Cheukting/mathqa huggingface dataset:
Question (general): 20 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 90 %
Rationale: to maximize the percentage of companies offering both , let ' s assume that all 20 % of companies which offer wireless internet also offer snacks . the answer is a .
Answer: a
Question (physics): in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 54 km / hr ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: speed = 54 * 5 / 18 = 15 m / s time = 180 / 15 = 12 seconds the answer is b .
Answer: b
Question (physics): if 20 typists can type 40 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 180 , e ) 400
Rationale: "20 typists can type 40 letters , so 30 typists can type = 40 * 30 / 20 40 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 40 * 30 * 60 / 20 * 20 = 180 d is the answer"
Answer: d
Question (physics): there are 4 people who has to cross a stretch of 300 km . they normally run at a speed of 10 kmph . one of them has a bike that travels at 50 kmph . the bike first takes one person alone and crosses the stretch while the other two keep running . then he comes back without wasting time and picks up another person from the way , drives him across the stretch , and does the same for the last person . how long does this whole process take ?
Options: a ) 24 hrs , b ) 16 hrs , c ) 56 / 3 hrs , d ) 58 / 3 hrs , e ) 18 hrs
Rationale: expl : time taken to carry 2 nd person = 300 / 50 = 6 hrs . time taken to meet 3 rd person = ( 300 - 6 * 10 ) / ( 50 + 10 ) = 4 hrs time taken to carry 3 rd person = 4 hours time taken to meet 4 th person = ( 300 – 140 ) / 60 = 8 / 3 total time = 6 + 4 + 4 + 8 / 3 + 8 / 3 = 58 / 3 hours answer : d
Answer: d
Question (physics): a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 15 cm by 13 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18078 , c ) 11076 , d ) 11456 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 1800 ã — 1200 / 15 ã — 13 ) = 11076 option c"
Answer: c
Question (physics): if one length of a square is tripled , and the original parameter is 4 y . what is the new length of one of the sides ?
Options: a ) 12 y / 3
b ) 2 y / 2
c ) 6 y / 3
d ) 12 y / 4
e ) 4 y / 3
Rationale: if the original parameter is 4 y , each length of the square is 4 y / 4 . if the parameter is tripled , then each length becomes 3 ( 4 y ) / 4 . this is 12 y / 4 . answer option d .
Answer: d
Question (other): an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the ?
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 1 , d ) 8 : 2 , e ) 8 : 4
Rationale: "let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer : b"
Answer: b
Question (gain): 80 % of a number is added to 20 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 100 , e ) 281
Rationale: ( 80 / 100 ) * x + 20 = x 4 x + 100 = 5 x x = 100 answer : : d
Answer: d
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg , what is his percent ?
Options: a ) 28 % , b ) 25 % , c ) 55 % , d ) 28 % , e ) 28.2 %
Rationale: "780 - - - 220 100 - - - ? = > 28.2 % answer : e"
Answer: e
Question (physics): angelina walked 840 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 16 , e ) 30
Rationale: "let the speed be x . . . so time taken from home to grocery = 840 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 840 / x - 240 / x = 40 . . 600 / x = 40 . . x = 15 m / secs . . so grocery to gym = 2 * 15 = 30 m / s . . . e"
Answer: e
Question (general): david obtained 74 , 65 , 82 , 67 and 90 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 76
Rationale: "average = ( 74 + 65 + 82 + 67 + 90 ) / 5 = 380 / 5 = 76 . answer : e"
Answer: e
Question (gain): john makes $ 60 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.8 % , d ) 18 % , e ) 19.5 %
Rationale: "increase = ( 10 / 60 ) * 100 = ( 1 / 6 ) * 100 = 16.66 % . b"
Answer: b
Question (other): a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many e acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn e = 4 * 94 = 376 correct option - c"
Answer: c
Question (gain): at an elementary school , 70 % of the faculty members are women and 60 % of the faculty members are married . if 2 ⁄ 3 of the men are single , what fraction of the men are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 20 - - - - - 20 - - - - - - - - - 40 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married man / total man , so 10 / 30 = 1 / 3 c"
Answer: c
Question (general): when n is divided by 24 , the remainder is 5 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6 , e ) 7
Rationale: "let n = 5 ( leaves a remainder of 5 when divided by 24 ) 4 n = 4 ( 5 ) = 20 , which leaves a remainder of 4 when divided by 8 . answer c"
Answer: c
Question (geometry): question : a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 180 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 195 for the purchase ? options :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: imo it should be c that is c reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 180 1 b + 6 c = 190 solving both we get b that is bat = 40 and c that is ball = 25 new equation 195 to be divided in equal 3 b + 3 c = 195 3 * 40 + 3 * 25 = 195 120 + 75 = 195
Answer: c
Question (physics): a train 400 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 ) 277 m , b ) 700 m , c ) 900 m , d ) 187 m , e ) 1678 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 400 + x ) / 60 = 65 / 3 x = 900 m . answer : c"
Answer: c
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 8000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 29.8 % , b ) 16 % , c ) 18 % , d ) 82 % , e ) 23 %
Rationale: "total cp = rs . 42000 + rs . 8000 = rs . 50000 and sp = rs . 64900 profit ( % ) = ( 64900 - 50000 ) / 50000 * 100 = 29.8 % answer : a"
Answer: a
Question (gain): machine p and machine q are each used to manufacture 990 sprockets . it takes machine p 10 hours longer to produce 990 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 990 / x = 990 / 1.1 x + 10 1.1 ( 990 ) = 990 + 11 x 11 x = 99 x = 9 the answer is e ."
