Cheukting/mathqa huggingface dataset:
Question (general): there are 7 thieves . they stole diamonds from a diamond merchant and ran away . while running , night sets in and they decide to rest in the jungle . when everybody was sleeping , two of them woke up and decided to divide the diamonds equally among themselves . but when they divided the diamonds equally , one diamond is left . so they woke up the 3 rd thief and tried to divide the diamonds equally again but still one diamond was left . then they woke up the 4 th thief to divide the diamonds equally again , and again one diamond was left . this happened with the 5 th and 6 th thief – one diamond was still left . finally , they woke up the 7 th thief and this time the diamonds were divided equally . how many diamonds did they steal in total ?
Options: a ) 1560 , b ) 1561 , c ) 1559 , d ) 1557 , e ) none of the above
Rationale: we need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2 , 3 , 4 , 5 , and 6 . the least common multiple of these numbers is 60 . so , we need a multiple of 7 that is 1 greater than a multiple of 60 . answer b
Answer: b
Question (general): in a race where 15 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 8 and that z will win is 1 / 12 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 11 / 24 , d ) 10 / 15 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 8 + 1 / 12 = 11 / 24 answer : c"
Answer: c
Question (gain): find the compound interest on $ 26,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.93 , b ) 2552.26 , c ) 2524.23 , d ) 4098.25 , e ) 2512.23
Rationale: "principal = $ 26000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 26000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 30098.25 ci . = $ ( 30098.25 - 26000 ) = $ 4098.25 answer d ."
Answer: d
Question (gain): some of 50 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 3 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "40 % is 20 % - points above 20 % and 10 % - points below 50 % . thus the ratio of 20 % - solution to 50 % - solution is 1 : 2 . 1 / 3 of the original paint was replaced . the answer is a ."
Answer: a
Question (physics): shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 50 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 46 hence answer is e"
Answer: e
Question (general): how many three digit numbers r are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples r - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Question (gain): the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "volume of pool = 60 * 150 * 10 cu . ft , 80 % full = 60 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 150 * 10 * 0.8 / 60 min = 1200 min c"
Answer: c
Question (gain): a shopkeeper labeled the price of his articles so as to earn a profit of 50 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 35 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 150 . sp = rs . 150 - 10 % of 150 = rs . 150 - 15 = rs . 135 . gain = rs . 135 â € “ rs . 100 = rs . 35 therefore , gain / profit percent = 35 % . answer : option a"
Answer: a
Question (general): to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 770 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 193 , c ) 195 , d ) 212 , e ) 213
Rationale: "total movies submitted are 770 . as per question we need to take 1 / 4 of 770 to be considered for top 10 movies = 192.25 approximate the value we 193 imo option b is the correct answer . . ."
Answer: b
Question (general): 1 / 3 of girls , 1 / 2 of boys go to canteen . what factor and total number of classmates go to canteen .
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 2 / 5 , e ) 2 / 3
Rationale: let total girls be 3 . . . and total boys be 2 . . . so total girls going to canteen = 1 boys going to canteen = 1 total no . of classmates = 5 ( only suppose . . . . . . to find out the factor of students going to canteen . . . ) factor of classmates going to canteen = 2 / 5 . answer : d
Answer: d
Question (general): suraj has a certain average of runs for 9 innings . in the 10 th innings he scores 200 runs thereby increasing his average by 8 runs . what is his average after the 10 th innings ?
Options: a ) 149 , b ) 190 , c ) 128 , d ) 178 , e ) 190
Rationale: "to improve his average by 8 runs per innings he has to contribute 9 x 8 = 72 runs for the previous 8 innings . thus , the average after the 9 th innings = 200 - 72 = 128 . answer : c"
Answer: c
Question (gain): at a particular graduation party with 220 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 12 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 36 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 220 . . 70 % of 220 = 154 got gifts . . 66 did not get gift , out of which 12 are males , so remaining 60 - 12 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"
Answer: b
Question (general): if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 3 = 1 / ( 2 * ( 10 ) ^ 3 ) , then m =
Options: a ) 4 , b ) 3 , c ) 1 , d ) 6 , e ) 8
Rationale: "1 / 5 ^ m * 1 / 4 ^ 3 = 2 * 1 / 2 ^ 3 * 5 ^ 3 * 8 2 ^ 3 * 5 ^ 3 * 8 / 4 ^ 3 = 5 ^ m or 5 ^ 3 = 5 ^ m m = 3 b"
Answer: b
Question (gain): in town x , 64 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 34 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 42 are employed males , hence 22 % are employed females . ( employed females ) / ( total employed people ) = 22 / 64 = 34 % answer : d ."
