Cheukting/mathqa huggingface dataset:
Question (other): a bag contains 6 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 5 / 14 , b ) 8 / 21 , c ) 12 / 21 , d ) 43 / 91 , e ) 47 / 91
Rationale: the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 43 / 91 the answer is d .
Answer: d
Question (physics): a walks at 30 kmph and 30 hours after his start , b cycles after him at 45 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2700 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 45 = 30 x = 2700 km answer is d"
Answer: d
Question (geometry): a snooker tournament charges $ 40.00 for vip seats and $ 10.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 190
b ) 180
c ) 170
d ) 160
e ) 148
Rationale: let no of sits in vip enclosure is x then x * 40 + 10 ( 320 - x ) = 7500 or 25 x = 7500 - 3200 , x = 4300 / 25 = 172 vip = 172 general = 320 - 172 = 148 e
Answer: e
Question (general): if a and b are positive integers , and a = 2 b + 6 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 12
Rationale: "since a = 2 b + 6 , so we can say b = ( a / 2 - 3 ) . so we need to find not possible gcd values for a , ( a / 2 - 3 ) . a . 1 , we can easily get this value by making a = 8 . b . 2 . we can again get this value as gcd by keeping a = 10 c . 3 we will get this as gcd by keeping a = 12 d . 6 we can get gcd 6 by keeping ( a / 2 - 3 ) = 6 and a as 18 . e . 12 this is not possible as for 12 ( 2 ^ 2 * 3 ) to be gcd = 2 ^ 2 * 3 both a and a / 2 - 3 should be divisible by 4 and 3 . so a has to be a multiple of 4 . this means a / 2 has to be even and even - odd will be odd and odd number wont be divisible by 4 . this 12 cant be the gcd . answer e ."
Answer: e
Question (general): naomi drives to the beauty parlor in 60 minutes . on the way back , her average speed is half the average speed as it was to the way to the parlor . how much time will it take naomi to travel two round trips to the beauty parlor ?
Options: a ) 3 hours . , b ) 4 hours . , c ) 4 hours and 20 minutes . , d ) 5 hours and 50 minutes , e ) 6 hours .
Rationale: s 1 = 2 s 2 since , speed is inversely proportional to time we have , s 1 / s 2 = 2 / 1 = t 2 / t 1 therefore , the time taken for one trip = 60 + 120 = 180 minutes total = 180 * 2 = 360 minutes = 6 hours answer : e
Answer: e
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 39 ° is ?
Options: a ) 40 m 2 , b ) 45 m 2 , c ) 49 m 2 , d ) 51 m 2 , e ) 55 m 2
Rationale: "39 / 360 * 22 / 7 * 12 * 12 = 49 m 2 answer : c"
Answer: c
Question (gain): jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 2000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c )
Answer: c
Question (physics): the radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 100 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 175 cm . then , circumference of wheel = 2 ï € r = 350 ï € = 1100 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 1100 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 1100 = 100 answer a"
Answer: a
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 60 % profit on the first article and 60 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 600
Rationale: "profit on first article = 60 % of 1000 = 600 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e"
Answer: e
Question (physics): how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 15 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 500 / ( 25 / 6 ) = 120 seconds the answer is b ."
Answer: b
Question (other): the compound ratio of 5 : 7 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 7 , b ) 6 : 5 , c ) 6 : 7 , d ) 4 : 7 , e ) 6 : 9
Rationale: "5 / 7 * 3 / 2 * 4 / 5 = 6 / 7 6 : 7 answer : c"
Answer: c
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 = > 450 hence answer will be ( d ) 450"
Answer: d
Question (other): the ratio of the incomes of rajan and balan is 7 : 6 and the ratio of their expenditure is 6 : 5 . if at the end of the year , each saves $ 1000 then the income of rajan is ?
Options: a ) $ 7600 , b ) $ 7000 , c ) $ 8000 , d ) $ 9000 , e ) $ 5000
Rationale: let the income of rajan and balan be $ 7 x and $ 6 x let their expenditures be $ 6 y and $ 5 y 7 x - 6 y = 1000 - - - - - - - 1 ) 6 x - 5 y = 1000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 rajan ' s income = 7 x = 7 * 1000 = $ 7000 answer is b
Answer: b
Question (physics): two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 12 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 36 , e ) 96
Rationale: d 36 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 12 mph = 36 miles
Answer: d
Question (physics): a 300 meter long train crosses a platform in 51 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 550 , b ) 289 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 51 = 50 / 3 3 ( x + 300 ) = 2550 è x = 550 m . answer : a"
Answer: a
Question (geometry): find the perimeter and area of the rectangle of length 15 cm and breadth 11 cm .
Options: a ) 71 cm 2 , b ) 121 cm 2 , c ) 165 cm 2 , d ) 171 cm 2 , e ) 221 cm 2
Rationale: "length = 15 cm , breadth = 11 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 15 + 11 ) cm = 2 × 26 cm = 52 cm we know that the area of rectangle = length × breadth = ( 15 × 11 ) cm 22 = 165 cm 2 answer : c"
Answer: c
Question (general): a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 43 , b ) 26 , c ) 33 , d ) 21 , e ) 28
Rationale: "b 26 let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 26 ."
