Cheukting/mathqa huggingface dataset:
Question (other): what is the largest power of 3 contained in 200 !
Options: a ) 88 , b ) 48 , c ) 66 , d ) 97 , e ) 39
Rationale: "in real basic terms , we ' re asked to find all of the ' 3 s ' in 200 ! we can figure out that 200 / 3 = 66 , so we know that there are at least 66 ' 3 s ' in 200 ! while that answer is among the 5 choices , it seems a bit too ' easy ' , so let ' s do a bit more work and list out the first few numbers that we know have a ' 3 ' in them : 3 = 3 x 1 6 = 3 x 2 9 = 3 x 3 notice how both 3 and 6 have just one 3 in them , but 9 has two 3 s ( there ' s an ' extra ' 3 that we have to account for ) . this implies that there are probably other numbers that include ' extra 3 s ' that we have to figure out : to find those extra 3 s , we have to look at numbers that contain ' powers of 3 ' . . . 3 ^ 2 = 9 3 ^ 3 = 27 3 ^ 4 = 81 3 ^ 5 = 243 , but that ' s too big ( we ' re only going up to 200 ) . keep in mind that a multiple of 81 is also a multiple of 9 and 27 , so we do n ' t want to count any of those values more than once . 200 / 9 = 22 , so we know that there are at least 22 extra 3 s ( and certainly more because of the 27 and 81 ) . with the 66 3 s that we already have , those 22 extra 3 s increase the total to 88 . with the other extra 3 s , we ' ll end up with more than 88 3 s . there ' s only one answer that fits that logic . . . answer : d"
Answer: d
Question (general): reeya obtained 40 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average
Options: a ) 66 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "explanation : ( 40 + 60 + 70 + 80 + 80 / 5 ) = 66 option a"
Answer: a
Question (physics): the distance from city a to city b is 100 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the time it takes bob to drive to city b is 100 / 40 = 2.5 hours . alice needs to take less than 2 hours for the trip . alice needs to exceed a constant speed of 100 / 2 = 50 miles per hour . the answer is c ."
Answer: c
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with thrice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 3 units of water was used to make 4 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 4 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 4 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 4 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 4 * x - - > x = $ 0.3 . answer : c ."
Answer: c
Question (general): 8597 - ? = 7429 - 4358
Options: a ) 3567 , b ) 6424 , c ) 6835 , d ) 5526 , e ) none of these
Rationale: "d 7429 - 4358 = 3071 let 8597 - x = 3071 then , x = 8597 - 3071 = 5526"
Answer: d
Question (general): when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 24 , what is the remainder when k is divided by 7 ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 3 , e ) 8
Rationale: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 } ( less than 24 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 } ( less than 24 ) 17 is the only common number in both the sets . hence k = 17 answer : d"
Answer: d
Question (general): is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e"
Answer: e
Question (physics): how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 12.6 , b ) 12.0 , c ) 12.1 , d ) 12.3 , e ) 12.2
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 20 = 12.1 sec . answer : b"
Answer: b
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 , b ) 288 , c ) 120 , d ) 776 , e ) 991
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 6 = 120 m . answer : c"
Answer: c
Question (general): mary ' s income is 60 % more than tim ' s income and tim ' s income is 60 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 124 % , b ) b . 120 % , c ) 64 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.4 = 40 m = 40 * 1.6 = 64 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 64 * 100 / 100 = 64 ans : c"
Answer: c
Question (other): 11 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1540
Rationale: "no . of ways of picking 2 biology books ( from 11 books ) = 11 c 2 = ( 11 * 10 ) / 2 = 55 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 55 * 28 = 1540 ( option e )"
Answer: e
Question (physics): pipe a can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes . how long it will take to fill the tank if both pipes are operating together ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: pipe a fills 1 / 30 th of the tank in a minute and pipe b empties 1 / 90 th of the tank ( 1 / 30 ) - ( 1 / 90 ) = ( 1 / x ) 2 / 90 = 1 / x = > x = 45 answer : d
Answer: d
Question (physics): an electric pump can fill a tank in 4 hours . because of a leak in the tank , it took 8 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
Rationale: work done by the leak in 1 hour = 1 / 4 - 1 / 8 = 1 / 8 the leak will empty the tank in 8 hours answer is c
Answer: c
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 203 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,120 , e ) 2,256
Rationale: "i think it should be d . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 6 20 - pack for 3.05 * 5 = $ 18.30 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2120"
Answer: d
Question (physics): sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 07 : 00 and starts climbing at a constant pace . ken starts climbing only at 09 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: "both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 9 : 00 , in 5 hrs , the time will be 14 : 00 answer ( c )"
Answer: c
Question (physics): if 3 girls can do 3 times of a particular work in 3 days , then , 7 girls can do 7 times of that work in
Options: a ) 1 1 / 5 days , b ) 2 days , c ) 2 1 / 5 days , d ) 3 days , e ) 4 days
Rationale: answer : option ' d ' that is , 1 girl can do one time of the work in 3 days . therefore , 7 girls can do 7 times work in the same 3 days itself .
