Cheukting/mathqa huggingface dataset:
Question (gain): mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 462 ?
Options: a ) 25.6 % , b ) 21 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 462 , discount = 621 - 462 = 159 discount % = 159 / 621 * 100 = 25.6 % answer : a"
Answer: a
Question (gain): the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 16 % ?
Options: a ) 31.25 % , b ) 35.5 % , c ) 37.5 % , d ) 39.5 % , e ) 30.5 %
Rationale: "let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 84 gain % = 20 / 64 * 100 = 31.25 % . a"
Answer: a
Question (general): what is the value of 3 x ^ 2 − 1.8 x + 0.8 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0.8 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.8 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.8 = 0 + 0.8 = 0.8 answer : b"
Answer: b
Question (gain): a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 64.50 , his capital is ?
Options: a ) 24,602 , b ) 28,888 , c ) 25,800 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 64.50 32 x - 31 x = 6450 * 4 x = 25,800 . answer : c"
Answer: c
Question (general): what is the sum of all digits for the number 10 ^ 27 - 48 ?
Options: a ) 212 , b ) 222 , c ) 232 , d ) 242 , e ) 252
Rationale: "10 ^ 27 is a 28 - digit number : 1 followed by 27 zeros . 10 ^ 27 - 48 is a 27 - digit number : 25 9 ' s and 52 at the end . the sum of the digits is 25 * 9 + 5 + 2 = 232 . the answer is c ."
Answer: c
Question (general): what is the units digit of ( 493 ) ( 913 ) ( 381 ) ( 756 ) ( 29 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 3 , 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 3 . imo d ."
Answer: d
Question (general): the greatest number which on dividing 1557 and 2037 leaves remainders 7 and 5 respectively , is :
Options: a ) 123 , b ) 127 , c ) 2 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1557 - 7 ) and ( 2037 - 5 ) = h . c . f . of 1550 and 2032 = 2 . answer : c"
Answer: c
Question (geometry): there is a right angle triangle inside a circle of diameter 18 cm . inside this triangle , there is another circle of diameter 6 cm . find the perimeter of the triangle .
Options: a ) 24 cm
b ) 36 * 2 ^ 1 / 2 cm
c ) 36 cm
d ) 54 cm
e ) 42 cm
Rationale: 1 ) the radius of the incircle of a right triangle with legs a and b and hypotenuse c is r = ( a + b - c ) / 2 2 ) the radius of the circumcircle is half the length of the hypotenuse r = c / 2 3 ) thus the sum of the circumradius and the inradius is half the sum of the legs r + r = ( a + b ) / 2 from 2 nd rule c = 18 cm from 3 rd rule a + b = 2 * ( 9 + 3 ) = 24 cm hence perimeter a + b + c = 24 + 18 = 42 cm answer : e
Answer: e
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 14 % ?
Options: a ) 20 % , b ) 29 % , c ) 13 1 / 30 % , d ) 12 % , e ) 13 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 86 2 / 3 sp 1 = 86 sp 1 = 129 100 - - - 29 = > 29 % answer : b"
Answer: b
Question (physics): p and q can complete a work in 10 days and 6 days respectively . p alone started the work and q joined him after 2 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 10 work done by q in 1 day = 1 / 6 work done by p in 2 days = 2 ã — ( 1 / 10 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 10 + 1 / 6 = 4 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 4 / 15 ) = 3 total days = 2 + 3 = 5 answer : option a"
Answer: a
Question (general): david is 18 years older than his daughter rosy . in 6 years david will be twice as old as rosy . what is rosy current age .