Answer: e
Question (general): what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 40 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 105 , e ) 110
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 40 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 40 = ( 2 ^ 2 * 5 ^ 2 ) ^ 40 = 2 ^ 80 * 5 ^ 80 answer : a"
Answer: a
Question (general): if the product of 2 integers is negative , at most how many of the integers can be negative ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the product of 2 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 1 correct option : a"
Answer: a
Question (gain): what will be the difference between simple and compound interest @ 10 % per annum on the sum of rs 1000 after 4 years
Options: a ) rs 62.10 , b ) rs 63.10 , c ) rs 64.10 , d ) rs 65.10 , e ) none of these
Rationale: explanation : s . i . = 1000 ∗ 10 ∗ 4 / 100 = 400 c . i . = [ 1000 ( 1 + 10 / 100 ) 4 − 1000 ] = 464.10 so difference between simple interest and compound interest will be 464.10 - 400 = 64.10 option c
Answer: c
Question (general): find k if 16 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 16 / k = 4 and 16 / 4 = 4 , then k = 4 correct answer d"
Answer: d
Question (geometry): the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 sq . ft , how much will it cost to paint outside of a cube having 8 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 546 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 82 = 384 sq . ft quantity of paint required = ( 384 / 16 ) = 24 kg cost of painting = 36.5 x 24 = rs . 876 answer : d"
Answer: d
Question (general): in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.3 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 2040
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 2040 : ri = 100 , ro = 130 thus ans : e"
Answer: e
Question (general): the simple interest on a sum of money will be rs . 800 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 1600 , e ) 1732
Rationale: "p - - - 10 - - - - 800 p - - - 5 - - - - - 400 3 p - - - 5 - - - - - 1200 - - - - - - = > 1600 answer : d"
Answer: d
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 66 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 138 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 66 seconds . thus x = 6 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 138 seconds . answer a"
Answer: a
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 50 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "annie earned 40 x + 10 ( 2 x ) = 60 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 60 x ( 1.5 x ) ( h ) = 75 x h = 50 hours the answer is c ."
Answer: c
Question (geometry): a box measuring 25 inches long by 30 inches wide by 15 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 88 , e ) 90
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 25 , 30 and 15 . thus side of cube must be 5 , and total number of cubes = 25 / 5 * 30 / 5 * 15 / 5 = 90 ans e ."
Answer: e
Question (probability): in lottery , there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1
Rationale: total number of outcomes possible , n ( s ) = 10 + 25 = 35 . total number of prize , n ( e ) = 10 p ( e ) = n ( e ) / n ( s ) = 10 / 35 = 2 / 7 answer is option b
Answer: b
Question (general): 0.999991 + 0.111119 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.11111 , e ) 1.1111
Rationale: "0.999991 + 0.111119 = 0.999991 + 0.11111 + 0.00009 = ( 0.999991 + 0.00009 ) + 0.11111 = 1 + 0.11111 = 1.11111 d"
Answer: d
Question (gain): from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 30 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 ) 35 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.30 x = 45 - - > 13 / 10 * x = 45 - - > x = 45 * 10 / 13 = 450 / 13 = ~ 35 . answer : a ."
