Cheukting/mathqa huggingface dataset:
Question (general): tom read a book containing 100 pages by reading the same number of pages each day . if he would have finished the book 10 days earlier by reading 30 pages a day more , how many days did tom spend reading the book ?
Options: a ) 7 , b ) 7.68 , c ) 8 , d ) 9 , e ) 10
Rationale: actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 100 ( we want to find the days , sop = 100 / d ) 2 ) ( p + 30 ) ( d - 10 ) = 100 = > pd - 10 p + 30 d - 300 = 100 as the 1 ) stated u can put 1 ) into 2 ) = > 100 - 10 p + 30 d - 300 = 100 = > 30 d - 10 p = 100 put the bold one into it = > 30 d - 10 ( 100 / d ) = 100 the we get the final equation 30 d ^ 2 - 1000 = 100 d ( divide 16 ) = > d ^ 2 - 5 d - 150 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 7.68 days . ans : ( b )
Answer: b
Question (general): the sum of the squares of three numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
Options: a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c"
Answer: c
Question (physics): the speed of a boat in still water is 18 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 14 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 5.1 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 18 + 4 ) kmph = 22 kmph . distance travelled = ( 22 x 14 / 60 ) km = 5.1 km option c"
Answer: c
Question (gain): the present worth of rs . 169 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 169 / ( 1 + 4 / 100 ) ² ] = rs . ( 169 x 25 / 26 x 25 / 26 ) = rs . 156.25 answer c"
Answer: c
Question (general): how many positive integers less than 350 are there such that they are multiples of 17 or multiples of 18 ?
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "350 / 17 = 20 ( plus remainder ) so there are 20 multiples of 17 350 / 18 = 19 ( plus remainder ) so there are 19 multiples of 18 we need to subtract 1 because 17 * 18 is a multiple of both so it was counted twice . the total is 20 + 19 - 1 = 38 the answer is c ."
Answer: c
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 8 % of bananas were rotten . find the percentage of fruits in good condition .
Options: a ) 87.8 % , b ) 87.9 % , c ) 37.8 % , d ) 87.7 % , e ) 22.8 %
Rationale: "otal number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 8 % of 400 = 8 / 100 × 400 = 3200 / 100 = 32 therefore , total number of rotten fruits = 90 + 32 = 122 therefore number of fruits in good condition = 1000 - 122 = 878 therefore percentage of fruits in good condition = ( 878 / 1000 × 100 ) % = ( 87800 / 1000 ) % = 87.8 % answer : a"
Answer: a
Question (gain): reema took a loan of rs 1800 with simple interest for as many years as the rate of interest . if she paid rs . 632 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5.925 % , b ) 5.253 % , c ) 7 % , d ) 6.52 % , e ) 5.200 %
Rationale: "explanation : let rate = r % then time = r years . = > 1800 ∗ r ∗ r / 100 = 632 = > r 2 = 35.11 = > r = 5.925 % option a"
Answer: a
Question (geometry): 12 points lie on a circle . how many cyclic quadrilaterals can be drawn by using these points ?
Options: a ) 334
b ) 377
c ) 495
d ) 766
e ) 261
Rationale: explanation : for any set of 4 points we get a cyclic quadrilateral . number of ways of choosing 4 points out of 12 points is \ inline { \ color { black } 12 c _ 4 { } } = 495 . therefore , we can draw 495 quadrilaterals answer : c ) 495
Answer: c
Question (physics): there are 15 members in a family . it takes 180 days for a women to complete the work , however man completes in 120 days . they take 17 days to complete the work if men work on alternate days and women work every third day . if all of them started together on the 1 st day , then how many men are there in the family
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let the number of men be m and so the number of women = 15 - m out of 17 days , men and women work together on 1,4 , 7,10 , 13,16 th days ( total of 6 days ) from the start . men work on alternate days , that is 1 , 3,5 , 7,9 , 11,13 , 15,17 th days ( total of 9 days ) . let the total work be 360 units ( lcm of 180 and 120 ) . 1 man does 360 / 120 = 3 units per day 1 woman does 360 / 180 = 2 units per day based on above facts , total work by men + women in these 17 days = 360 units m * 9 * 3 + ( 15 - m ) * 6 * 2 = 360 , 27 m + 180 - 12 m = 360 , solving m = 12 . num of men = 12 answer : d"
Answer: d
Question (physics): there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 hours . the speed of the bus is 3 / 4 th of the speed of the train . how many kilometers will the car cover in 4 hours ?
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: "the speed of the bus is 480 / 8 = 60 km / hr the speed of the train is ( 60 * 4 ) / 3 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 4 hours is 75 × 4 = 300 km the answer is c ."
Answer: c
Question (general): farm tax is levied on the 75 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) 16.667 %
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 75 ) = 16.667 % the correct answer is ( e ) ."
