regisss/math_qa huggingface dataset:
Problem: jennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 20
Rationale: "1 / 5 x $ 150 = $ 30 for sandwich 1 / 6 x $ 150 = $ 25 for museum 1 / 2 x $ 150 = $ 75 for book $ 30 + $ 25 + $ 75 = $ 130 spent $ 150 - $ 130 = $ 20 left over correct answer e"
Answer: e
Problem: excluding the stoppages , the speed of a bus is 32 km / hr and including the stoppages the speed of the bus is 16 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 10 min , c ) 12 min , d ) 30 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 32 km / hr speed of the bus with stoppage = 16 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 32 ) hr = 1 / 2 hr = 30 min answer : d"
Answer: d
Problem: what is the sum of all the multiples of 10 between 0 and 75 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 280
Rationale: "the multiples of 10 between 0 and 99 are 10 , 20 , 30 , 40 , 50 , 60 , 70 . if these are all added together , the result is 280 . final answer : e"
Answer: e
Problem: the sum of the non - prime numbers between 10 and 20 , non - inclusive , is
Options: a ) 60 , b ) 75 , c ) 90 , d ) 105 , e ) 120
Rationale: "sum of consecutive integers from 11 to 19 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 11 + 19 ) / 2 * 9 = 15 * 9 = 135 sum of non - prime numbers b / w 10 and 20 , non inclusive = = = > 135 - 60 ( i . e . , 11 + 13 + 17 + 19 , being the prime # s in the range ) = 75 answer : b"
Answer: b
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 2210 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 340 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 2210 x = 80 required perimeter = 2 ( 80 + 90 ) = 340 c"
Answer: c
Problem: the sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq . m . find the perimeter of rectangle .
Options: a ) 121 , b ) 123 , c ) 125 , d ) 122 , e ) 126
Rationale: "let 6 x and 5 x be sides of the rectangle 6 x × 5 x = 1331 11 xpower 2 = 1331 xpower 2 = 1331 / 11 = 121 = > x = 11 length = 6 x = 6 × 11 = 66 breadth = 5 x = > 5 × 11 = 55 perimeter = 2 ( l + b ) = > 2 ( 66 + 55 ) = 121 m answer is a ."
Answer: a
Problem: the ratio of the volumes of two cubes is 729 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 81 : 126 , c ) 81 : 189 , d ) 81 : 176 , e ) 81 : 117
Rationale: "ratio of the sides = ³ √ 729 : ³ √ 1331 = 9 : 11 ratio of surface areas = 92 : 112 = 81 : 121 answer : a"
Answer: a
Problem: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 4 years ?
Options: a ) 4 % , b ) 3.57 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 4 xr ) / 100 r = 3.57 % answer : option b"
Answer: b
Problem: roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be three times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108
Rationale: "r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d ."
Answer: d
Problem: having scored 95 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 23 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 95 = 19 ( n + 4 ) = > n = 19 so , average score after 19 th innings = x + 4 = 23 . answer : c"
Answer: c
Problem: if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the shorter sides ?
Options: a ) 4
b ) 7
c ) 8
d ) 13
e ) 26
Rationale: assume the sides to be x and y . perimeter = 2 x + 2 y = 42 hence x + y = 21 - ( i ) area = xy = 104 - ( ii ) since these are the sides of a billboard , we are dealing with positive numbers only and the options tell us that they are integers . 104 can be written as a product of two numbers as 104 * 1 or 52 * 2 or 26 * 4 or 13 * 8 of these , only 13 * 8 satisfies the equation ( i ) hence the lengths are 13 and 8 length of shorter side = 8 answer : c
Answer: c
Problem: in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 3 / 5 , b ) 7 / 10 , c ) 11 / 15 , d ) 23 / 30 , e ) 31 / 45
Rationale: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.6 * 1200 = 720 the number of males older than 70 years old is 900 - 720 = 180 the number of people who are either male or younger than 70 is 1800 + 180 = 1980 . p ( a person is younger than 70 or male ) = 1980 / 2700 = 11 / 15 the answer is c ."