Answer: b
Question (general): when 1 / 10 percent of 2,000 is subtracted from 1 / 10 of 2,000 , the difference is
Options: a ) 1980 , b ) 1998 , c ) 198 , d ) 200 , e ) 20
Rationale: "( 1 / 10 ) * 2000 - ( 1 / 10 ) % * 2000 = 200 - ( 1 / 1000 ) * 2000 = 200 - 2 = 198 the answer is c ."
Answer: c
Question (gain): find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2875 , b ) 2654 , c ) 2645 , d ) 2456 , e ) 2522
Rationale: principal = rs . 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = rs . [ 16000 x ( 1 + ( 5 / 100 ) ) 3 ] = rs . 18522 . ci . = rs . ( 18522 - 16000 ) = rs . 2522 answer : e
Answer: e
Question (general): a number is doubled and 9 is added . if the resultant is trebled , it becomes 51 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 51 2 x = 8 = > x = 4 answer : e"
Answer: e
Question (other): a certain quantity of 40 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "original quantity = a substituted quantity = b then : ( a * 0.4 + 0.25 * b т а у 0.4 * b ) / a = 0.35 0.4 + ( b / a ) * ( - 0.15 ) = 0.35 b / a = - 0.05 / - 0.15 = 1 / 3 answer : b"
Answer: b
Question (physics): on the first day of her vacation , louisa traveled 250 miles . on the second day , traveling at the same average speed , she traveled 350 miles . if the 250 - mile trip took 3 hours less than the 350 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 31 , b ) 33.33 , c ) 35 , d ) 37 , e ) 39.33
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 250 / t = 350 / ( t + 3 ) - - > 5 / t = 7 / ( t + 3 ) - - > 5 t + 15 = 7 t - - - - > 2 t = 15 . t = 7.5 - - - - > ( rate ) = 250 / 7.5 = 33.33 answer : b"
Answer: b
Question (gain): a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e ."
Answer: e
Question (physics): if an object travels at six feet per second , how many feet does it travel in one hour ?
Options: a ) 21600 , b ) 3778 , c ) 12788 , d ) 18000 , e ) 2881
Rationale: "explanation : if an object travels at 6 feet per second it covers 6 x 60 feet in one minute , and 6 x 60 x 60 feet in one hour . answer = 21600 answer : a ) 21600"
Answer: a
Question (geometry): 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq . m . find the length of each stone slab ?
Options: a ) 150 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 67.5 / 30 m 2 = 2.25 m 2 length of each slab √ 2.25 = 1.5 m = 150 cm"
Answer: a
Question (physics): machine r takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine r to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of r is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and r reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of r . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Question (gain): i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) rs . 28 , b ) rs . 280 , c ) rs . 140 , d ) rs . 70 , e ) rs . 80
Rationale: x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 answer : b
Answer: b
Question (geometry): a gardener changed the size of his rectangle shaped garden by increasing it ' s length by 40 % & decreasing is ' s width by 20 % . find area of new garden .
Options: a ) 1.04
b ) 1.12
c ) 1.24
d ) 1.4
e ) 1.5
Rationale: a 1 = l * b a 2 = ( l * 140 / 100 ) * ( b * 80 / 100 ) = 1.12 * lb so , area of garden is by 1.12 times of old area . answer : b
Answer: b
Question (gain): the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and dennison have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and dennison submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Question (general): what is the sum of the integers from - 190 to 191 inclusive ?
Options: a ) 0 , b ) 191 , c ) 375 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 191 / 2 = 0.5 number of items ( n ) = b - a + 1 = 191 - ( - 190 ) + 1 = 195 + 191 = 382 . sum = average * n = 0.5 * 382 = 191 . answer is b"
Answer: b
Question (general): 9000 + 16 2 / 3 % of ? = 10500
Options: a ) 2387 , b ) 2888 , c ) 9000 , d ) 2837 , e ) 2271
Rationale: "explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c"
Answer: c
Question (gain): the ratio of the cost price and selling price is 2 : 3 . the profit percent is ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 100 %
Rationale: let the c . p . = $ 2 x then s . p . = $ 3 x then , gain = 3 x - 2 x = $ x gain % = x / 2 x * 100 = 50 % answer is c
Answer: c
Question (general): 10 is 6 % of a , and 6 is 10 % of b . c equals b / a . what is the value of c ?
Options: a ) 3 / 10 , b ) 6 / 17 , c ) 9 / 25 , d ) 10 / 33 , e ) 12 / 35
Rationale: "6 a / 100 = 10 a = 500 / 3 b / 10 = 6 b = 60 c = b / a = 60 * 3 / 500 = 9 / 25 the answer is c ."
