Cheukting/mathqa huggingface dataset:
Question (general): in a competitive examination in a state a , 10 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 12 % candidates got selected with 100 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 4000 , b ) 5000 , c ) 5500 , d ) 6500 , e ) 4200
Rationale: "let the number of candidates appeared be x then , 12 % of x - 10 % of x = 100 2 % of x = 100 x = 100 * 100 / 2 = 5000 answer is b"
Answer: b
Question (gain): if it is assumed that 80 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 375 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 80 % = 300 / 0.8 = 375 option a"
Answer: a
Question (general): when a number is divided by 6 & then multiply by 12 the answer is 13 what is the no . ?
Options: a ) 6.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 13 = > 2 x = 13 = > x = 6.5 a"
Answer: a
Question (general): in arun ' s opinion , his weight is greater than 66 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 69 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 67.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 66 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 69 . the values satisfying all the above conditions are 67 and 68 . required average = ( 67 + 68 ) / 2 = 67.5 kg answer : b"
Answer: b
Question (general): find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 20 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1634 , d ) 1678 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 20 5 x = 1345 x = 269 large number = 269 + 1365 = 1634 c"
Answer: c
Question (gain): by selling 9 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 4 , e ) 6
Rationale: "80 % - - - 9 120 % - - - ? 80 / 120 * 9 = 6 answer : e"
Answer: e
Question (gain): in a public show 62 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 228
Rationale: "75 % of 600 = 62 / 100 × 600 = 372 therefore , the number of vacant seats = 600 - 372 = 228 . answer : e"
Answer: e
Question (general): there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 4576 , then what was the price of the article initially ?
Options: a ) rs . 5000 , b ) rs . 3000 , c ) rs . 4000 , d ) rs . 2000 , e ) rs . 6000
Rationale: "let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 4576 for 114.4 - - - > 100 ; 4576 - - - > ? required price = ( 4576 * 100 ) / 114.4 = 40 * 100 = rs . 4000 . answer : c"
Answer: c
Question (general): 50 boys and 100 girls are examined in a test ; 50 % of the boys and 40 % of the girls pass . the percentage of the total who failed is ?
Options: a ) 42.5 % , b ) 62.1 % , c ) 56.7 % , d ) 39.9 % , e ) 51.4 %
Rationale: "total number of students = 50 + 100 = 150 number of students passed = ( 50 % of 50 + 40 % of 100 ) = 25 + 40 = 65 number of failures = 85 * 100 / 150 = 56.7 % answer is c"
Answer: c
Question (general): if ( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) = > 5 ^ 5 * 3 ^ 6 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 5 * 3 ^ 6 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 5 answer a"
Answer: a
Question (general): 5356 x 51 = ?
Options: a ) 273156 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258
Rationale: "5356 x 51 = 5356 x ( 50 + 1 ) = 5356 x 50 + 5356 x 1 = 267800 + 5356 = 273156 . a"
Answer: a
Question (general): marts income is 60 percent more than tims income and tims income is 60 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 64 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 160 / 100 ) t t = ( 40 / 100 ) j = > m = ( 64 / 100 ) j answer b ."
Answer: b
Question (physics): a man swims downstream 16 km and upstream 10 km taking 2 hours each time , what is the speed of the man in still water ?
Options: a ) 7.0 , b ) 8.2 , c ) 6.5 , d ) 7 , e ) 6
Rationale: "16 - - - 2 ds = 8 ? - - - - 1 10 - - - - 2 us = 5 ? - - - - 1 m = ? m = ( 8 + 5 ) / 2 = 6.5 answer : c"
Answer: c
Question (gain): the manufacturing cost of a shoe is rs . 190 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 234 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 190 + ( 500 / 100 ) = 195 . gain = 20 % = > sp = 1.2 cp = 1.2 x 195 = 234 answer : a"
Answer: a
Question (geometry): what is the area of a circle having the same perimeter as that of a square whose area is 121 .