Answer: c
Problem: the marks obtained by vijay and amith are in the ratio 4 : 4 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 3 : 2 , b ) 6 : 1 , c ) 6 : 5 , d ) 6 : 2 , e ) 6 : 3
Rationale: "4 : 4 3 : 2 - - - - - - - 12 : 12 : 8 12 : 8 3 : 2 answer : a"
Answer: a
Problem: 5 x + y = 19 , and x + 3 y = 1 . find the value of 3 x + 2 y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5
Rationale: add these two equations 6 x + 4 y = 20 divide by 2 ( to get 3 x + 2 y ) answer will be d . 10
Answer: d
Problem: a number is increased by 50 % and then decreased by 50 % . find the net increase or decrease per cent .
Options: a ) 25 % , b ) 18 % , c ) 17 % , d ) 13 % , e ) 16 %
Rationale: "let the number be 100 . increase in the number = 50 % = 50 % of 100 = ( 50 / 100 ã — 100 ) = 50 therefore , increased number = 100 + 50 = 150 this number is decreased by 50 % therefore , decrease in number = 50 % of 150 = ( 50 / 100 ã — 150 ) = 7500 / 100 = 75 therefore , new number = 150 - 75 = 75 thus , net decreases = 100 - 75 = 25 hence , net percentage decrease = ( 25 / 100 ã — 100 ) % = ( 2500 / 100 ) % = 25 % answer : a"
Answer: a
Problem: the unit digit in the product ( 115 * 297 * 196 * 108 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 0 , e ) 8
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 7 * 6 * 8 ) = 0 answer : d"
Answer: d
Problem: if 0.75 : x : : 5 : 8 , then x is equal to :
Options: a ) 1.12 , b ) 1.2 , c ) 1.25 , d ) 1.3 , e ) none
Rationale: "( x * 5 ) = ( 0.75 * 8 ) x = 6 / 5 x = 1.20 answer = b"
Answer: b
Problem: the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half - yearly is :
Options: a ) 6.09 % , b ) 6.08 % , c ) 6.1 % , d ) 6.07 % , e ) 6.05 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = 100 x ( 1 + 3 / 100 ) ^ 2 = 106.09 therefore effective rate = ( 106.09 - 100 ) % = 6.09 % answer a ) 6.09 %"
Answer: a
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) s . 40 , b ) s . 46 , c ) s . 49 , d ) s . 41 , e ) s . 60
Rationale: "1200 * ( 25 / 100 ) = 300 - - - - 5 ? - - - - 1 = > rs . 60 answer : e"
Answer: e
Problem: if 50 % of ( x - y ) = 20 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 43 %
Rationale: "50 % of ( x - y ) = 20 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 20 / 100 ) ( x + y ) 5 ( x - y ) = 2 ( x + y ) 3 x = 7 y x = 7 / 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 7 / 3 ) y ) x 100 ) = 43 % answer is e ."
Answer: e
Problem: ashwin rented a power tool from a rental shop . the rent for the tool was $ 25 for the first hour and $ 10 for each additional hour . if ashwin paid a total of $ 125 , excluding sales tax , to rent the tool , for how many hours did she rent it ?
Options: a ) 11 , b ) 12 , c ) 15 , d ) 18 , e ) 16
Rationale: 25 + 10 n = 125 n = 10 total time = n + 1 hrs = 10 + 1 hrs = 11 hrs answer : a
Answer: a
Problem: b as a percentage of a is equal to a as a percentage of ( a + b ) . find b as a percentage of a .
Options: a ) 62 % , b ) 73 % , c ) 41 % , d ) 71 % , e ) none of these
Rationale: explanation : according to the question : - = > b / a = a / ( a + b ) . as b is a percent of a , let us assume b = ax . then , equation ( 1 ) can be re - written as = > x = 11 + x . = > x ( 1 + x ) = 1 . = > x 2 + x + 1 = 0 . = > x = − 1 ± 5 / √ 2 thus , x = − 1 + 5 / √ 2 = > 0.62 . = > 62 % . answer : a
Answer: a
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 390 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 780 , c ) 197 , d ) 287 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 390 ) = 2 + 2 ( extra ) = > 2 x - 780 = x = > x = 780 . answer : b"
Answer: b
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 40 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 112 mtr . , e ) 17 mtr .
Rationale: "20 men is 6 days can build 112 metres 25 men in 3 days can build = 112 * ( 40 / 20 ) x ( 3 / 6 ) = 112 meters answer : d ."
Answer: d
Problem: a certain junior class has 1,000 students and a certain senior class has 400 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 20,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 400 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 400 * 1000 ) = 3 / 20,000 a"
Answer: a
Problem: a train running at the speed of 180 km / hr crosses a pole in 8 seconds . find the length of the train .