Answer: c
Question (geometry): the slant height of a cone is 12 cm and radius of the base is 4 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 28 , c ) 48 , d ) 26 , e ) 28
Rationale: "π * 12 * 4 = 48 answer : c"
Answer: c
Question (physics): points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 5 cm , and bd = 6 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 5 ( ac = 5 ) d - 8 ( bd = 6 ) cd is 8 - 5 = 3 . ans c
Answer: c
Question (other): in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 8 and the other one , that is cheaper , costs $ 3 . the factory holds a $ 100 worth stock of 25 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "so the number of $ 3 modules must be 20 so that the leftover 5 modules are of $ 8 which will give a total value $ 100 . 20 * 3 + 5 * 8 = 60 + 40 = 100 . answer : b"
Answer: b
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 1000 , d ) d ) 2393 , e ) e ) 2009
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 500 = > x = 500 . b ' s share = rs . 2 x = 2 * 500 = rs . 1000 . answer : c"
Answer: c
Question (physics): due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 19.1 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 20 = 10 * 3 = 30 time difference = 19.1 ans : d"
Answer: d
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 11 , 0 ) , ( 0 , - 3.5 ) , ( - 11 , 0 ) ?
Options: a ) 56 , b ) 77 , c ) 112 , d ) 116 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 11 + 11 = 22 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 22 * 7 = 77 b is the answer"
Answer: b
Question (gain): a 21 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 210 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 21 , money invested = rs . ( 100 / 10 x 21 ) = rs . 210 . â ˆ ´ market value of rs . 100 stock = rs . 210 answer b"
Answer: b
Question (general): which no . need to add to 859622 to get a no . exactly divisible by 456 ?
Options: a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622
Rationale: dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e
Answer: e
Question (geometry): right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 864 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 4 ( 9 horizontal dots and 4 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 4 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 3 c 1 , ( 4 - 1 = 3 as 1 vertical dot is already occupied by a ) . 9 c 1 * 4 c 1 * 8 c 1 * 3 c 1 = 864 . answer : c ."
Answer: c
Question (general): at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "well , first let ’ s take care of the “ totals ” . the numbers in the “ totals ” row must add up . if 90 are females , the other 250 – 90 = 160 must be males . similarly , the numbers in the “ totals ” column must add up . if 40 are managers , then the other 250 – 40 = 210 must be associates . now , in the “ associate ” row , 135 + e = 210 , which means e = 75 — the other 75 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the “ female ” column : b + 75 = 90 , which means b = 15 . there are fifteen female managers in this company . thus , the answer = ( a ) ."
Answer: a
Question (gain): a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is
Options: a ) 15 % , b ) 12 % , c ) 8 % , d ) 7 % , e ) 5 %
Rationale: "explanation : simple interest for 3 years = ( rs . 12005 - rs . 9800 ) = rs . 2205 simple interest for 5 years = 22053 × 5 = rs . 3675 principal ( p ) = ( rs . 9800 - rs . 3675 ) = rs . 6125 r = 100 × si / pt = 100 × 3675 / 6125 × 5 = 12 % answer : option b"
Answer: b
Question (general): if 3 / p = 5 & 3 / q = 15 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 2 / 15 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 3 / 5 , q = 3 / 15 = > q = 1 / 5 therefore p - q = ( 3 / 5 ) - ( 1 / 5 ) = 2 / 15 answer : c"
Answer: c
Question (gain): a invested some money in 8 % stock at 96 . if b wants to invest in an equally good 10 % stock , he must purchase a stock worth of :
Options: a ) rs . 120 , b ) rs . 60 , c ) rs . 128 , d ) rs . 130 , e ) rs . 140
Rationale: "solution for an income of rs . 8 , investment = rs . 96 . for an income of rs . 10 , investment = rs . ( 96 / 8 x 10 ) = rs . 120 answer a"
Answer: a
Question (general): how many digits 2 ^ 400 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 121
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e"
Answer: e
Question (general): a committee is reviewing a total of 40 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 20 / 11 , b ) 16 / 11 , c ) 17 / 11 , d ) 10 / 11 , e ) 19 / 11
Rationale: "say x = y = 10 . in this case we would have : 40 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 40 color films , thus total of 44 films were selected . color films thus compose 40 / 44 = 10 / 11 of the selected films . answer : d"
Answer: d
Question (general): a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 6 / 25 , b ) 5 / 16 , c ) 4 / 9 , d ) 3 / 7 , e ) 2 / 5
Rationale: let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 8 ( 1 - x ) p 12 xp = 8 p - 8 xp 20 xp = 8 p x = 2 / 5 the answer is e .
Answer: e
Question (general): if x is equal to the sum of the integers from 50 to 70 , inclusive , and y is the number of even integers from 50 to 70 , inclusive , what is the value of x + y ?
Options: a ) 1211 , b ) 1231 , c ) 1251 , d ) 1271 , e ) 1291
Rationale: "x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d ."
Answer: d
Question (general): 12 times a positive integer is more than its square by 36 , then the positive integer is
Options: a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a"
Answer: a