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 23
Rationale: now : rosy = x , david = x + 18 in 6 years rosy = x + 6 , david = x + 18 + 6 or 2 ( x + 6 ) x + 24 = 2 x + 12 x = 12 rosy is 12 years old answer : a
Answer: a
Question (general): you collect pens . suppose you start out with 20 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 65 , d ) 42 , e ) 43
Rationale: solution start with 20 pens . mike gives you 22 pens : 20 + 22 = 42 pens . cindy doubles the number of pens you have : 42 ã — 2 = 84 pens . sharon takes 19 pens from you : 84 - 19 = 65 pens . so you have 65 at the end . correct answer : c
Answer: c
Question (physics): a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 210 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 5
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 210 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 it takes a total of nine hours to cover the 210 mile distance . answer : a 6"
Answer: a
Question (physics): sarah is driving to the airport . after driving at 40 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 50 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 340 , c ) 210 , d ) 245 , e ) 280
Rationale: "after driving at 40 miles per hourfor one hour , this distance left to cover is d - 40 . say this distance is x miles . now , we know that the difference in time between covering this distance at 40 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 40 - x / 50 = 3 / 2 - - > 5 x / 200 - 4 x / 200 = 3 / 2 - - > x / 200 = 3 / 2 - - > x = 300 . total distance = x + 40 = 340 miles . answer : b"
Answer: b
Question (general): the sum of the 1 st and 3 rd of 3 consecutive odd integers is 131 less than 3 times the second integer . find the 3 integers ?
Options: a ) 121 , b ) 133 , c ) 145 , d ) 150 , e ) 165
Rationale: let x , x + 2 and x + 4 be three integers . the sum of the first x and third x + 4 is given by x + ( x + 4 ) 131 less than three times the second 3 ( x + 2 ) is given by 3 ( x + 2 ) - 131 ` ` the sum of the first and third is 131 less than three times the second ' ' gives x + ( x + 4 ) = 3 ( x + 2 ) - 131 solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 as an exercise , check that the sum of the first and third is 131 less than three times b
Answer: b
Question (gain): a local business made a $ 125000 profit on its first $ 1 million in sales and a $ 80000 profit on its next $ 2 million in sales . by approximately what percent did the ratio of profit to sales decrease from the first $ 1 million in sales to the next $ 2 million in sales ?
Options: a ) 100 % , b ) 150 % , c ) 200 % , d ) 250 % , e ) 300 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first 1 million in sales , and the second ratio will be for the next 2 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 1 million profit / sales = 125 / 1000 = 1 / 8 next 2 million profit / sales = 8 / 200 = 2 / 50 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 400 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 1 million royalties / sales = ( 1 / 8 ) x 400 = 50 next 2 million royalties / sales = ( 2 / 50 ) x 400 = 16 we can plug 5 and 6 into our percent change formula : ( new – old ) / old x 100 [ ( 16 – 50 ) / 16 ] x 100 = - 34 / 16 x 100 so approximately a 200 % decrease . answer c .
Answer: c
Question (gain): in town x , 64 percent of the population are employed , and 44 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 55 % , c ) 29 % , d ) 40 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 20 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 20 / 64 = 29 c"
Answer: c
Question (general): for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score t for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean t = 74 . answer : a ."
Answer: a
Question (gain): √ 5 percent of 5 √ 5 =
Options: a ) 0.05 , b ) 0.25 , c ) 0.5 , d ) 2.5 , e ) 25
Rationale: "√ / 1005 / 100 * 55 √ 5 = ( 5 * 5 ∗ 5 − − √ 5 ∗ 5 ) / 100 = ( 5 * 5 ) / 100 = 25 / 100 = . 25 answer : b"
Answer: b
Question (general): how many numbers from 10 to 31 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 7 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 . 7 numbers . 10 / 3 = 3 and 31 / 3 = 10 = = > 10 - 3 = 7 . therefore 7 digits d )"
Answer: d
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 4 more than the average of 10 , 70 , and what number ?
Options: a ) 28 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 4 = 36 sum of second list = 36 * 3 = 108 therefore the number = 108 - 80 = 28 answer : a"
Answer: a
Question (general): what is the least number . which should be added to 221 to make it a perfect square ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 6 , e ) 7
Rationale: "221 + 4 = 225 15 ^ 2 answer : c"
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 42 . if n / j = 204.07 , what is value of j ?