Answer: a
Question (gain): if $ 5,000 is invested in an account that earns 10 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 10
Rationale: solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.10 / 2 ) ^ 2 = 5410 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 10 / 100 ) = 5400 difference = 5410 - 5400 = 10 $ e
Answer: e
Question (general): line q has the equation 5 y – 3 x = 15 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "5 y - 3 x = 15 and so y = 3 x / 5 + 3 when x = 0 , then y = 3 . when y = 0 , then x = - 5 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 5 , 0 ) , 0 = - 5 ( - 5 ) / 3 + c the y - intercept is c = - 25 / 3 < - 8 . thus the perpendicular line s can have y - intercepts from - 8 up to 2 . the number of possible lines is 8 + 2 + 1 = 11 the answer is b ."
Answer: b
Question (general): mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 35 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 23 %
Rationale: "lets assume that candidate got 35 % votes and total votes is 100 . candidate won = 35 remaining = 65 to get 50 % , candidate requires 15 votes from 100 which is 15 % and 15 votes from 65 . 15 / 65 = 23.07 which is approx 23 % . hence the answer is e"
Answer: e
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 5 cm ?
Options: a ) 827 cm 2 , b ) 216 cm 2 , c ) 95 cm 2 , d ) 80 cm 2 , e ) 176 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 5 ) = 95 cm 2 answer : c"
Answer: c
Question (general): a family pays $ 900 per year for an insurance plan that pays 80 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,300 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 900 $ family needs to pay 20 % of first 1000 $ in expense = 200 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 900 + 200 = 1100 $ total amount paid by insurance plan for first 1000 $ = 900 $ total amount paid by family will equal amount paid by plan when medical expense = 1300 $ ( since insurance plan will pay 100 % of amount that exceeds 1100 $ ) answer c"
Answer: c
Question (general): at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 28.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 16.2 , b ) 16.4 , c ) 16.6 , d ) 16.8 , e ) 17.0
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 28.9 x ^ 2 = 2.89 x = 1.7 at 4 : 00 pm , the amount of bacteria was 10 ( 1.7 ) = 17 grams . the answer is e ."
Answer: e
Question (general): rahul played weel in this season . his current batting averagge is 53 . if he score 78 runs in today match . his batting average will become 58 . how many matches had he played in this season .
Options: a ) 4 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "53 x + 78 = 58 ( x + 1 ) = > 5 x = 20 = > x = 4 answer : a"
Answer: a
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units
b ) 158 sq . units
c ) 187 sq . units
d ) 607 sq . units
e ) 815 sq . units
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : a
Answer: a
Question (gain): 33 1 / 3 % of 390 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 390 = 130 e )"
Answer: e
Question (general): sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6600 ?
Options: a ) 5591 , b ) 2477 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6600 x 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 answer : a"
Answer: a
Question (physics): a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 186 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 11
Rationale: at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 186 - $ 120 = $ 66 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 66 / $ 6 = 11 ans is e
Answer: e
Question (physics): 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days c do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time c = 3 days to finish the task imo a
Answer: a
Question (physics): a man can row 9 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 . what is the total distance traveled by the man ?
Options: a ) 5.98 , b ) 9.98 , c ) 9.06 , d ) 9.87 , e ) 9.82
Rationale: "m = 9 s = 1.2 ds = 7.2 us = 10.8 x / 10.8 + x / 7.8 = 1 x = 4.53 d = 4.53 * 2 = 9.06 answer : c"
Answer: c
Question (general): jacob is 12 years old . he is 4 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 18
Rationale: "j = 12 ; j = 4 b ; b = 12 / 4 = 3 ; twice as old so b = 3 ( now ) + ( 3 ) = 6 ; jacob is 12 + 6 = 18 answer : e"
Answer: e
Question (physics): a type q machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type q machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . q need 5 hours to complete and b needs 7 hours to compete so 2 q + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Question (gain): a fellow borrowed a certain sum of money at 3 % per annum at simple interest and in 3 years the interest amounted to rs . 1820 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 2000 , e ) 1110
Rationale: "p - 1820 = ( p * 3 * 3 ) / 100 p = 2000 answer : d"
Answer: d
Question (gain): a sum amounts to rs . 3969 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 3600 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 3969 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 3969 = p [ 21 / 20 ] ^ 2 3969 [ 20 / 21 ] ^ 2 3600 answer : a"
Answer: a
Question (gain): a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party r . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( r and b ) = 35 only r = 20 ( r and b ) / b = 1 / 2 let ( r and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Question (physics): how many pieces of 85 cm length can be cut from a rod of 38.25 meters long ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "number of pieces = 3825 / 85 = 45 the answer is c ."
Answer: c