Cheukting/mathqa huggingface dataset:
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 90 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 85.7
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 90 kilometers per hour is 1 / 90 hours = 3,600 / 90 seconds = 40 seconds ; time to cover this distance at regular speed is 40 + 2 = 42 seconds = 42 / 3,600 hours = 7 / 600 hours ; so , we get that to cover 1 kilometer 1 / ( 7 / 600 ) hours is needed - - > regular speed 85.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."
Answer: e
Question (physics): a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 5 / 6 , b ) 5 / 12 , c ) 7 / 12 , d ) 11 / 12 , e ) 11 / 15
Rationale: "the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 5 / 30 = 1 / 6 . the probability that he will stay in the dark is 1 - 1 / 6 = 5 / 6 the answer is a ."
Answer: a
Question (physics): on a map , 1 inch represents 28 miles . how many v inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "v inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Question (physics): 36 welders work at a constant rate they complete an order in 5 days . if after the first day , 12 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 4 , e ) 6
Rationale: "1 . we need to find out the time taken by 24 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 36 * 5 = 180 days 4 . but on day 1 thirty - six workers had already worked finishing 1 / 5 of the job . so 24 workers have to finish only 4 / 5 of the job . 5 . total time taken by 24 workers can be got from formula used at ( 2 ) . i . e . , 24 * total time taken = 180 . total time taken by 6 workers to finish the complete job is 180 / 24 = 7.5 days . 6 . time taken by 24 workers to finish 4 / 5 of the job is 4 / 5 * 7.5 = 6 days . the answer is choice e"
Answer: e
Question (probability): there are 23 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1254 , b ) 1482 , c ) 1771 , d ) 1875 , e ) 1923
Rationale: "23 c 3 = 23 * 22 * 21 / 6 = 1771 the answer is c ."
Answer: c
Question (geometry): the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than thevolume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?
Options: a ) 40 %
b ) 50 %
c ) 75 %
d ) 80 %
e ) 90 %
Rationale: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c
Answer: c
Question (physics): the length of the bridge , which a train 150 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 225 , c ) 245 , d ) 238 , e ) 236
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 = = > 2 ( 150 + x ) = 750 = = > x = 225 m . answer : option b"
Answer: b
Question (physics): speed of a boat in standing water is 7 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 32.44 hours , b ) 31.44 hours , c ) 30.44 hours , d ) 29.44 hours , e ) 28.44 hours
Rationale: "speed upstream = 5.5 kmph speed downstream = 8.5 kmph total time taken = 105 / 5.5 + 105 / 8.5 = 31.44 hours answer is b"
Answer: b
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 37 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 12 , d ) 83 , e ) 11
Rationale: "explanation : t = 8 / 45 * 60 = 11 answer : option e"
Answer: e
Question (physics): a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 600 = 1800 3 x / 2 = 1200 x = 800 km the answer is b ."
Answer: b
Question (general): the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in :
Options: a ) 5.5 min . , b ) 6 min . , c ) 4.9 min . , d ) 5.28 min . , e ) 5 min .
Rationale: "let both of them meet after t min 4500 m are covered by suresh in 60 m . in t min he will cover 4500 t / 60 likewise , in t min suresh ' s wife will cover 3750 t / 60 given , ( 4500 t / 60 ) + ( 3750 t / 60 ) = 726 t = 5.28 minutes answer : d"
Answer: d
Question (other): a and b have monthly incomes in the ratio 5 : 6 and monthly expenditures in the ratio 3 : 4 . if they save rs . 1800 and rs . 1600 respectively , find the monthly income of b
Options: a ) rs . 3400 , b ) rs . 2700 , c ) rs . 1720 , d ) rs . 7200 , e ) rs . 8200
Rationale: explanation : incomes of a and b = 5 x and 6 x and expenses of a and b = 3 y and 4 y then , savings of a = 5 x - 3 y = 1800 — ? ( 1 ) savings of b = 6 x - 4 y = 1600 — ? ( 2 ) by solving equations ( 1 ) and ( 2 ) y = 1400 monthly income of b = expenses of b + savings of b = 4 y + 1600 = 4 ( 1400 ) + 1600 = rs . 7200 answer : d
Answer: d
Question (general): mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 40 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 ) 20 %
Rationale: "lets assume that candidate got 40 % votes and total votes is 100 . candidate won = 40 remaining = 60 to get 50 % , candidate requires 10 votes from 100 which is 10 % and 10 votes from 60 . 10 / 60 = 1 / 6 = . 166 = 16.67 % which is approx 17 % . hence the answer is d"
Answer: d
Question (other): a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 16 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 13 / 50 , c ) 1 / 2 , d ) 7 / 10 , e ) 9 / 10
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 16 - 2 cmb = 100 b - cb - mb - 2 cmb = 26 hence the probability = 26 / 100 = 13 / 50 . b"
Answer: b
Question (physics): if it is 5 : 14 in the evening on a certain day , what time in the morning was it exactly 2 , 880702 minutes earlier ? ( assume standard time in one location . )
Options: a ) 5 : 32 , b ) 5 : 36 , c ) 5 : 48 , d ) 5 : 54 , e ) 5 : 58
Rationale: 5 : 14 minus 2 , 880,702 must end with 2 , the only answer choice which ends with 2 is a . answer : a .