Options: a ) 200 , b ) 400 , c ) 800 , d ) 600 , e ) 1200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.07 here 204 is the quotient . given that remainder = 42 so , 204.07 = 204 + 42 / j so , j = 600 answer : d"
Answer: d
Question (general): 8796 x 223 + 8796 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 2658560 , d ) 2716740 , e ) none of them
Rationale: "= 8796 x ( 223 + 77 ) ( by distributive law ) = 8796 x 300 = 2638800 answer is b"
Answer: b
Question (gain): an agent , gets a commission of 5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 887 , d ) 250 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 5 % . of x = 12.50 < = > ( 5 / 100 * x ) = 125 / 10 < = > x = 250 . answer : d"
Answer: d
Question (general): 121 x 5 ^ 4 = ?
Options: a ) 75625 , b ) 68225 , c ) 72325 , d ) 71225 , e ) 72225
Rationale: explanation : 121 × 5 ^ 4 = 121 × ( 10 / 2 ) ^ 4 = ( 121 × 10000 ) / 16 = 7.5625 × 10000 = 75625 answer is a
Answer: a
Question (general): the number n is h , 284 , where h represents the 10 ' s digit . if n is divisible by 6 , what is the value of h ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: if the number is divisible by 6 , then the sum of the digits must also be divisible by both 3 and 2 . only 1 yields such a number . answer : a
Answer: a
Question (physics): a 360 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 140 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 360 / 9 = 500 / 9 = > x + 360 = 500 = > x = 140 so the length of the train is 140 meters option c"
Answer: c
Question (physics): how long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length ?
Options: a ) 22 sec , b ) 20 sec , c ) 15 sec , d ) 23 sec , e ) 16 sec
Rationale: "d = 100 + 245 = 345 m s = 54 * 5 / 18 = 15 t = 345 * 1 / 15 = 23 sec answer : d"
Answer: d
Question (general): a certain store sells all maps at one price and all books at another price . on monday the store sold 9 maps and 6 books for a total of $ 20.00 , and on tuesday the store sold 9 maps and 8 books for a total of $ 30.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 3.9 , e ) $ l . 25
Rationale: "9 x + 6 y = 20 9 x + 8 y = 30 subtracting 1 from 2 - 2 y = - 10 y = 5 therefore x = 1.1 difference in price = 3.9 d"
Answer: d
Question (physics): the ratio of efficiency of a is to c is 5 : 3 . the ratio of no . of days taken by b is to c is 2 : 3 . a takes 6 days less than c , when a and c completes the work individually . b and c left the work after 2 days . the no of days taken by a to finish the remaining work ?
Options: a ) 4.5 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: a : b : c efficiency 10 : 9 : 6 no of days 9 x : 10 x : 15 x given = > 15 x - 9 x = 6 hence , x = 1 number of days taken by a = 9 and daily work done = 10 number of days taken by b = 10 and daily work done = 9 ( total work = 90 ) number of days taken by c = 15 and daily work done = 6 work done by b and c in initial 2 days = 30 rest work = 60 number of days required by a to finish = 60 / 10 = 6 days answer : c
Answer: c
Question (physics): a train covers a distance of 16 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 16 / 10 * 60 ) km / hr = ( 96 * 5 / 18 ) m / sec = 80 / 3 m / sec . length of the train = 80 / 3 * 6 = 160 m . answer : c"
Answer: c
Question (physics): a man sitting in a train which is traveling at 70 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 42 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 70 ) kmph = 42 kmph . answer : e"
Answer: e
Question (general): if s = { 8 , 16 , 24 , 32 , 40 , 48 } , what is the product of mean and median of the numbers in s ?
Options: a ) 652 , b ) 589 , c ) 456 , d ) 620 , e ) 784
Rationale: mean = ( 8 + 16 + 24 + 32 + 40 + 48 ) / 6 = 28 median = ( 24 + 32 ) / 2 = 28 product = 28 * 28 = 784 option e
Answer: e
Question (physics): after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.2 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.2 , c ) 4.0 , d ) 6.5 , e ) 8.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.2 x = 3.2 alternate solution : try to backsolve . initial volume = 3.2 after one hour - - > ( 1 / 4 ) 3.2 = 0.8 after two hours - - > ( 1 / 4 ) 0.8 = 0.2 answer : b"
Answer: b
Question (gain): one fourth of a solution that was 22 % sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.22 + 1 / 4 * x = 1 * 0.35 - - > x = 0.74 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.22 + 25 * x = 100 * 0.35 - - > x = 0.74 . answer : a ."