Answer: e
Question (general): what is x if 2 x - y = 14 and y = 2 ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: substitute y by 2 in 2 x - y = 14 2 x - 2 = 14 2 x = 16 if we substitute x by 8 , we have 2 ( 8 ) = 16 . hence x = 8 correct answer b
Answer: b
Question (geometry): the radius of the circle is reduced from 5 cm to 4 cm then the % change of area .
Options: a ) 36 %
b ) 37 %
c ) 35 %
d ) 38 %
e ) 39 %
Rationale: for 5 cm - > pi * r ^ 2 - - > 3.14 * 5 ^ 2 - > 78.539 for 4 cm - > pi * r ^ 2 - - > 3.14 * 4 ^ 2 - > 50.265 % change - > ( 1 - 50.265 / 78.539 ) * 100 = 36 ie 36 % answer : a
Answer: a
Question (physics): in what time will a train 200 m long cross an electric pole , it its speed be 216 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 8.5 sec , d ) 3.3 sec , e ) 4.5 sec
Rationale: "speed = 216 * 5 / 18 = 60 m / sec time taken = 200 / 60 = 3.3 sec . answer : d"
Answer: d
Question (general): if t = 1 / ( 1 * 2 ) + 1 / ( 2 * 3 ) + 1 / ( 3 * 4 ) + 1 / ( 4 * 5 ) + . . . . . . . . . 1 / [ n ( n + 1 ) ] , for some positive integer n , what is the smallest value of n such that t > 097 ?
Options: a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33
Rationale: we can break the t as : ( n + 1 - n ) / n ( n + 1 ) - - - - for n = 1 to n 1 / n - 1 / n + 1 plug value , 1,2 . . n we will get a pattern 1 - 1 / 2 - - - for 1 1 / 2 - 1 / 3 - - for 2 1 / 3 - 1 / 4 - - for 4 now work with options . . for 31 , t = 1 - 1 / 32 = 30 / 31 = 0.968 for 32 , t = 1 - 1 / 33 = 0,9696 for 33 , t = 1 - 1 / 34 = 33 / 34 - 0.97 so e is correct answer
Answer: e
Question (physics): jack and jill work at a hospital with 6 other workers . for an internal review , 2 of the 8 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 1 / 28 , e ) 2 / 3
Rationale: "1 / 8 c 2 = 1 / 28 . answer : d ."
Answer: d
Question (general): a pupil ' s marks were wrongly entered as 83 instead of 70 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 26 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 70 ) = > x / 2 = 13 = > x = 26 . answer : c"
Answer: c
Question (general): calculate the average of all the numbers between 18 and 57 which are divisible by 7 .
Options: a ) 36.9 , b ) 38.5 , c ) 18.5 , d ) 32.5 , e ) 28.5
Rationale: "explanation : numbers divisible by 7 are 21,28 , 35,42 , 49,56 , average = ( 21 + 28 + 35 + 42 + 49 + 56 , ) / 6 = 231 / 6 = 38.5 answer : b"
Answer: b
Question (other): what is the square root of 6,561 ?
Options: a ) 18 , b ) 9 , c ) 45 , d ) 62 , e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 81 * 81 = 6,561 6561 divided by x = 81 x = 81 ( e ) 81"
Answer: e
Question (general): how many positive integers less than 100 are neither multiples of 2 or 5 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 40 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 2 till 100 = 100 / 2 = 50 2 ) multiples of 5 till 100 = 100 / 5 = 20 add the two 50 + 20 = 70 ; subtract common terms that are multiple of both 2 and 5 . . lcm of 2 and 5 = 10 multiples of 10 till 100 = 100 / 10 = 10 so total multiples of 2 and 5 = 70 - 10 = 6 ans = 100 - 60 = 40 c"
Answer: c
Question (general): a trained covered x km at 50 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22 , b ) 99 , c ) 25 , d ) 66 , e ) 887
Rationale: "total time taken = x / 50 + 2 x / 20 hours = 6 x / 50 = 3 x / 25 hours average speed = 3 x / ( 3 x / 25 ) = 25 kmph answer : c"
Answer: c
Question (general): two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 3 , what is the value of y / x ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 2 . , d ) 1 / 4 , e ) there is n ' t enough data to answer the question .
Rationale: "answer is d : 1 / 4 x - y = ( x + y ) / 3 solving for y / x = 1 / 4"
Answer: d
Question (general): a drink vendor has 60 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 137 , c ) 143 , d ) 310 , e ) 380
Rationale: "the number of liters in each can = hcf of 60 , 144 and 368 = 4 liters . number of cans of maaza = 60 / 4 = 15 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 15 + 36 + 92 = 143 cans . answer : c"
Answer: c
Question (general): when 1 / 10 % of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 396 , d ) 398 , e ) 400
Rationale: "1 / 10 % of 4000 = 4 1 / 10 of 4000 = 400 400 - 4 = 396 ans : c"
Answer: c
Question (gain): if 15 % of 30 % of 50 % of a number is 99 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 99 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 99 = > a = 10 * 20 * 10 * 2 = 4400 . answer : c
Answer: c
Question (physics): working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 600 , b ) 480 , c ) 1000 , d ) 1200 , e ) 1500
Rationale: answer : b .