Options: a ) 150 , b ) 88 , c ) 480 , d ) 288 , e ) 400
Rationale: "speed = 180 * ( 5 / 18 ) m / sec = 50 m / sec length of train ( distance ) = speed * time 50 * 8 = 400 meter answer : e"
Answer: e
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds b in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out b : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 600 , find the original price per kg ?
Options: a ) s . 11 , b ) s . 14 , c ) s . 15 , d ) s . 21 , e ) s . 29
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 600 - - - 80 ? - - - 2 = > rs . 15 answer : c"
Answer: c
Problem: what is the remainder when 3 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 3 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? d
Answer: d
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 42 years , was replaced by a new person . find the age of the new person ?
Options: a ) 22 , b ) 18 , c ) 12 , d ) 88 , e ) 66
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 42 + q = > q = 12 answer : c"
Answer: c
Problem: what is the sum of the squares of the first 20 natural numbers ( 1 to 20 ) ?
Options: a ) 2870
b ) 2000
c ) 5650
d ) 6650
e ) 7650
Rationale: n ( n + 1 ) ( 2 n + 1 ) / 6 20 ( 21 ) ( 21 ) / 6 = 2870 answer : a
Answer: a
Problem: the average of 9 observations was 7 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 27 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 7 = 63 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 63 = 27 option a"
Answer: a
Problem: the guests at a football banquet consumed a total of 319 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 159 * 2 ( max possible amount of food a guest could consume ) = 318 pounds , so there must be more than 159 guests , next integer is 160 . answer : a ."
Answer: a
Problem: 8 persons can build a wall 140 m long in 42 days . in how many days can 30 persons complete a similar wall 100 m long ?
Options: a ) 12 , b ) 10 , c ) 8 , d ) 6 , e ) 5
Rationale: explanation : more persons , less days ( indirect proportion ) more length of the wall , more days ( direct proportion ) ⇒ 8 × 100 × 42 = 30 × 140 × x ⇒ x = ( 8 × 100 × 42 ) / ( 30 × 140 ) = ( 8 × 100 × 14 ) / ( 10 × 140 ) = ( 8 × 100 ) / ( 10 × 10 ) = 8 . answer : option c
Answer: c
Problem: what is the prime factors ’ number of 48 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 4 * 3 ^ 1 prime factors ’ number will be 4 + 1 = 5 . hence , answer is d .
Answer: d
Problem: in a group of cows and hens , the number of legs are 20 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 20 4 x + 2 y = 2 x + 2 y + 20 2 x = 20 x = 10 answer : c"
Answer: c
Problem: the compound interest on a sum of money for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound interest and simple interest for 3 years
Options: a ) 98.5 , b ) 08.56 , c ) 98.56 , d ) 98.86 , e ) 98.46
Rationale: explanation : difference in c . i and s . i in 2 years = rs . 32 s . i for 1 year = rs . 400 s . i for rs . 400 for one year = rs . 32 rate = [ 100 * 32 ) / ( 400 * 1 ) % = 8 % difference between in c . i and s . i for 3 rd year = s . i on rs . 832 = rs . ( 832 * 8 * 1 ) / 100 = rs . 66.56 answer : c ) rs . 98.56
Answer: c
Problem: if 5 ^ 21 x 4 ^ 11 = 2 x 10 ^ n . what is the value of n ?
Options: a ) 11 , b ) 21 , c ) 22 , d ) 23 , e ) 32
Rationale: "if 5 ^ 21 x 4 ^ 11 = 2 x 10 ^ n what is the value of n 4 ^ 11 = ( 2 ^ 2 ) ^ 11 = 2 ^ 22 10 ^ n = ( 5 x 2 ) ^ n = 5 ^ n x 2 ^ n 5 ^ 21 x 2 ^ 22 = 2 x 2 ^ n x 5 ^ n = 2 ^ n + 1 x 5 ^ n = 2 ^ 22 x 5 ^ 21 n = 21 option b"
Answer: b
Problem: from below option 51 is divisible by which one ?
Options: a ) a ) 4 , b ) b ) 5 , c ) c ) 6 , d ) d ) 3 , e ) e ) 7
Rationale: "51 / 3 = 17 d"
Answer: d
Problem: each child has 2 pencils and 13 skittles . if there are 11 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 11 = 22 . answer is d .
