Cheukting/mathqa huggingface dataset:
Question (gain): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (probability): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): . 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
Question (general): 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
Question (gain): 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
Question (geometry): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (geometry): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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