Answer: b
Question (physics): if a farmer wants to plough a farm field on time , he must plough 100 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 720 , d ) 1400 , e ) 1679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 100 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 100 x = 85 ( x + 2 ) + 40 15 x = 210 x = 14 so the farmer planned to have the work done in 6 days , and the area of the farm field is 100 ( 14 ) = 1400 hectares correct answer d"
Answer: d
Question (other): in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those 3 teams , how many ny mets fans are there in this town ?
Options: a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135
Rationale: the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b .
Answer: b
Question (general): a retailer sells 5 shirts . he sells first 2 shirts for $ 30 and $ 20 . if the retailer wishes to sell the 5 shirts for an overall average price of over $ 30 , what must be the minimum average price of the remaining 3 shirts ?
Options: a ) $ 28.50 , b ) $ 30.50 , c ) $ 33.33 , d ) $ 40.50 , e ) $ 50.00
Rationale: first 2 shirts are sold for $ 30 and $ 20 = $ 50 . to get average price of $ 30 , total sale should be 5 * $ 30 = $ 150 so remaining 3 shirts to be sold for $ 150 - $ 50 = $ 100 answer should be 100 / 3 = $ 33.33 that is c
Answer: c
Question (other): ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age .
Options: a ) 12 , b ) 15 , c ) 20 , d ) 22 , e ) 24
Rationale: explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 16 so deepak age is = 3 ( 4 ) = 12 option a
Answer: a
Question (gain): difference of two numbers is 1760 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2640 , 1000 , b ) 3660 , 4400 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1760 5 * y / 3 – y = 1760 2 * y / 3 = 1760 y = [ ( 1760 * 3 ) / 2 ] = 2640 . one number = 2640 , second number = 5 * y / 3 = 4400 . answer b ."
Answer: b
Question (physics): if a clock strikes 12 in 33 seconds , it will strike 6 in how many seconds ?
Options: a ) 33 ⁄ 2 , b ) 15 , c ) 12 , d ) 22 , e ) none of these
Rationale: in order to strike 12 , there are 11 intervals of equal time = 33 ⁄ 11 = 3 seconds each therefore , to strike 6 it has 5 equal intervals , it requires 5 × 3 = 15 sec . answer b
Answer: b
Question (physics): car a runs at the speed of 50 km / hr & reaches its destination in 8 hr . car b runs at the speed of 25 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 4 : 1 , b ) 11 : 8 , c ) 13 : 7 , d ) 15 : 7 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 50 × 8 = 400 km distance travelled by car b = 25 × 4 = 100 km ratio = 400 / 100 = 4 : 1 answer : a"
Answer: a
Question (gain): from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 25 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 36 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.25 x = 45 - - > 5 / 4 * x = 45 - - > x = 45 * 4 / 5 = 180 / 5 = 36 . answer : a ."
Answer: a
Question (physics): if 3 people a , b , c can do a work simultaneously in 6 days . a and b can do work in 10 days . b and c can do work in 15 days . c and a can do the same work in 20 days . in how many days that a can complete the same work alone ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 24 , e ) 19
Rationale: a + b + c = 1 / 6 ( one day work ) a + b = 1 / 10 ; b + c = 1 / 15 ; c + a + 1 / 20 b = 1 / 15 - c ; c = 1 / 20 - a ; - - - - - - - - - ( 2 ) substitute equation 2 in a + b = 1 / 10 a = 1 / 10 - b ; a = 1 / 10 - 1 / 15 + c ; a = 1 / 10 - 1 / 15 + 1 / 20 - a ; 2 a = 1 / 10 - 1 / 15 + 1 / 20 ; a = 1 / 24 ( one day work ) that is the no of days that a can work alone is 24 days the option d is answer
Answer: d
Question (general): a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 170 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 30 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 170 = > . 1 x + 3 / 4 x = 170 = > x = 200 200 - 170 = pure gala = 30 . answer a"
Answer: a
Question (general): a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 44 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 46 ) + 2 = 2 ( x + 2 ) x + 48 = 2 x + 4 x = 44 . answer : a"
Answer: a
Question (physics): pipe a that can fill a tank in an hour and pipe b that can fill the tank in half an hour are opened simultaneously when the tank is empty . pipe b is shut 10 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 37 mins , b ) 35 mins , c ) 40 mins , d ) 32 mins , e ) 36 mins
Rationale: the last 10 minutes only pipe a was open . since it needs 1 hour to fill the tank , then in 10 minutes it fills 1 / 5 th of the tank , thus 5 / 6 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 5 / 6 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 5 / 6 ) / 3 = 5 / 18 hours = 27 minutes . total time = 10 + 27 = 37 minutes . answer : a .