Answer: d
Problem: . a car covers a distance of 390 km in 4 hours . find its speed ?
Options: a ) 104 , b ) 55 , c ) 66 , d ) 98 , e ) 100
Rationale: 390 / 4 = 98 kmph answer : d
Answer: d
Problem: find the sum of all 3 digit natural numbers , which are divisible by 8
Options: a ) 61376 , b ) 54411 , c ) 612314 , d ) 64170 , e ) 64171
Rationale: "the three digit natural numbers divisible by 8 are 104 , 112 , 120 , … . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 answer a 61376"
Answer: a
Problem: a man buys 25 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 25 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 55 , b ) 82 , c ) 73 , d ) 75 , e ) 85
Rationale: "20 % in 25 lts is 5 . so water = 25 - 5 = 20 lts . 30 % of 25 lts = 7.5 . so water in 2 nd mixture = 25 - 7.5 = 17.5 lts . now total quantity = 25 + 25 = 50 lts . total water in it will be 20 + 17.5 = 37.5 lts . % of water = ( 100 * 37.5 ) / 50 = 75 . answer : d"
Answer: d
Problem: find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm .
Options: a ) 221 cm 2 , b ) 211 cm 2 , c ) 231 cm 2 , d ) 236 cm 2 , e ) 241 cm 2
Rationale: "given : length = 17 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 17 + 13 ) cm = 2 × 30 cm = 60 cm we know that the area of rectangle = length × breadth = ( 17 × 13 ) cm 22 = 221 cm 2 answer : a"
Answer: a
Problem: john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 45 * 2 + 3 * 55 = 255 miles . answer c"
Answer: c
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 555 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 6 , e ) 19
Rationale: "30 * 25 = 750 455 - - - - - - - - - - - 195 25 + 7.50 = 32.5 195 / 32.5 = 6 d"
Answer: d
Problem: a does 4 / 5 th of a work in 20 days . he then calls in b and they together finish the remaining work in 3 days . how long b alone would take to do the whole work ?
Options: a ) 23 days , b ) 37 days , c ) 37 ½ days , d ) 40 days , e ) 41 days
Rationale: explanation : a can finish the whole work in 20 × 5 / 4 days = 25 days a and b together finish the whole work in 5 × 3 days = 15 days therefore , b can finish the whole work in 25 b / 25 + b = 15 25 b = 15 ( 25 + b ) = 375 + 15 b 10 b = 375 and b = 375 / 10 = 37 ½ days . answer : option c
Answer: c
Problem: a and b can do a work in 12 days and 36 days respectively . if they work on alternate days beginning with b , in how many days will the work be completed ?
Options: a ) 11 , b ) 17 , c ) 10 , d ) 17 , e ) 18
Rationale: the work done in the first two days = 1 / 12 + 1 / 36 = 1 / 9 so , 9 such two days are required to finish the work . i . e . , 18 days are required to finish the work . answer : e
Answer: e
Problem: a train , 140 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 140 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 140 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 140 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 140 + x = > 45 ã — 10 ã — 10 / 12 = 140 + x = > 15 ã — 10 ã — 10 / 4 = 140 + x = > 15 ã — 25 = 140 + x = 375 = > x = 375 - 140 = 235 answer : option c"
Answer: c
Problem: if 12 : 18 : : x : 9 , then find the value of x
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: explanation : treat 12 : 18 as 12 / 18 and x : 9 as x / 9 , treat : : as = so we get 12 / 18 = x / 9 = > 18 x = 108 = > x = 6 option c
Answer: c
Problem: an error 2 % in excess is made while measuring the side of asquare . the % of error in the calculated area of the square is ?
Options: a ) 4.00 % , b ) 4.04 % , c ) 4.26 % , d ) 4.56 % , e ) 4.67 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b"
Answer: b
Problem: a can do a piece of work in 30 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 30 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: 10 / 30 + 10 / 30 + 10 / x = 1 x = 30 days answer : a
Answer: a
Problem: the distance between towns a and b is 300 km . one train departs from town a and another train departs from town b , both leaving at the same moment of time and heading towards each other . we know that one of them is 10 km / hr faster than the other . find the speeds of both trains if 2 hours after their departure the distance between them is 40 km .
