Cheukting/mathqa huggingface dataset:
Question (general): a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 28 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 2 ) = ( x + 30 + 2 ) = > 2 x + 4 = x + 32 = > x = 28 years option a"
Answer: a
Question (general): lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 94,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.20304
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 394000 x \ therefore required percentage = \ inline \ frac { 800 x } { 394000 } \ times 100 = 0.20304 e"
Answer: e
Question (physics): the length of the bridge , which a train 110 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 265 , b ) 244 , c ) 245 , d ) 238 , e ) 236
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 = = > 2 ( 110 + x ) = 750 = = > x = 265 m . answer : option a"
Answer: a
Question (physics): cole drove from home to work at an average speed of 60 kmh . he then returned home at an average speed of 100 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 60 time from work to home = x / 100 total time = 2 hrs ( x / 60 ) + ( x / 100 ) = 2 solving for x , we get x = 75 time from home to work in minutes = ( 75 ) * 60 / 60 = 75 minutes ans = d"
Answer: d
Question (geometry): if the radius of a circle is decreased 50 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 75 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.5 * old radius so new area = ( 0.5 ) ^ 2 old area = > 0.25 of old area = > 25 % old area ans : c"
Answer: c
Question (physics): sakshi can do a piece of work in 30 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 16 , c ) 14 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 30 : x ⇒ x = ( 30 x 4 / 5 ) ⇒ x = 24 days . hence , tanya takes 16 days is complete the work . answer c"
Answer: c
Question (general): what is the greatest prime factor of 3 ^ 8 - 1 ?
Options: a ) 29 , b ) 31 , c ) 37 , d ) 41 , e ) 43
Rationale: "3 ^ 8 - 1 = ( 3 ^ 4 - 1 ) ( 3 ^ 4 + 1 ) = 80 * 82 = 8 * 10 * 2 * 41 the answer is d ."
Answer: d
Question (general): calculate the ratio between x and y if 90 % of x equal to 60 % of y ?
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 3 : 2 , d ) 3 : 4 , e ) 5 : 2
Rationale: "explanation : 90 x = 60 y x : y = 90 : 60 = 3 : 2 answer : c"
Answer: c
Question (geometry): find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm ?
Options: a ) 100 cm 2 , b ) 150 cm 2 , c ) 200 cm 2 , d ) 250 cm 2 , e ) 500 cm 2
Rationale: "1 / 2 * 50 ( 15 + 5 ) = 500 cm 2 answer : e"
Answer: e
Question (physics): a train 1200 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 277 , c ) 500 , d ) 100 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1200 + x ) / 60 = 65 / 3 x = 100 m . answer : d"
Answer: d
Question (general): the average of first five prime numbers greater than 5 is ?
Options: a ) 13.4 , b ) 12.26 , c ) 12.3 , d ) 32.8 , e ) 32.4
Rationale: "7 + 11 + 13 + 17 + 19 = 67 / 5 = 13.40 answer : a"
Answer: a
Question (geometry): a right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube . if the volume of the cube is 343 cc , what approximately is the volume of the cone ?
Options: a ) 80 cc
b ) 90 cc
c ) 110 cc
d ) 105 cc
e ) 100 cc
Rationale: edge of the cube = 3 √ 334 = 7 cm ∴ radius of cone = 3.5 cm height = 7 cm volume of cone = 1 ⁄ 3 π r 2 h 1 ⁄ 3 π r 2 h = 1 ⁄ 3 × 22 ⁄ 7 × ( 3.5 ) 2 × 7 = 1 ⁄ 3 × 22 × 12.25 ≈ 90 sec answer b
Answer: b
Question (gain): if the given two numbers are respectively 7 % and 28 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these
Rationale: "here , l = 7 and m = 28 therefore , first number = l / m x 100 % of second number = 7 / 28 x 100 % of second number = 25 % of second number answer : b"
Answer: b
Question (general): a pupil ' s marks were wrongly entered as 83 instead of 53 . 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 ) 60 , 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 - 53 ) = > x / 2 = 30 = > x = 60 . answer : c"
Answer: c
Question (geometry): the area of a rhombus is equal to the area of a rectangle whose length is 20 cm and the breadth is 10 cm . if one of the diagonals is 32 cm what is the length of other diagonal ?