Options: a ) 306
b ) 307
c ) 308
d ) 309
e ) 310
Rationale: side of the square = sqrt ( 12 ) = 11 perimeter of the square = 44 2 * pie * r = 44 r = 44 / 2 * pie area of the circle = pie * r ^ 2 = 308 answer : c
Answer: c
Question (gain): the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 20 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.09
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 20 % are damaged - - > available tomatoes to sell = 80 80 * x - 80 = 0.08 * 80 80 x - 80 = 6.4 80 x = 86.64 x = 86.64 / 80 = 87 / 80 ( approx ) = 1.0875 x is slightly under 1.0875 = 1.09 answer : e"
Answer: e
Question (gain): a sum fetched a total simple interest of rs . 4016.25 at the rate of 3 % p . a . in 5 years . what is the sum ?
Options: a ) 26775 , b ) 28772 , c ) 28821 , d ) 89255 , e ) 28871
Rationale: "principal = ( 100 * 4016.25 ) / ( 3 * 5 ) = rs . 26775 . answer : a"
Answer: a
Question (general): what is the units digit of ( 498 ) ( 915 ) ( 381 ) ( 756 ) ( 29 )
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 2 . imo c ."
Answer: c
Question (general): a certain store sells all maps at one price and all books at another price . on monday the store sold 12 maps and 10 books for a total of $ 42.00 , and on tuesday the store sold 20 maps and 15 books for a total of $ 70.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 3.5 , d ) $ 2.5 , e ) $ l . 25
Rationale: "12 x + 10 y = 42 20 x + 15 y = 70 multiply eq 1 by 5 and eq 2 by 3 60 x + 50 y = 42 * 5 60 x + 45 y = 70 * 3 subtracting 1 from 2 5 y = 210 - 210 y = 0 therefore x = 3.5 difference in price = 3.5 c"
Answer: c
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: let the weekly sales of both = x 590 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c
Answer: c
Question (general): the least number which when divided by 2 , 3 , 5 and 6 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 16 , b ) 63 , c ) 73 , d ) 83 , e ) none of these
Rationale: "explanation : l . c . m of 2 , 3 , 5 , 6 = 30 therefore required number is of the form 30 k + 3 . least value of k for which ( 30 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 30 x 2 + 3 ) = 63 . answer : b"
Answer: b
Question (general): how many 4 - digit numbers ( abcd ) can be formed such that | a – d | = 2 ?
Options: a ) 2000 , b ) 1900 , c ) 1800 , d ) 1600 , e ) 1,500
Rationale: digit a can be filled in 9 ways ( excluding 0 ) digit b can be filled in 10 ways digit c can be filled in 10 ways digit d can be filled in 2 ways ( because of modulus a - d ) the answer will be 9 * 10 * 10 * 2 = 1800 ans c
Answer: c
Question (general): find the smallest number of 6 digits which is exactly divisible by 111 ?
Options: a ) 12000 , b ) 15550 , c ) 100011 , d ) 158993 , e ) 100010
Rationale: "smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer b"
Answer: b
Question (general): if the mean of numbers 28 , x , 42 , 78 and 104 is 90 , then what is the mean of 128 , 255 , 511 , 1023 and x ?
Options: a ) 395 , b ) 275 , c ) 355 , d ) 423 , e ) 365
Rationale: the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 90 * 5 - - > x = 198 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 198 ) / 5 = 423 . answer : d .
Answer: d
Question (physics): a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 12 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 25 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 12 / 60 ) = 5 kmhr speed in still water = 1 / 2 ( 2 + 5 ) = 3.5 kmhr time taken in stationary = 5 / 3.5 = 1 hrs 25 min answer : c"
Answer: c
Question (general): the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 7 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 360 km , d ) 550 km , e ) 630 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 7 h is 90 × 7 = 630 km ans . ( e )"
Answer: e
Question (general): the average of 64 numbers is 48 . if two numbers namely 35 and 45 are discarded , the average of remaining numbers is ?
Options: a ) 35.5 , b ) 37.5 , c ) 39.5 , d ) 34.5 , e ) 47.9
Rationale: total of 50 numbers = 64 * 48 = 3072 average of 62 numbers = 3072 - ( 45 + 55 ) / 62 = 2972 / 62 = 47.9 answer is e .