Options: a ) 22 , b ) 27 , c ) 236 , d ) 90 , e ) 81
Rationale: let the speed of the slower train be xx km / hr . then the speed of the faster train is ( x + 10 ) ( x + 10 ) km / hr . in 2 hours they cover 2 x 2 x km and 2 ( x + 10 ) 2 ( x + 10 ) km , respectively . therefore if they did n ' t meet yet , the whole distance from a to b is 2 x + 2 ( x + 10 ) + 40 = 4 x + 602 x + 2 ( x + 10 ) + 40 = 4 x + 60 km . however , if they already met and continued to move , the distance would be 2 x + 2 ( x + 10 ) − 40 = 4 x − 202 x + 2 ( x + 10 ) − 40 = 4 x − 20 km . so we get the following equations : 4 x + 60 = 3004 x + 60 = 300 4 x = 2404 x = 240 x = 60 x = 60 or 4 x − 20 = 3004 x − 20 = 300 4 x = 3204 x = 320 x = 80 x = 80 hence the speed of the slower train is 60 km / hr or 80 km / hr and the speed of the faster train is 70 km / hr or 90 km / hr . answer : d
Answer: d
Problem: tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 2 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 12 , b ) 15 , c ) 10 , d ) 20 , e ) 14
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 480 ( we want to find the days , sop = 480 / d ) 2 ) ( p + 16 ) ( d - 2 ) = 480 = > pd - 2 p + 16 d - 32 = 480 as the 1 ) stated u can put 1 ) into 2 ) = > 480 - 2 p + 16 d - 32 = 480 = > 16 d - 2 p = 32 put the bold one into it = > 16 d - 2 ( 480 / d ) = 80 the we get the final equation 16 d ^ 2 - 960 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 60 = 0 ( d - 12 ) ( d + 5 ) = 0 so d = 12 days ans : a"
Answer: a
Problem: a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 00000 and the monthly manufacturing expenses is rs 1 , 50000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 69 / 70 ) â ˆ ’ 150000 ã — ( 69 / 70 ) â ˆ ’ 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,000 = > rs . 5,000 . answer : d
Answer: d
Problem: a fruit seller sells mangoes at the rate of rs . 14 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 15 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 18.94 , d ) rs . 12.31 , e ) none
Rationale: "solution 85 : 14 = 115 : x x = ( 14 ã — 115 / 85 ) = rs . 18.94 hence , s . p per kg = rs . 18.94 answer c"
Answer: c
Problem: for a 3 - digit number xyz , where x , y , and z are the digits of the number , f ( xyz ) = 5 ^ x 2 ^ y 3 ^ z . if f ( abc ) = 3 * f ( def ) , what is the value of abc - def ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 27
Rationale: since f ( abc ) = 3 * f ( def ) , i would assume that f = c - 1 from the function above . the answer should be ( a )
Answer: a
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length
Options: a ) 33 , b ) 44 , c ) 55 , d ) 77 , e ) 22
Rationale: "t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer : c"
Answer: c
Problem: a truck covers a distance of 392 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 70 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 392 / 8 = 49 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 48 + 18 ) = 66 kmph distance travelled by car = 392 + 70 = 462 km time taken by car = distance / speed = 462 / 66 = 7 hours . answer – c"
Answer: c
Problem: the area of a triangle is with base 4 m and height 8 m ?
Options: a ) 11 , b ) 10 , c ) 787 , d ) 16 , e ) 12
Rationale: "1 / 2 * 4 * 8 = 16 m 2 answer : d"
Answer: d
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 70 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220070
Rationale: "( 555 + 445 ) * 2 * 110 + 70 = 220000 + 70 = 220070 e"
Answer: e
Problem: the average of 45 results is 10 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 10 * 45 - 15 * 22 + 20 * 22 = 450 - 330 + 440 = 560 answer is e"
Answer: e
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 140 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,260
Rationale: "10 / 100 p = 140 > > p = 140 * 100 / 10 = 1400 1400 - 140 = 1260 answer : e"
Answer: e
Problem: a professional janitor can clean a certain high school in ( 4 + 4 ) hours , working at a constant rate . a student sentenced to detention can clean that same high school in 20 hours , also working at a constant rate . if the student is paid $ 7 total per hour and the janitor is paid $ 21 per hour , how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together ?