Answer: a
Question (physics): a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . how far is the place ?
Options: a ) 2.29 , b ) 2.88 , c ) 2.2 , d ) 2.12 , e ) 2.14
Rationale: "m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"
Answer: b
Question (general): when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 6 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 4 . . d"
Answer: d
Question (general): a sports equipment store sold ping pong rackets for a total of $ 539 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 55 , b ) 100 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 539 x = 55 pairs were sold . answer : a"
Answer: a
Question (gain): a retailer bought a machine at a wholesale price of $ 80 and later on sold it after a 20 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the wholesale price , what is the retail price of the machine ?
Options: a ) $ 80 , b ) $ 100 , c ) $ 120 , d ) 135 , e ) 160
Rationale: "the price after the discount was 1.2 * 80 = $ 96 let x be the retail price . 0.8 x = $ 96 x = 96 / 0.8 = $ 120 the answer is c ."
Answer: c
Question (general): there are 7 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 42 , e ) 64
Rationale: "every team plays with 6 teams . . . so total no of matches = 7 x 6 = 42 . now , each match is played twice = > 42 x 2 but 2 teams play a match = > 42 x 2 / 2 = 42 . answer : d"
Answer: d
Question (general): in expressing a length of 61.472 km as nearly as possible with the 3 significant digits , find the percentage error ?
Options: a ) 0.35 % , b ) 0.4 % , c ) 0.045 % , d ) 0.6 % , e ) none of these
Rationale: explanation : error = ( 61.5 - 61.472 ) = 0.028 required percentage = 0.028 / 61.472100 = 0.045 answer : c
Answer: c
Question (general): if x + y + z = 1 . then xy + yz + zx is
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: 1 / 2 + 1 / 2 + 0 = 1 xy = 1 / 2 * 1 / 2 = 1 / 4 answer : c
Answer: c
Question (general): in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 2 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 3600 , e ) 6000
Rationale: "sugar : flour = 5 : 2 = 25 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 25 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 25 x = 6000 answer : e ."
Answer: e
Question (physics): machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 9800 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 9800 envelopes b will take 9800 / 1400 hrs = 7 hrs so the answer is choice e"
Answer: e
Question (general): difference between two numbers is 5 , 6 times of the smaller lacks by 8 from the 4 times of the greater . find the numbers ?
Options: a ) 5,1 , b ) 7,3 , c ) 9,8 , d ) 11,6 , e ) 13,7
Rationale: explanation : x – y = 5 4 x – 6 y = 8 x = 11 y = 6 d )
Answer: d
Question (physics): angelina walked 600 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 ) 9 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 600 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 600 / x - 240 / x = 40 . . 360 / x = 40 . . x = 9 m / secs . . so grocery to gym = 2 * 9 = 18 m / s . . . d"
Answer: d
Question (physics): a train running at the speed of 180 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 450 m , b ) 500 m , c ) 550 m , d ) 600 m , e ) 650 m
Rationale: "speed = ( 180 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 36 ) m = 600 m . answer : d"
Answer: d
Question (general): two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores 1 / 4 , what is the value of y / x ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 5 , d ) 1 / 3 . , e ) there is n ' t enough data to answer the question .
Rationale: "answer is c : 1 / 5 x - y = ( x + y ) / 4 solving for y / x = 1 / 5"
Answer: c
Question (gain): walking 3 / 2 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 12 , b ) 99 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 3 / 2 = 2 : 3 time ratio = 3 : 2 1 - - - - - - - - 3 4 - - - - - - - - - ? 12 m . answer : a"
Answer: a
Question (general): when 5 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 150 , c ) 60 , d ) 27 , e ) 11
Rationale: "explanation : let the number be 5 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 5 = a / 30 = > a = 150 answer : b"
Answer: b
Question (general): in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 440 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "440 = 1 * 5 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Question (geometry): 9 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 99 , d ) 90 , e ) 45
Rationale: there are 9 business exec and in each handshake 2 business execs are involved . hence 9 c 2 = 36 also , each of 9 exec will shake hand with every 7 other chairmen for total of 63 handshake . total = 36 + 63 = 99 ans : c
Answer: c
Question (probability): from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king or queen ?
Options: a ) 2 / 13 , b ) 3 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 3 / 52
Rationale: "p ( club ) = 1 / 4 p ( king or queen ) = 2 / 13 p ( club then a king / queen ) = 1 / 4 * 2 / 13 = 1 / 26 the answer is c ."
Answer: c
Question (general): a container has 40 l milk . 4 l milk is taken out and replaced with water , the process done 3 times . what is the amount of milk now left ?
