of rs . 6450 due in 4 years at 5 % per annum ?
Options: a ) 1500 , b ) 1400 , c ) 1700 , d ) 1800 , e ) 1600
Rationale: "explanation : he amount needs to be repaid in 4 years = rs . 6450 suppose rs . x is paid annually to repay this debt then , amount paid after 1 st year = rs . x interest for this rs . x for the remaining 3 years = x × 5 × 3 / 100 = 15 x / 100 then , amount paid after 2 nd year = rs . x interest for this rs . x for the remaining 2 years = x × 5 × 2 / 100 = 10 x / 100 amount paid after 3 rd year = rs . x interest for this rs . x for the remaining 1 year = x × 5 × 1 / 100 = 5 x / 100 amount paid after 4 th year = rs . x and this closes the entire debt = > x + 15 x / 100 + x + 10 x / 100 + x + 5 x / 100 + x = 6450 = > 4 x + 30 x / 100 = 6450 = > 4 x + 3 x / 10 = 6450 = > 40 x + 3 x = 64500 = > 43 x = 64500 = > x = 1500 answer : option a"
Answer: a
Problem: in township k each property is taxed at 8 percent of its assessed value . if the assessed value of a property in township k is increased from $ 18,000 to $ 28,000 , by how much will the property tax increase ?
Options: a ) $ 320 , b ) $ 800 , c ) $ 320 , d ) $ 600 , e ) $ 850
Rationale: "increase in house value = $ 28,000 - $ 18,000 = $ 10000 so , tax increase = 8 % of $ 10000 = $ 800 answer : b"
Answer: b
Problem: at a special sale , 8 tickets can be purchased for the price of 6 tickets . if 8 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 8 tickets ?
Options: a ) 25 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 8 tickets cost 800 8 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 200 , % of 6 tickets = ( 200 / 800 ) * 100 = 25 % answer : a"
Answer: a
Problem: when y is divided by 276 , the remainder is 44 . what is the remainder when the same y is divided by 23 ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "y = 276 * a + 44 = ( 23 * 12 ) * a + 23 + 21 the answer is c ."
Answer: c
Problem: the cricket team of 11 members is 29 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 26 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 29 + 32 ) = 9 ( x - 1 ) = > 11 x - 9 x = 52 = > 2 x = 52 = > x = 26 . so , average age of the team is 26 years . d"
Answer: d
Problem: what is the greater of the two numbers whose product is 2560 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 70 , e ) none of these
Rationale: let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2560 / s = 80 . answer : e
Answer: e
Problem: a cistern which could be filled in 5 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 90 hrs , e ) 10 hrs
Rationale: "1 / 5 - 1 / x = 1 / 10 = > 10 hrs answer : e"
Answer: e
Problem: excluding stoppages , the speed of a train is 60 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 12 , b ) b ) 18 , c ) c ) 24 , d ) d ) 30 , e ) e ) 36
Rationale: "explanation : t = 24 / 60 * 60 = 24 answer : option c"
Answer: c
Problem: find value for x from below equation ? x + 1 = 3
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 3 - 1 2 . simplify both sides : x = 2 e"
Answer: e
Problem: the angle between the minute hand and the hour hand of a clock when the time is 12.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 195 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 12 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 12 − 30 / 5 ) + 30 / 2 = 30 ( 12 − 6 ) + 15 = 30 × 6 + 15 = 195 ° answer is d ."
Answer: d
Problem: jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 12 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "check two extreme cases : jane = 18 , child = 9 , years ago = 32 - 18 = 14 - - > child ' s age now = 9 + 14 = 23 ; jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 . answer : d ."
Answer: d
Problem: what is the remainder of r = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , r = when divided by 10 , the remainder must be 7 . d"
Answer: d