Options: a ) - $ 56 , b ) - $ 6 , c ) $ 0 , d ) $ 6 , e ) $ 8
Rationale: a professional janitor can clean a certain high school in ( 4 + 4 ) or 8 hours so ( applying rule # 1 ) , the janitor can clean 1 / 8 of the school in one hour a student sentenced to detention can clean that same high school in 20 hours so ( applying rule # 1 ) , the student can clean 1 / 20 of the school in one hour so , combined , the student and janitor can clean ( 1 / 8 + 1 / 20 ) of the school in one hour 1 / 8 + 1 / 20 = 5 / 40 + 2 / 40 = 7 / 40 so , in one hour they can clean 7 / 40 of the school . applying rule # 2 , it will takethem 40 / 7 hoursto clean the entire school . the janitor earns $ 21 / hour and the student earns $ 7 / hour , so their combined rate is $ 28 / hour . theircombined wages = ( pay rate ) ( time ) = ( $ 28 / hour ) ( 40 / 7 hours ) = $ 160 working alone , the janitor takes 8 hours and earns $ 21 / hour so , working alone , the janitor ' s earnings = ( pay rate ) ( time ) = ( $ 21 / hour ) ( 8 hours ) = $ 168 $ 168 - $ 160 = $ 8 , so the answer is e
Answer: e
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 2 men and 3 women will do that task .
Options: a ) 1 / 2 , b ) 1 / 10 , c ) 1 / 18 , d ) 1 / 16 , e ) 1 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 2 m + 3 w = 7 w answer is 7 / 14 = 1 / 2 answer : a"
Answer: a
Problem: a light has a rating of 60 watts , it is replaced with a new light that has 12 % higher wattage . how many watts does the new light have ?
Options: a ) 105 , b ) 67 , c ) 80 , d ) 60 , e ) 100
Rationale: "final number = initial number + 12 % ( original number ) = 60 + 12 % ( 60 ) = 60 + 7 = 67 answer b"
Answer: b
Problem: a sum of money becomes 7 / 6 of itself in 6 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 9 , b ) 50 / 13 , c ) 50 / 17 , d ) 25 / 9 , e ) 5 5 / 1
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 6 years . rate = ( 100 * x ) / ( x * 6 * 6 ) = 25 / 9 % . answer : d"
Answer: d
Problem: find the missing figures : 0.3 % of ? = 0.15
Options: a ) 50 , b ) 45 , c ) 150 , d ) 450 , e ) 500
Rationale: let 0.3 % of x = 0.15 . then , 0.30 * x / 100 = 0.15 x = [ ( 0.15 * 100 ) / 0.3 ] = 50 . answer is a .
Answer: a
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 265 , then the mean profit for the last 15 days would be
Options: a ) rs . 435 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: average would be : 350 = ( 265 + x ) / 2 on solving , x = 435 . answer : a
Answer: a
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 5 females and 5 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 5 ) = 2 x - 5 x = 10 there were 3 x = 30 people at the party originally . the answer is c ."
Answer: c
Problem: the least number which when increased by 8 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 869 , d ) 856 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 8 = 864 - 8 = 856 . answer d"
Answer: d
Problem: find the length of the wire required to go 10 times round a square field containing 53824 m 2 .
Options: a ) 15840
b ) 9280
c ) 2667
d ) 8766
e ) 66711
Rationale: a 2 = 53824 = > a = 232 4 a = 928 928 * 10 = 9280 answer : b
Answer: b
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 4 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 4 / 100 x 12000 ) = rs . 480 . answer e"
Answer: e
Problem: what should be added to 4329 so that it may become a perfect square ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "66 x 66 = 4356 4356 - 4329 = 27 if added to 27 get perfect square answer = d"
Answer: d
Problem: the number of the members of a club is more than 20 and less than 50 . when 4 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 8 - people groups , how many people will be left ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the number of members is 7 k + 4 = 6 j + 4 the only number in this range which satisfies this is 46 . 46 / 8 = 5 ( 8 ) + 6 the answer is d ."
Answer: d
Problem: the income of a company increases 20 % per annum . if its income is 2664000 in the year 1999 what was its income in the year 1997 ?
Options: a ) 2220000 , b ) 2850000 , c ) 2121000 , d ) 1855000 , e ) none of these
Rationale: let income in 1997 = x according to the question , income in 1998 = x + x ⁄ 5 = 6 x ⁄ 5 income in 1999 = 6 x ⁄ 5 + 6 x ⁄ 25 = 36 x ⁄ 25 but given , income in 1999 = 2664000 ∴ 36 x ⁄ 25 = 2664000 ⇒ x = 1850000 answer e
Answer: e
Problem: when 242 is divided by a certain divisor the remainder obtained is 11 . when 698 is divided by the same divisor the remainder obtained is 18 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 9 . what is the value of the divisor ?