Answer: e
Question (general): a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 250.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.40
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 250 = > 125 * s = 175 = > s = 1.4 answer e"
Answer: e
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 65 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . age of the youngest child = x = 7 years . d )"
Answer: d
Question (physics): a toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters , at 10 meters per minute . however , the toy train is defective and it now produces only two different tunes at random . what is the probability that the toy train produces 3 music tunes of the same type ( 1 in _____ ) ?
Options: a ) 3 , b ) 9 , c ) 8 , d ) 4 , e ) 5
Rationale: 1 / 2 ^ 3 = 1 / 8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 2 * 1 / 8 = 1 / 4 so ans is 4 answer : d
Answer: d
Question (general): evaluate : 56 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 48 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 56 - 12 * 3 * 2 = 56 - 8 = 48 correct answer b"
Answer: b
Question (general): if a - b = 3 and a ^ 2 + b ^ 2 = 31 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 11 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 31 - 9 = 22 ab = 11 . answer is d ."
Answer: d
Question (general): if x , y , and z are positive real numbers such that x ( y + z ) = 132 , y ( z + x ) = 152 , and z ( x + y ) = 180 , then xyz is
Options: a ) 40 , b ) 60 , c ) 160 , d ) 100 , e ) 120
Rationale: xy + xz = 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 152 + 28 xz + zy = yz + yx + 28 xz = yx + 28 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 160 xz = 80 xyz has to be multiple of 80 , only 160 fits in answer = c
Answer: c
Question (gain): a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party q . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: s = 100 not ( q and b ) = 35 only q = 20 ( q and b ) / b = 1 / 2 let ( q and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans
Answer: a
Question (physics): there is enough provisions for 100 girls in a hostel for 50 days . if there were 20 men less , how long will the provision last ?
Options: a ) 250 , b ) 255 , c ) 260 , d ) 265 , e ) 270
Rationale: we have , m 1 d 1 = m 2 d 2 100 * 50 = 20 * d 2 d 2 = 100 * 50 / 20 = 250 days . answer : a
Answer: a
Question (other): at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years arun ' s age will be 26 years . what is the age of the deepak ?
Options: a ) 15 , b ) 20 , c ) 18 , d ) 22 , e ) 35
Rationale: "let the present age of arun and deepak be 4 x and 3 x 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a"
Answer: a
Question (general): what is the greatest integer m for which the number 40 ! / 14 ^ m is an integer ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: 14 ^ m = 2 ^ m * 7 ^ m . let ' s figure out how many 7 ' s are in the prime factorization of 40 ! the multiples of 7 are : 7 , 14 , 21 , 28 , 35 . thus 7 ^ 5 will divide 40 ! but 7 ^ 6 will not . clearly 2 ^ 5 will divide 40 ! so m = 5 is the largest possible integer . the answer is d .
Answer: d
Question (gain): the price of a book is increased from $ 300 to $ 480 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 480 â € “ rs 300 = rs 180 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 180 300 ) * 100 = 60 % e"
Answer: e
Question (general): m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 21 ) both lie on the line defined by the equation x = ( y / 7 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x = ( y / 7 ) - ( 2 / 5 ) , and so y = 7 x + 14 / 5 . the slope is 7 . ( n + 21 - n ) / ( m + p - m ) = 7 p = 3 the answer is c .
Answer: c
Question (physics): let a be the event that a randomly selected two digit number is divisible by 10 and let b be the event that a randomly selected two digit number is divisible by 5 . what is p ( a and b ) ?
Options: a ) 1 / 50 , b ) 1 / 30 , c ) 1 / 15 , d ) 1 / 10 , e ) 1 / 5
Rationale: p ( a and b ) = 1 / 10 * 1 / 5 = 1 / 50 the answer is a .
Answer: a
Question (general): in a group of cows and hens , the number of legs are 12 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 12 2 x = 12 x = 6 . answer : b"
Answer: b
Question (general): find the least number which when divided by 12,24 , 36,42 leaves remainder 9,21 , 33,39 respectively .