Answer: d
Question (general): if n divided by 7 has a remainder of 1 , what is the remainder when 3 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 1 for some integer p hence 3 n = > 21 q + 3 = > remainder = > 6 for some integer q alternatively = > n = 2 > 3 n = > 3 = > 3 divided by 7 will leave a remainder 3 hence c"
Answer: c
Question (general): how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 53 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 3 . so , one more solution , where a = b is not possible . so , answer will be c ."
Answer: c
Question (general): in a house , there are 4 birds , 3 dogs , and 18 cats living with the human family . if the total number of feet in the house are 74 more than the number of heads in the house , how many family members are there ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: explanation : let number of family members be x . then , total number of feet = 2 x 4 + 4 x 3 + 4 x 18 + 2 x = 2 x + 92 . total number of heads = 4 + 3 + 18 + x = 25 + x . therefore ( 2 x + 92 ) = ( 25 + x ) + 74 or x = 7 . answer : d
Answer: d
Question (gain): what will be the fraction of 33.33 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 3 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 33.33 * 1 / 100 = 1 / 3 answer : option c"
Answer: c
Question (other): the ratio of the adjacent angles of a parallelogram is 6 : 9 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 6 x + 9 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 72 ° and 108 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 72 ° + 84 ° = 156 ° answer : c"
Answer: c
Question (general): the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are
Options: a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none
Rationale: "solution out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 answer d"
Answer: d
Question (physics): if the length and breadth of a room are increased by y feet each , the perimeter increases by 16 feet . find y
Options: a ) 8
b ) 2
c ) 6
d ) 4
e ) 3
Rationale: 2 ( l + b ) = x ; 2 ( l + y + b + y ) = x + 16 ; 2 ( l + b ) + 4 y = x + 16 ; x + 4 y = x + 16 ; y = 4 answer : d
Answer: d
Question (physics): jack and paul are running 1000 m . jack runs 1.5 km / hr faster than paul but also finishes the race 1.5 sec earlier . what is the speed of jack ? ?
Options: a ) 19.6 , b ) 20.6 , c ) 21.6 , d ) 22.6 , e ) 23.6
Rationale: distance ( given ) 1000 m paul speed ( let ) = x m / s time ( paul take ) = 1000 / x sec jack speed = x + 1.5 * ( 5 / 18 ) m / s tym ( jack ) = 1000 / ( x + 7.5 / 18 ) s tym ( paul ) - tym ( jack ) = 1.5 solving for x we get 20.20 speed of jack is 20.20 + 7.5 / 18 = 20.61 answer : b
Answer: b
Question (physics): the speed of boat in still water is 20 km / hr . if it travels 26 km downstream and 14 km upstream in same time , what is the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2
Rationale: explanation : let x be speed of stream speed of boat downstream = ( 20 + x ) speed of boat upstream = ( 20 – x ) it is given that boat takes same time to travel 26 km downstream and 14 km upstream [ 26 / ( 20 + x ) ] = [ 14 / ( 20 – x ) ] 520 – 26 x = 280 + 14 x 40 x = 240 x = 6 km / hr answer : a
Answer: a
Question (physics): on my sister ' s birthday , she was 147 cm in height , having grown 5 % since the year before . how tall was she the previous year ?
Options: a ) 145 cm , b ) 140 cm , c ) 142 cm , d ) 138 cm , e ) 135 cm
Rationale: "let the previous year ' s height be x . 1.05 x = 147 x = 140 the answer is b ."
Answer: b
Question (general): if the sum of the 4 th term and the 12 th term of an arithmetic progression is 10 , what is the sum of the first 15 terms of the progression ?
Options: a ) 65 , b ) 75 , c ) 60 , d ) 55 , e ) 50
Rationale: "4 th term + 12 th term = 10 i . e . , ( a + 3 d ) + ( a + 11 d ) = 10 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 10 - - - - - - - - - - - - - - - from ( 1 ) = 75 answer : b"
Answer: b
Question (gain): during a certain season , a team won 65 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 80 , b ) 75 , c ) 56 , d ) 50 , e ) 105
Rationale: "we are first given that a team won 65 percent of its first 100 games . this means the team won 0.65 x 100 = 65 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 65 + 0.5 t – 50 = 0.7 t 15 = 0.2 t 150 = 2 t 75 = t answer is b ."
Answer: b
Question (physics): worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job .
Options: a ) 4 / 9 , b ) 2 4 / 9 , c ) 3 4 / 9 , d ) 4 4 / 9 , e ) none of these
Rationale: "explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as , a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 4 4 / 9 option d"
Answer: d
Question (physics): a man can row downstream at 18 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 30 = > x = 15 , y = 3 . answer : a"
Answer: a
Question (gain): the weight of a glass of jar is 25 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 7 / 15
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 25 g weight of coffee beans = 75 g weight of jar and remaining beans = 60 g weight of remaining beans = 35 g fraction remaining = 35 / 75 = 7 / 15 answer is e ."