Options: a ) 10
b ) 12.5
c ) 15
d ) 16
e ) 17.5
Rationale: area of rectangle = 20 x 10 = 200 cm â ² let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b
Answer: b
Question (gain): if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2160 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2700 , d ) 3200 , e ) 11500
Rationale: p - 2160 = ( p * 5 * 4 ) / 100 p = 2700 answer : c
Answer: c
Question (general): a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 948 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 51
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 948 - 640 = 308 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 308 / 28 = 77 / 7 = 11 total hrs = 40 + 11 = 51 answer e 51"
Answer: e
Question (general): a line has a slope of 3 / 4 and intersects the point w ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point w of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Question (general): a salesman commission is 5 % on all sales upto $ 10000 and 4 % on all sales exceeding this . he remits $ 31100 to his parent company after deducting his commission . find the total sales ?
Options: a ) $ 30000 , b ) $ 32500 , c ) $ 35120 , d ) $ 41520 , e ) $ 25460
Rationale: let his total sales be x total sales - commission = $ 31100 x - [ ( 5 % of 10000 ) + 4 % of ( x - 10000 ) ] = 31100 x - 500 - ( x - 10000 ) / 25 = 31100 x = 32500 answer is b
Answer: b
Question (gain): how much 60 % of 50 is greater than 34 % of 30 ?
Options: a ) 18 , b ) 19.8 , c ) 11 , d ) 17 , e ) 12
Rationale: ( 60 / 100 ) * 50 – ( 34 / 100 ) * 30 30 - 10.2 = 19.8 answer : b
Answer: b
Question (physics): a man can row 5 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 5.7 , c ) 5.76 , d ) 4.2 , e ) 5.71
Rationale: "m = 5 s = 2 ds = 7 us = 3 x / 7 + x / 3 = 1 x = 2.1 d = 2.1 * 2 = 4.2 answer : d"
Answer: d
Question (physics): how long does a truck of 200 m long traveling at 60 kmph takes to cross a bridge of 180 m in length ?
Options: a ) 36.7 , b ) 26.8 , c ) 22.8 , d ) 21.1 , e ) 16.2
Rationale: d = 200 + 180 = 380 m s = 60 * 5 / 18 = 50 / 3 t = 380 * 3 / 50 = 22.8 sec answer : c
Answer: c
Question (geometry): difference between the length & breadth of a rectangle is 10 m . if its perimeter is 206 m , then its area is ?
Options: a ) 2400 m ^ 2
b ) 1500 m ^ 2
c ) 2520 m ^ 2
d ) 1200 m ^ 2
e ) 2580 m ^ 2
Rationale: solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d
Answer: d
Question (general): 1370 , 1320 , x , - 180 , - 6430
Options: a ) 1070 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ."
Answer: a
Question (general): machine x takes 50 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 3.6 , c ) 25 , d ) 11 , e ) 9
Rationale: "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 50 so , x = 50 . hence 6 x = 6 * 50 = 300 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 300 = 3.6 hence option ( b ) ."
Answer: b
Question (general): for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) can not be determined
Rationale: "factorization of 45 = 3 * 3 * 5 factorization of 80 = 5 * 2 ^ 4 means the smallest value of k is \ sqrt { 3 ^ 2 * 5 * 2 ^ 4 } = 3 * 5 * 2 ^ 2 k ^ 3 = 3 ^ 3 * 5 ^ 3 * 2 ^ 6 * x = 3 ^ 3 * 2 * 4000 * x where x can be any integer k ^ 3 / 4000 = 3 ^ 3 * 2 * x = 54 x which obviously has different units digit depending on x answer : d"
Answer: d
Question (general): paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 40 % of his income to sam and 60 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?