Options: a ) 11 , b ) 17 , c ) 13 , d ) 20 , e ) none of these
Rationale: "let that divisor be x since remainder is 11 or 18 it means divisor is greater than 18 . now 242 - 11 = 231 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 18 = 680 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 231 + 680 ) + 11 + 18 = x ( k + l ) + 29 when we divide this number by x then remainder will be equal to remainder of ( 29 divided by x ) = 9 hence x = 29 - 9 = 20 hence d"
Answer: d
Problem: anil brought a scooter for a certain sum of money . he spent 10 % of the cost on repairs and sold the scooter for a profit of rs . 1100 . how much did he spend on repairs if he made a profit of 20 % ?
Options: a ) 220 , b ) 420 , c ) 250 , d ) 700 , e ) 500
Rationale: e c . p . be rs . x . then , 20 % of x = 1100 20 / 100 * x = 1100 = > x = 5500 c . p . = rs . 5500 , expenditure on repairs = 10 % actual price = rs . ( 100 * 5500 ) / 110 = rs . 5000 expenditures on repairs = ( 5500 - 5000 ) = rs . 500 .
Answer: e
Problem: if 7 persons can do 7 times of a particular work in 7 days , then , 9 persons can do 9 times of that work in ?
Options: a ) 3 days , b ) 8 days , c ) 9 days , d ) 11 days , e ) 7 days
Rationale: that is , 1 person can do one time of the work in 7 days . therefore , 9 persons can do 9 times work in the same 7 days itself . option ' e '
Answer: e
Problem: the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 90 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.15 for 3 lbs , how much did a pound of green tea cost in july ?
Options: a ) $ 4 , b ) $ 0.1 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: "lets assume price of coffee in june = 100 x price of green tea in june = 100 x price of coffee in july = 200 x ( because of 100 % increase in price ) price of green tea in july = 10 x ( because of 90 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of green tea in july will be = 300 x + 15 x = 315 x as per question 315 x = 3.15 $ x = 0.01 s so the price of green tea in july = 10 x = 10 x 0.01 = 0.1 $ / pound answer b"
Answer: b
Problem: if xy > 0 , 1 / x + 1 / y = 4 , and 1 / xy = 6 , then ( x + y ) / 2 = ?
Options: a ) 1 / 25 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 4 canbe solved as { ( x + y ) / xy } = 6 . substituting for 1 / xy = 6 , we get x + y = 4 / 6 = = > ( x + y ) / 2 = 4 / ( 6 * 2 ) = 1 / 3 . d"
Answer: d
Problem: what is 0.01 percent of 12,356 ?
Options: a ) 0.12356 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: "soln : - 0.01 % of 12,356 = 0 . 011000.01100 x 12,356 = 1100 ∗ 1001100 ∗ 100 x 12,356 = 12,356100 ∗ 10012,356100 ∗ 100 = 1.2356 answer : b"
Answer: b
Problem: indu gave bindu rs . 2500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 2 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2500 = d ( 100 / 2 ) 2 d = 1 answer : a"
Answer: a
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent e of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is e = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Problem: for what values of k will the pair of equations 3 ( 3 x + 4 y ) = 36 and kx + 12 y = 30 does not have a unique solution ?
Options: a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5
Rationale: "we have 2 equations 1 . 3 ( 3 x + 4 y ) = 36 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b"
Answer: b
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 5 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 26 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 26 hours d"
Answer: d
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total r of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) r 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
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 5 cups of tea . last week mo drank a total of 36 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 ) 5 , b ) 3 , c ) 4 , d ) 2 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 36 t - c = 14 - > t = 25 . c = 11 . mo drinks 5 cups of tea a day then number of days that are not rainy = 25 / 5 = 5 so number of rainy days = 7 - 5 = 2 d is the answer ."
Answer: d
Problem: there are 2 sections a and b in a class , consisting of 16 and 14 students respectively . if the average weight of section a is 20 kg and that of section b is 25 kg , find the average of the whole class ?