Options: a ) 499 , b ) 501 , c ) 452 , d ) 365 , e ) 325
Rationale: "the difference of 12 - 9 = 3 , 24 - 21 = 3 , 36 - 33 = 3 , 42 - 39 = 3 lcm of 12,24 , 36,42 = 504 required number = 504 - 3 = 501 answer is b"
Answer: b
Question (general): the difference between a 6 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 3 , b ) 92439 , c ) 30813 , d ) 10271 , e ) 10272
Rationale: another approach is to test a number . let ' s say the original number is 123004 so , the reversed number is 400321 the difference = 400321 - 123004 no check the answer choices 277317 is a multiple of 3,92439 , 30813,10271 10272 is not a multiple of 277317 answer : e
Answer: e
Question (other): sandy is younger than molly by 12 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72
Rationale: "s = m - 12 s / m = 7 / 9 9 s = 7 m 9 ( m - 12 ) = 7 m m = 54 the answer is c ."
Answer: c
Question (physics): two pipes can fill a tank in 20 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 5 minutes , b ) 17 minutes , c ) 15 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 20 + 1 / 15 - 1 / 45 = ( 9 + 12 - 4 ) / 180 = 17 / 180 so , the tank becomes full in 5 minutes . answer : a"
Answer: a
Question (general): the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 10 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 17 %
Rationale: "the original output increases by 10 % and then 10 % . total % change = a + b + ab / 100 total % change = 10 + 10 + 10 * 10 / 100 = 21 % now , you want to change it to 0 , so , 0 = 21 + x + 21 x / 100 x = - 21 ( 100 ) / 121 = 17 % approximately answer is e"
Answer: e
Question (gain): a company recently conducted a survey and found that 25,000 of its customers live in rural areas . if the number of customers who live in urban areas is 120 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 50,000 , b ) 55,000 , c ) 60,000 , d ) 65,000 , e ) 70,000
Rationale: "the number of customers in urban areas is 25,000 + 1.2 * 25,000 = 55,000 . the answer is b ."
Answer: b
Question (physics): how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 142 m length ?
Options: a ) 82.1 sec . , b ) 12.6 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 142 = 252 m . required time = 252 / 20 = 12.6 sec . answer : b"
Answer: b
Question (general): 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration q of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration q would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Question (geometry): in measuring the sides of a rectangle , one side is taken 10 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 4.5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 110 * 95 = 10,450 , which is 4.5 % greater than the actual area . answer : d ."
Answer: d
Question (general): if 2 x + y = 7 and x + 2 y = 5 , then 4 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 4 * 3 * 1 ) / 3 = 12 / 3 = 4 e"
Answer: e
Question (general): rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 760 , b ) $ 750 , c ) $ 810 , d ) $ 800 , e ) $ 780
Rationale: 50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 5 ) + 30 ( 5 + 4 ) + 20 ( 5 + 4 + 4 ) = 250 + 270 + 260 = 780 answer - e
Answer: e
Question (general): 0.2 x 0.7 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.01 , d ) 0.14 , e ) none of these
Rationale: "explanation : 2 x 7 = 14 . sum of decimal places = 2 0.2 x 0.7 = 0.14 answer - d"
Answer: d
Question (gain): the cost price of a radio is rs . 1860 and it was sold for rs . 1340 , find the loss % ?
Options: a ) 18 % , b ) 12 % , c ) 22 % , d ) 27 % , e ) 21
Rationale: "1860 - - - - 520 100 - - - - ? = > 27 % answer : d"
Answer: d
Question (physics): in a kilometer race , a beats b by 16 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 176 sec , d ) 716 sec , e ) 615 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 16 = 625 sec . time taken by a = 625 - 10 = 615 sec . answer : e"
Answer: e
Question (general): if 15 students in a class average 75 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 81 % , b ) 82 % , c ) 83 % , d ) 84 % , e ) 85 %
Rationale: "( 15 * 75 + 10 * 95 ) / 25 = 83 % the answer is c ."
Answer: c