Options: a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 27 / 19
Rationale: make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 7.6 and q 10.8 so 10.8 / 7.6 = 2.7 / 1.9 ans : e
Answer: e
Question (general): if p / q = 3 / 7 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16
Rationale: "let p = 3 , q = 7 then 2 * 3 + 7 = 13 so 2 p + q = 13 . answer : c"
Answer: c
Question (general): in a box of 9 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 6 / 11 , d ) 7 / 12 , e ) 8 / 15
Rationale: "# defective pens = 2 # good pens = 7 probability of the 1 st pen being good = 7 / 9 probability of the 2 nd pen being good = 6 / 8 total probability = 7 / 9 * 6 / 8 = 7 / 12 the answer is d ."
Answer: d
Question (general): sum of two numbers is 63 . their difference is 1 / 8 of their sum . their l . c . m is
Options: a ) 231 , b ) 153 , c ) 351 , d ) 345 , e ) 355
Rationale: "explanation : let the numbers be x and y according to the problem x + y = 63 x - y = 1 / 8 ( x + y ) x - y = 1 / 8 * 63 , x - y = 9 2 x = 72 , x = 36 and y = 27 l . c . m of 36 and 27 is 351 answer : option c"
Answer: c
Question (physics): if 36 men can do a piece of work in 25 hours , in how mwny hours will 15 men do it ?
Options: a ) 22 , b ) 38 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirct proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 15 } = 60 hence , 15 men can do it in 60 hours . answer : c ) 60"
Answer: c
Question (general): the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . the average percent increase of population per year is :
Options: a ) 1 % , b ) 2 % , c ) 3 % , d ) 5 % , e ) 4 %
Rationale: "d 5 % increase in 10 years = ( 262500 - 175000 ) = 87500 . increase % = ( 87500 / 175000 x 100 ) % = 50 % . required average = ( 50 / 10 ) % = 5 % ."
Answer: d
Question (general): last year the price range ( per kg ) for 100 varieties of apples in wholesale market was $ 100 . if the prices of each of the 100 varieties increased by 10 percent this year over what it was last year , what is the range of the wholesale prices of the 1000 varieties of apples this year ?
Options: a ) $ 50 , b ) $ 100 , c ) $ 110 , d ) $ 600 , e ) $ 300
Rationale: let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c
Answer: c
Question (gain): the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) rs . 2000 , b ) rs . 2200 , c ) rs . 2400 , d ) data inadequate , e ) can not be determined
Rationale: "explanation : let the c . p . of the article be rs . x given that % profit earned by selling article at rs . 1920 = % loss incurred by selling article at rs . 1280 ( 1920 − x / x ) ∗ 100 = ( x − 1280 / x ) ∗ 100 = > 1920 - x = x - 1280 = > 2 x = 3200 = > x = 1600 s . p . for 25 % profit = rs . 1600 + 25 % of rs . 1600 = rs . 1600 * ( 125 / 100 ) = rs . 2000 answer : a"
Answer: a
Question (physics): the tailor has a 10 meter long piece of fabric for which to sew a ball room dress . she has to cuts this fabric into strips of 200 centimeters each . how long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ?
Options: a ) 150 , b ) 200 , c ) 188 , d ) 245 , e ) 123
Rationale: the tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes . the answer is d
Answer: d
Question (general): find 60 / 42 * 4
Options: a ) 14.7653 , b ) 0.5897 , c ) 3.6974 , d ) 0.3571 , e ) 1.2587
Rationale: "answer = 60 / 42 * 4 = 60 / 168 = 0.3571 option d is correct"
Answer: d
Question (general): find the average of all prime numbers between 30 and 50 ?