Answer: d
Question (gain): a sum fetched a total simple interest of 4043.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8985 , c ) 2345 , d ) 6474 , e ) 8723
Rationale: "principal = ( 100 x 4043.25 ) / ( 9 x 5 ) = 404325 / 45 = 8985 . answer b"
Answer: b
Question (general): when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.68 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 2 digits after decimal total no . of decimals = 4 req . no . of digits = ( n - 1 ) = ( 4 - 1 ) = 3 answer : d"
Answer: d
Question (physics): arun is travelling on his cycle and has calculated to reach point a at 2 pm if he travels at 10 kmph . he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 12 kmph , c ) 10 kmph , d ) 14 kmph , e ) 15 kmph
Rationale: let distance be x km travelling at 10 kmph reach at 2 pm travelling at 15 kmph reach at 12 noon = > time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs x / 10 - x / 15 = 2 3 x - 2 x * 30 x = 60 time needed if travelled at 10 kmph = 60 / 10 = 6 hrs = > reach at 1 pm = > ( 6 - 1 ) = 5 hrs req speed = 60 / 5 = 12 kmph answer b
Answer: b
Question (gain): rs . 600 amounts to rs . 900 in 3 years at simple interest . if the interest is increased by 4 % , it would amount to how much ?
Options: a ) 672 , b ) 246 , c ) 258 , d ) 856 , e ) 653
Rationale: "( 600 * 3 * 4 ) / 100 = 72 600 + 72 = 672 answer : a"
Answer: a
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions .
Options: a ) 843.03 m , b ) 844.03 m , c ) 845.03 m , d ) 846.03 m , e ) 847.03 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84403 cm = 844.03 m answer : b"
Answer: b
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 7.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 55 ° , d ) 45 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 7 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 7 − 30 / 5 ) + 30 / 2 = 30 ( 7 − 6 ) + 15 = 30 × 1 + 15 = 45 ° answer is d ."
Answer: d
Question (general): find the least number which when divided by 26 , 36 and 46 leaves the remainders 12 , 22 and 32 respectively .
Options: a ) 10570 , b ) 10750 , c ) 17050 , d ) 10075 , e ) 10085
Rationale: "explanation : the difference between any divisor and the corresponding remainder is 14 , l . c . m of 26 , 36,46 - 14 = 10764 - 14 = 10750 answer : option b"
Answer: b
Question (other): a certain bag contains 100 balls â € ” 50 white , 25 green , 10 yellow , 7 red , and 8 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.85 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 25 + 10 ) / 100 = 85 / 100 = 0.85 . answer is b
Answer: b
Question (physics): a 1 k . m . long wire is held by n poles . if one pole is removed , the length of the gap becomes 12 / 3 m . what is the number of poles initially ?