Options: a ) 29.16 l , b ) 29.19 l , c ) 29.12 l , d ) 29.11 l , e ) 29.14 l
Rationale: explanation : in regard to the problem let after n times liquid in the container is x and liquid removed is y = > liquid in container = x = > liquid removed = y after one trial , quantity of pure liquid = x - ( 1 - y / x ) after n trials quantity of pure liquid = x - ( 1 - y / x ) n therefore , putting the values ( x = 40 l y = 4 l n = 3 ) and solving = > 40 - ( 1 - 4 / 40 ) 3 = 29.16 l answer : a
Answer: a
Question (geometry): if the length of rectangle is three times of its breadth . if the area of rectangle is 6075 sq . m , then calculate the length ?
Options: a ) 145
b ) 135
c ) 75
d ) 140
e ) none of these
Rationale: let breadth = x , length = 3 x . area of rectangle = length * breadth = 3 x ^ 2 = 6075 x ^ 2 = 2025 , x = √ 2025 = 45 m length = 135 m answer b
Answer: b
Question (general): the average of 9 observations was 9 , that of the 1 st of 4 being 10 and that of the last 4 being 8 . what was the 5 th observation ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "1 to 9 = 9 * 9 = 81 1 to 4 = 4 * 10 = 40 4 to 9 = 6 * 8 = 48 5 th = 48 + 40 = 88 – 81 = 7 answer : d"
Answer: d
Question (general): how much water must be added to 48 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 48 litres of milk = ( 1 ⁄ 4 × 48 ) litres = 12 litres . answer b"
Answer: b
Question (general): a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 100 more than that by the previous schema , his sales were worth ?
Options: a ) s . 14,000 , b ) s . 12,000 , c ) s . 32,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 100 x = 32000 answer : c"
Answer: c
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 24 seconds . the ratio of their speeds is ?
Options: a ) 3 / 6 , b ) 3 / 2 , c ) 7 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 24 = = > 27 x + 17 y = 24 x + 24 y = = > 3 x = 7 y = = > x / y = 7 / 3 . answer : c"
Answer: c
Question (gain): 32 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 80
Rationale: "i came up with ( e ) 80 think of 100 people total : from the first fact , 32 of these are women with fair hair . from the second fact , these 30 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 32 equals the number of fair haired men , which is 48 men with fair hair . add this 48 to the 32 women and get 80 fair haired men and women out of 100 total men and women . 80 % e"
Answer: e
Question (geometry): while visiting a small town in the united states , i lost my overcoat in a bus . when i reported the matter to the bus company i was asked the number of the bus . though i did not remember the exact number i did remember that the bus number bad a certain peculiarity about it . the number plate showed the bus number as a perfect square and also if the plate was turned upside down . ? the number would still be a perfect square — of course it was not ? i came to know from the bus company they had only 5 100 buses numbered from 1 to 500 . from this i was able to deduce the bus number . can you tell what was the other number .
Options: a ) 127 , b ) 196 , c ) 116 , d ) 140 , e ) 234
Rationale: b 196 the only numbers that can be turned upside down and still read as a number are 0 , 1 , 6 , 8 and 9 . the numbers 0 , 1 and 8 remain 0 , 1 and 8 when turned over , but 6 becomes 9 and 9 becomes 6 . therefore the possible numbers on the bus were 9 , 16 , 81 , 100 , 169 or 196 . however , the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31 . therefore 196 is the correct answer .
Answer: b
Question (physics): a car traveled from san diego to san francisco at an average speed of 51 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 34 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 51 x total distance traveled = 2 * 51 x = 102 x total time taken = x + 2 x = 3 x average speed = 102 x / 3 x = 34 answer : b"
Answer: b
Question (physics): in what time will a train 150 metres long cross an electric pole , if its speed be 122 km / hr ?
Options: a ) 2.42 , b ) 6.42 , c ) 5.42 , d ) 4.42 , e ) 3.42
Rationale: "solution speed = ( 122 x 5 / 18 ) m / sec = 33.88 m / sec time taken = ( 150 / 33.88 ) sec = 4.42 sec . answer d"
Answer: d
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 16 and 36 ?
Options: a ) 148 , b ) 222 , c ) 144 , d ) 157 , e ) 164
Rationale: "prime factorization of the given numbers 16 = 2 ^ 4 36 = 2 ^ 2 * 3 * 2 greatest common factor = 2 ^ 2 = 4 lowest common multiple = 2 ^ 4 * 3 ^ 2 = 144 sum = 4 + 144 = 148 answer a"
Answer: a
Question (general): x is a positive integer less than 100 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 14 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 100 n = 14.42 or n = 14 answer : - a"
Answer: a
Question (general): a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum mark is
Options: a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) 800
Rationale: "the student got 125 marks and still failed by 40 marks = 125 + 40 = 165 therefore 33 % of the total marks = 165 100 % of the total = 165 * 100 / 33 = 55 max mark = 500 answer b"
Answer: b