Answer: e
Question (general): one ton has 2500 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 2000 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2500 pound = 13 * 2500 * 16 ounces . hence the answer is ( 13 * 2500 * 16 ) / 260 = 2000 . answer : a ."
Answer: a
Question (general): in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these
Rationale: girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d
Answer: d
Question (general): for what value of x , is | x – 5 | + | x + 4 | + | x | = 14 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) - 4 , e ) 5
Rationale: "for what value of x , is | x – 5 | + | x + 4 | + | x | = 14 ? it ' s easiest just to plug in answer choices : ( e ) : 5 | x – 5 | + | x + 4 | + | x | = 14 ? | 5 - 5 | + | 5 + 4 | + | 5 | = 14 ? | 0 | + | 9 | + | 5 | = 14 ( e )"
Answer: e
Question (other): an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 3 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 2000 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 3 x and r = 7 x . then , 5 x = 1500 ? x = 500 . p = 1500 , q = 1500 and r = 3500 . hence , ( r - p ) = ( 3500 - 1500 ) = 2000 answer : d"
Answer: d
Question (general): a , b and c are employed to do apiece of work for rs . 529 . a and c are supposed to finish 19 / 23 of the work together . how much shall be paid to b ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 16
Rationale: c 12 12 men can complete a work in 18 days . six days after they started working , 4 more men joined them . how many days will all of them together complete the remaining work ?
Answer: c
Question (physics): a train 990 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 ) 310 , d ) 297 , 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 , ( 990 + x ) / 60 = 65 / 3 x = 310 m . answer : c"
Answer: c
Question (physics): calculate how many days it will take for 5 boys to paint a 30 m long fence if 2 boys can paint a 20 m long fence in 3 days ,
Options: a ) 6.80 days , b ) 4.80 days , c ) 3.80 days , d ) 2 days , e ) 1.80 days
Rationale: "the length of wall painted by one boy in one day = 20 / 2 * 1 / 3 = 3.33 m no . of days required to paint 50 m cloth by 8 boys = 30 / 5 * 1 / 3.33 = 1.80 days . e"
Answer: e
Question (general): find the value of ( 28 + 48 / 69 ) × 69
Options: a ) 1980 , b ) 1982 , c ) 1930 , d ) 1988 , e ) 1680
Rationale: "= ( 28 + 48 / 69 ) × 69 = ( 1932 + 48 ) / 69 × 69 = 1980 / 69 × 69 = 1980 answer is a ."
Answer: a
Question (general): a soccer store typically sells replica jerseys at a discount of 20 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 50 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , e is the answer"
Answer: e
Question (general): a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 31 / 45 , e ) 11 / 15
Rationale: "i think d - 31 / 45 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 4 x so old = x , new = 3 x now 1 / 3 of x are occupied and 1 / 5 of 3 x are occupied which simplifies to ( 3 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 3 / 5 of x occupied in the new ward . add them up to get 14 / 15 of x there are 3 x beds in new tower so ratio is : ( 14 / 15 ) x / 3 x = 14 / 45 of x subtract that from 45 / 45 of x and you get the number of un - occupied beds to total capacity of new tower = 31 / 45 d"
Answer: d
Question (general): if jake loses 32 pounds , he will weigh twice as much as his sister . together they now weigh 212 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 152 , e ) 188
Rationale: lets say j is the weight of jack and s is the wt of his sister . if he loses 32 pounds , he s twice as heavy as his sister . j - 32 = 2 * s also , together they weight 212 pounds j + s = 212 solvong the 2 equation , we get j = 152 pounds ! d
Answer: d
Question (physics): a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 225 km / hr , b ) 50 km / hr , c ) 99 km / hr , d ) 88 km / hr , e ) 66 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = > x = 50 km / hr . answer : b"
Answer: b
Question (physics): how many cuboids of length 6 m , width 4 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 2.6 , b ) 5.8 , c ) 6.2 , d ) 7.5 , e ) 1.2
Rationale: "( 18 ã — 15 ã — 2 ) / ( 6 ã — 4 ã — 3 ) = 7.5 answer is d ."
Answer: d
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 28 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 180 = 280 s = 36 * 5 / 18 = 10 mps t = 280 / 10 = 28 sec answer : option c"
Answer: c
Question (general): there are 36 students in a certain geometry class . if one third of the students are boys and one fourth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 3 , b ) 12 , c ) 18 , d ) 24 , e ) 27
Rationale: total students = 36 one third of the students are boys = 1 / 3 * 36 = 12 one fourth of the boys are under six feet tall = 1 / 4 * 12 = 3 . . . therefore number of boys in the class under six feet tall = 3 . . . answer a . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 4 of 1 / 3 of total students = 1 / 4 * 1 / 3 * 36 = 3 . . . answer a
Answer: a
Question (geometry): find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm ?
Options: a ) 225 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 30 ( 9 + 6 ) = 225 cm 2 answer : a"
Answer: a