Options: a ) 500 , b ) 501 , c ) 502 , d ) 503 , e ) 504
Rationale: length after removing pole is 12 / 3 = 4 then before removing pole is 2 ( ' coz | 2 | 2 | is | 4 | ) i . e . gap between two poles is 2 m 1 km = 1000 m then split 1000 m by 2 m = > we have 500 sections or gaps then no . of poles is 500 + 1 st pole = 501 poles therefore n = 501 . answer : b
Answer: b
Question (gain): a certain deep blue paint contains 45 percent blue pigment and 55 percent red pigment by weight . a certain green paint contains 35 percent blue pigment and 65 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 2.75 , e ) 4.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 55 = 2.75 grams of red pigment
Answer: d
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 4.20 , is
Options: a ) 0 ° , b ) 5 ° , c ) 10 ° , d ) 20 ° , e ) none
Rationale: "solution angle traced by hour hand in 13 / 3 hrs = ( 360 / 12 x 13 / 3 ) ° = 130 ° angle traced by min . hand in 20 min = ( 360 / 60 x 20 ) ° = 120 ° required angle = ( 130 - 120 ) ° = 10 ° . answer c"
Answer: c
Question (gain): p and q started a business investing rs . 48,000 and rs . 24,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 2 : 6 , b ) 2 : 3 , c ) 2 : 1 , d ) 17 : 9 , e ) 17 : 4
Rationale: "p : q = 48000 : 24000 = 2 : 1 . answer : c"
Answer: c
Question (general): the average expenditure of a labourer for 6 months was 95 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 84
Rationale: "income of 6 months = ( 6 × 95 ) – debt = 570 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 840 average monthly income = 840 ÷ 10 = 84 answer e"
Answer: e
Question (general): the least number which must be subtracted from 6709 to make it exactly divisible by 9 is :
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "on dividing 6709 by 9 , we get remainder = 4 therefore , required number to be subtracted = 4 answer : c"
Answer: c
Question (physics): xavier starts from p towards q at a speed of 90 kmph and after every 12 mins increases his speed by 20 kmph . if the distance between p and q is 61 km , then how much time does he take to cover the distance ?
Options: a ) 52 , b ) 48 , c ) 44 , d ) 40 , e ) 36
Rationale: "first 12 min = 90 * 12 / 60 = 18 km 2 nd 12 min = 110 * 12 / 60 = 22 km 3 rd 12 min = 130 * 12 / 60 = 26 km total time 12.3 = 36 min e"
Answer: e
Question (gain): if 60 % of 3 / 5 of a number is 18 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 75 , d ) 50 , e ) none of these
Rationale: "let the number be x . then 60 % of 3 / 5 of x = 18 60 / 100 * 3 / 5 * x = 18 x = ( 18 * 25 / 9 ) = 50 required number = 50 . correct option : d"
Answer: d
Question (general): a driver just filled the car ' s gas tank with 18 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1 , b ) 1.5 , c ) 1.8 , d ) 2.4 , e ) 3
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 18 ) + x = 0.1 ( 18 + x ) 0.9 x = 1.8 - 0.9 x = 1 liter the answer is a ."
Answer: a
Question (physics): in covering a distance of 30 km , arun takes 22 hours more than anil . if arun doubles his speed , then he would take 1 hour less than anil . what is arun ' s speed ?
Options: a ) 8 kmph , b ) 5 kmph , c ) 4 kmph , d ) 7 kmph , e ) 9 kmph
Rationale: explanation : if arun doubles his speed , he needs 3 hour less . double speed means half time . hence , half of the time required by arun to cover 30 km = 3 hour i . e . , time required by arun to cover 30 km = 6 hour arun ' s speed = 30 / 6 = 5 kmph answer is b
Answer: b
Question (general): in the new budget the price of wheat rose by 8 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options: a ) 7.5 % , b ) 7.41 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %
Rationale: reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b
Answer: b
Question (physics): find the length of the wire required to go 12 times round a square field containing 104976 m 2 .