Answer: a
Question (general): what is the maximum value of vx - yz . if the value of v , x , y , z have to be chosen from the set a where a ( - 3 , - 2 , - 1 , 01 , 23 )
Options: a ) 15 , b ) 66 , c ) 25 , d ) 88 , e ) 17
Rationale: explanation : to maximize the value of vx - yz , we make yz negative and vx as maximum as possible using given value . vx − yz = ( − 3 ) 2 − ( − 3 × 2 ) vx − yz = ( − 3 ) 2 − ( − 3 × 2 ) = 15 answer : a
Answer: a
Question (general): x and y are two towns . ganesh covers the distance from x to y at an average speed of 54 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 34 , b ) 43.2 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 54 * 36 / 54 + 36 = 43.2 answer : b"
Answer: b
Question (gain): p runs 20 % faster than q so p gives q a 50 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: let d be the race distance that p ran . let t be the time it took to complete the race . let v be q ' s speed . t = d / 1.2 v = ( d - 50 ) / v d = 1.2 d - 60 0.2 d = 60 d = 300 meters . the answer is b .
Answer: b
Question (physics): suppose 10 monkeys take 10 minutes to eat 10 bananas . how many monkeys would it take to eat 70 bananas in 70 minutes ?
Options: a ) 9 , b ) 17 , c ) 11 , d ) 10 , e ) 13
Rationale: "one monkey takes 10 min to eat 1 banana , so in 70 mins 1 monkey will eat 7 bananas , so for 70 bananas in 70 min we need 70 / 7 = 10 monkeys answer : d"
Answer: d
Question (physics): a man walks at a rate of 10 mph . after every ten miles , he rests for 5 minutes . how much time does he take to walk 50 miles ?
Options: a ) 300 , b ) 318 , c ) 320 , d ) 324 , e ) 330
Rationale: to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 5 = 20 minutes . total time = 300 + 20 = 320 minutes . answer : c .
Answer: c
Question (physics): on a map , 4.5 inches represent 45 miles . how many miles approximately is the distance if you measured 254 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 1250 , e ) 1300
Rationale: "1 inch = 2.54 cm 4.5 inch = 2.54 * 4.5 cm 11.43 cm = 45 miles 254 cms = 45 / 11.43 * 254 = 1000 miles answer : a"
Answer: a
Question (general): what is the total number of positive integers that are less than 400 and that have no positive factor in common with 400 other than 1 ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 160 , e ) 180
Rationale: "since 400 = 2 ^ 4 * 5 ^ 2 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 200 odd numbers from 1 to 400 . we then need to eliminate the 40 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 395 . there are a total of 200 - 40 = 160 such numbers between 1 and 400 . the answer is d ."
Answer: d
Question (physics): john bought 9.25 m of cloth for $ 416.25 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 45 , d ) 56 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 416.25 cost per metre = 416.25 ÷ 9.25 the cost of the cloth per metre = $ 45 answers : c"
Answer: c
Question (general): if p is a prime number greater than 3 , find the remainder when p ^ 2 + 12 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 13 = 36 n ^ 2 + 12 n + 1 + 12 = 36 n ^ 2 + 12 n + 12 + 1 if p = 6 n - 1 , then p ^ 2 + 13 = 36 n ^ 2 - 12 n + 1 + 12 = 36 n ^ 2 - 12 n + 12 + 1 when divided by 12 , it must leave a remainder of 1 . the answer is b ."
Answer: b
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 432 , b ) 444 , c ) 2881 , d ) 287 , e ) 221
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 15 + 21 = 36 t = 12 d = 36 * 12 = 432 answer : a"
Answer: a
Question (gain): what is the rate percent when the simple interest on rs . 910 amount to rs . 260 in 4 years ?
Options: a ) 7.14 , b ) 6.14 , c ) 5.14 , d ) 3.14 , e ) 2.14
Rationale: "260 = ( 910 * 4 * r ) / 100 r = 7.14 % answer : a"
Answer: a
Question (general): in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 4 the number that used kennedy airport and 3 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.03
Rationale: "number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 4 = ~ 3.1 passengers using logan airport = 3.1 / 3 = ~ 1.03 so e"
Answer: e
Question (other): if $ 792 are divided between worker a and worker b in the ratio 5 : 6 , what is the share that worker b will get ?
Options: a ) 54.54 % , b ) 55.55 % , c ) 56.56 % , d ) 57.57 % , e ) 58.58 %
Rationale: "worker b will get 6 / 11 = 54.54 % the answer is a ."
Answer: a