Options: a ) 18.9 , b ) 19.8 , c ) 39.8 , d ) 29.8 , e ) 20.8
Rationale: "there are five prime numbers between 30 and 50 . they are 31,37 , 41,43 and 47 . therefore the required average = ( 31 + 37 + 41 + 43 + 47 ) / 5  199 / 5  39.8 answer c 39.8"
Answer: c
Question (general): in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 4720 votes were polled , then how many valid votes did b get ?
Options: a ) 1534 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 4720 32.5 k = 32.5 k / 100 k * 4720 = 1534 the number of valid votes polled in favour of b is 1534 . answer : a"
Answer: a
Question (other): if $ 1088 are divided between worker a and worker b in the ratio 5 : 11 , what is the share that worker b will get ?
Options: a ) 62.45 % , b ) 64.55 % , c ) 66.65 % , d ) 68.75 % , e ) 70.85 %
Rationale: "worker b will get 11 / 16 = 68.75 % the answer is d ."
Answer: d
Question (general): the average age of 6 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "20 + 24 + 6 * 2 = 56 / 2 = 28 answer : e"
Answer: e
Question (general): operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 4 , when a # b = 100 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 13 , e ) 17
Rationale: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 4 = 10 / 2 + 4 = 9 . the correct answer is b .
Answer: b
Question (physics): the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 500 per sq . metre .
Options: a ) $ 10312.50 , b ) $ 13512.50 , c ) $ 16512.50 , d ) $ 14512.50 , e ) $ 18512.50
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 500 hence , total cost = 5.5 × 3.75 × 500 = $ 10312.50 a"
Answer: a
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 21 , e ) 78
Rationale: "we have : l = 20 ft and lb = 10 sq . ft . so , b = 0.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 1 ) ft = 21 ft . answer : d"
Answer: d
Question (general): each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum k in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is
Options: a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %
Rationale: the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the “ 1 – x ” technique : what ’ s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn ’ t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don ’ t ) and in which z retains value ( while x and y don ’ t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it ’ s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated — and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent .
Answer: a
Question (general): how many positive integers less than 250 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64
Rationale: "multiples of 4 less than 250 = { 4 , 8,12 , . . . . . . 248 } = 62 numbers multiples of 4 which are multiples of 3 too = { 12 , 24,36 . . . . . 240 } = 20 numbers so required number = 62 - 20 = 42 choice c"
Answer: c
Question (general): a ferry can transport 50 tons of vehicles . automobiles range in weight from 1,600 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86
Rationale: to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d
Answer: d
Question (geometry): what is the ratio between perimeters of two squares one having 8 times the diagonal then the other ?
Options: a ) 3 : 6 , b ) 3 : 3 , c ) 3 : 8 , d ) 8 : 1 , e ) 3 : 2
Rationale: "d = 8 d d = d a √ 2 = 8 d a √ 2 = d a = 8 d / √ 2 a = d / √ 2 = > 8 : 1 answer : d"
Answer: d
Question (general): a bank pays interest to its customers on the last day of the year . the interest paid to a customer is calculated as 10 % of the average monthly balance maintained by the customer . john is a customer at the bank . on the last day , when the interest was accumulated into his account , his bank balance doubled to $ 5080 . what is the average monthly balance maintained by john in his account during the year ?
Options: a ) 2840 , b ) 5680 , c ) 6840 , d ) 25400 , e ) 28400
Rationale: bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d
Answer: d
Question (physics): a bus 75 m long is running with a speed of 21 km / hr . in what time will it pass a woman who is walking at 3 km / hr in the direction opposite to that in which the bus is going ?
Options: a ) 5.75 , b ) 7.62 , c ) 11.25 , d ) 4.25 , e ) 3.25
Rationale: "speed of bus relative to woman = 21 + 3 = 24 km / hr . = 24 * 5 / 18 = 20 / 3 m / sec . time taken to pass the woman = 75 * 3 / 20 = 11.25 sec . answer : c"
Answer: c