Options: a ) 15840 , b ) 3388 , c ) 2667 , d ) 8766 , e ) 15552
Rationale: "a 2 = 104976 = > a = 324 4 a = 1296 1296 * 12 = 15552 answer : e"
Answer: e
Question (general): three numbers are in the ratio 5 : 4 : 3 and their average is 360 . the largest number is :
Options: a ) 30 , b ) 450 , c ) 27 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be 5 x , 4 x and 3 x , then , ( 5 x + 4 x + 3 x ) / 3 = 360 = > 12 x = 360 * 3 = > x = 90 largest number 5 x = 5 * 90 = 450 answer : b"
Answer: b
Question (general): a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 9 / 24 ) × 8640 ] = rs . 3240 answer : option a
Answer: a
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction e of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Question (general): ( 4300331 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764713 , d ) 1675123 , e ) none of them
Rationale: "let 4300331 - x = 2535618 then x = 4300331 - 2535618 = 1764713 answer is c"
Answer: c
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 euro 1000 more than d , what is b ' s share ?
Options: a ) euro 1000 , b ) euro 3000 , c ) euro 5000 , d ) euro 4000 , e ) euro 2000
Rationale: "e euro 2000 let the shares of a , b , c and d be euro 5 x , euro 2 x , euro 4 x and euro 3 x respectively . then , 4 x - 3 x = 1000 x = 1000 . b ' s share = euro 2 x = euro ( 2 x 1000 ) = euro 2000 ."
Answer: e
Question (other): the simple form of the ratio 4 / 3 : 4 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 15 : 3 , d ) 5 : 3 , e ) 30 : 3
Rationale: "4 / 3 : 4 / 5 = 20 : 12 = 5 : 3 answer : d"
Answer: d
Question (gain): the s . i . on a certain sum of money for 5 years at 6 % per annum is half the c . i . on rs . 3000 for 2 years at 15 % per annum . the sum placed on s . i . is ?
Options: a ) 1525.2 , b ) 1256.3 , c ) 1612.5 , d ) 1548.5 , e ) 1254.5
Rationale: c . i . = [ 3000 * ( 1 + 15 / 100 ) 2 - 3000 ] = ( 3000 * 23 / 20 * 23 / 20 - 3000 ) = rs . 967.5 . sum = ( 483.75 * 100 ) / ( 5 * 6 ) = rs . 1612.5 answer : c
Answer: c
Question (general): if a and b are positive integers , and a = 20 b - 15 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 3 , c ) 18 , d ) 15 , e ) 5
Rationale: "if b is 1 , 3 , 5 , or 15 , then gcd of a and b is 1 , 3 , 5 , and 15 respectively . so , by poe the answer must be c . still : if b is a multiple of 18 , then a is 15 smaller than a multiple of 18 , so not a multiple of 18 , so both of them can not be divisive by 18 . answer : c ."
Answer: c
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 40 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 16 %
Rationale: "0.1 m = 0.60 e = > e / m = 1 / 6 * 100 = 16 % so answer is e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Question (geometry): the radius of the two circular fields is in the ratio 4 : 5 the area of the first field is what percent less than the area of the second ?
Options: a ) 42 % , b ) 39 % , c ) 38 % , d ) 36 % , e ) 26 %
Rationale: "r = 4 ï € r 2 = 16 r = 5 ï € r 2 = 25 25 ï € â € “ 9 ï € 100 - - - - ? = > 36 % . answer : d"
Answer: d
Question (gain): what is rate of interest if principal . amount be 400 , simple interest 80 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 80 = 800 r / 100 r = 80 / 8 = 10 % answer a"
Answer: a
Question (general): if 0.20 : x : : 4 : 2 , then x is equal to
Options: a ) 0.2 , b ) 0.3 , c ) 0.1 , d ) 0.5 , e ) none
Rationale: "sol . ( x × 4 ) = ( 0.20 × 2 ) ⇒ x = 0.4 / 4 = 0.1 . answer c"
Answer: c
Question (physics): along a yard 225 metres long , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "explanation : 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 option b"
Answer: b
Question (gain): a retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles . what is the percentage of profit made by the retailer ?
Options: a ) 66.67 % , b ) 33.33 % , c ) 40 % , d ) 25 % , e ) 20 %
Rationale: let cost price = x profit = y selling price = x + y 50 y = 20 ( x + y ) 30 y = 20 x percentage profit = y / x ∗ 100 = 20 / 30 ∗ 100 = 66.667 answer = a
Answer: a