Options: a ) 33.5 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 55.12 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 16 * 20 + 14 * 25 = 670 average weight of the class is = 670 / 20 = 33.5 kg answer is a"
Answer: a
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 60 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 60 = 1.25 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 1.25 + t » 100 / 40 = 1.25 + t » 2.5 = 1.25 + t » t = 1.25 back to 2 nd part of the trip formula : 25 / s = 1.25 » s = 20 ans b
Answer: b
Problem: the price of a jacket is reduced by 35 % . during a special sale the price of the jacket is reduced another 10 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 70.9 , b ) 75 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 35 % , therefore bringing down the price to $ 65 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 58.5 4 ) now 58.5 has to be added byx % in order to equal the original price . 58.5 + ( x % ) 58.5 = 100 . solving this eq for x , we get x = 70.9 ans is a ."
Answer: a
Problem: the number of stamps that p and q had were in the ratio of 7 : 3 respectively . after p gave q 13 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 5 : 4 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 10 , b ) 25 , c ) 40 , d ) 65 , e ) 90
Rationale: "p started with 7 k stamps and q started with 3 k stamps . ( 7 k - 13 ) / ( 3 k + 13 ) = 5 / 4 28 k - 15 k = 117 k = 9 p has 7 ( 9 ) - 13 = 50 stamps and q has 3 ( 9 ) + 13 = 40 stamps . the answer is a ."
Answer: a
Problem: if x and y are positive integers and 25 x = 10 y what is the least possible value of xy ?
Options: a ) 14 , b ) 25 , c ) 63 , d ) 84 , e ) 252
Rationale: "25 x = 10 y = > x / y = 2 / 5 = > 5 x = 2 y 5 ( 3 ) = 2 ( 3 ) = > x * y = 9 but it is not given 5 ( 5 ) = 2 ( 5 ) = > x * y = 25 b"
Answer: b
Problem: a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 27 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let x be the wholesale price . then 1.8 x = 27 and x = 27 / 1.8 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 3 more . the answer is c ."
Answer: c
Problem: the ratio of the volumes of two cubes is 2744 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 196 : 121 , b ) 81 : 127 , c ) 181 : 196 , d ) 81 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 2744 : ³ √ 1331 = 14 : 11 ratio of surface areas = 14 ^ 2 : 11 ^ 2 = 196 : 121 answer : option a"
Answer: a
Problem: evaluate 28 % of 350 + 45 % of 280
Options: a ) 224 , b ) 242 , c ) 252 , d ) 262 , e ) 282
Rationale: "explanation : = ( 28 / 100 ) * 350 + ( 45 / 100 ) * 280 = 98 + 126 = 224 answer : option a"
Answer: a
Problem: three unbiased coins are tossed . what is the probability of getting 1 heads , 1 tail ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 2 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { tht , hth } p ( e ) = n ( e ) / n ( s ) = 2 / 8 answer is e"
Answer: e
Problem: divide rs . 32000 in the ratio 3 : 7 ?
Options: a ) 12000 , 20000 , b ) 9600 , 22400 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: 3 / 10 * 32000 = 9600 7 / 8 * 32000 = 22400 answer : b
Answer: b
Problem: a train is running with a speed of 60 kmph and its length is 110 metres . calculate the time by which it will pass a man running opposite with speed of 6 kmph
Options: a ) 2 second , b ) 4 second , c ) 6 second , d ) 8 second , e ) 10 second
Rationale: explanation : from the given question , we will first calculate the speed of train relative to man , = > ( 60 + 6 ) = 66 km / hr ( we added 6 because man is running opposite ) convert it in metre / second = 66 ã — 5 / 18 = 55 / 3 m / sec time it will take to pass man = 110 ã — 3 / 55 = 6 seconds answer is c
Answer: c
Problem: the total of the ages of amar , akbar and anthony is 66 years . what was the total of their ages 4 years ago ?
Options: a ) 71 , b ) 44 , c ) 54 , d ) 16 , e ) 18
Rationale: explanation : required sum = ( 66 - 3 x 4 ) years = ( 66 - 12 ) years = 54 years . answer : c
Answer: c
Problem: kim finds a 3 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 8 / 15 , d ) 1 / 2 , e ) 7 / 5
Rationale: 3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is b
Answer: b
Problem: a certain country is divided into 8 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 8 p / 12 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e ."
Answer: e
Problem: n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 45 and 6 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: you have 6 digits : 12 , 3 , 4 , 5 , 6 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 1 and 6 in the hundreds places and reserve them for the tens places now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 265 and 314 ( difference is 49 ) or try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . we get 463 and 512 ( difference is 49 ) b
Answer: b