Answer: a
Question (general): if 2994 ã · 14.5 = 171 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 171 in the place of 2994 / 14.5 ] = 171 / 10 = 17.1 answer is a ."
Answer: a
Question (general): when positive integer n is divided by positive integer j , the remainder is 27 . if n / j = 204.09 , what is value of j ?
Options: a ) 300 , b ) 320 , c ) 360 , d ) 410 , e ) 420
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.09 here 204 is the quotient . given that remainder = 27 so , 204.09 = 204 + 27 / j so , j = 300 answer : a"
Answer: a
Question (general): there are 840 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 140 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 840 - x x / 2 + 840 - x / 4 = 1 / 3 * ( 840 ) = 280 x = 280 x / 2 = 140 is supposed to be the answer m is missing something correct option a"
Answer: a
Question (general): p alone can complete a job in 7 days . the work done by q alone in one day is equal to one - sixth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "p ' s rate is 1 / 7 q ' s rate is 1 / 42 the combined rate is 1 / 7 + 1 / 42 = 1 / 6 if they work together , the job will take 6 days . the answer is e ."
Answer: e
Question (general): there are 4 members in a family . their average income is rs . 10000 per month . 3 members get rs . 8000 , rs . 15000 , rs . 6000 respectively . therefore what is the income of the fourth member of the family ?
Options: a ) rs . 10000 , b ) rs . 11000 , c ) rs . 12000 , d ) rs . 9000 , e ) rs . 8500
Rationale: explanation total income of 3 members = rs . ( 8000 + 15000 + 6000 ) = rs . 29000 . required income = rs . [ ( 10000 x 4 ) – 29000 ] = rs . ( 40000 – 29000 ) = rs . 11000 . answer b
Answer: b
Question (general): if ( 3 / 2 ) x - 3 = 15 what is the value of x ?
Options: a ) - 12 , b ) 12 , c ) - 1 / 12 , d ) 1 / 12 , e ) 3
Rationale: ( 3 / 2 ) x - 3 = 15 = > 3 x - 6 = 30 = > 3 x = 36 = > x = 12 answer : b
Answer: b
Question (physics): a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 3.58 , b ) 3.68 , c ) 3.78 , d ) 3.88 , e ) 3.98
Rationale: "m = 8 s = 1.2 ds = 8 + 1.2 = 9.2 us = 8 - 1.2 = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.68 . answer : b"
Answer: b
Question (gain): a and b invests rs . 3000 and rs . 8000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 16 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 8 * 12 ) 54 : 96 = > 9 : 16 . answer : c"
Answer: c
Question (physics): a rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 34 , b ) 77 , c ) 36 , d ) 56 , e ) 91
Rationale: "explanation : perimeter of the plot = 2 ( 90 + 50 ) = 280 m no of poles = 280 / 5 = 56 m answer : d"
Answer: d
Question (general): the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 9.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 9.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 9.80 - 3.20 = 6.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 6.6 = t ( 5.4 x ) - > t = ( 6.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 6.6 / 5.4 = 9.3 answer c ."
Answer: c
Question (general): how many two - element subsets of { 1,2 , 3,4 } are there that do not contain the pair of elements 2 and 4 ?
Options: a ) one , b ) two , c ) four , d ) five , e ) six
Rationale: "{ 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } , { 3,4 } . or : c 24 − 1 = 5 answer : d ."
Answer: d
Question (physics): at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 16 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 39 = 19 + 16 + 12 - 4 - 2 x 2 x = 19 + 16 + 12 - 4 - 39 = 43 - 39 = 4 x = 2 a
Answer: a
Question (geometry): there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle ?
Options: a ) 6
b ) 5
c ) 8
d ) 6
e ) 3
Rationale: let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c
Answer: c
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to z . what is the value of 5.2 – 5.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b ."
Answer: b