Cheukting/mathqa huggingface dataset:
Question (general): a committee is reviewing a total of 40 x black - and - white films and 10 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 50 / 52 , b ) 55 / 52 , c ) 60 / 52 , d ) 40 / 52 , e ) 30 / 52
Rationale: "say x = y = 10 . in this case we would have : 40 x = 400 black - and - white films ; 10 y = 100 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 100 color films , thus total of 104 films were selected . color films thus compose 100 / 104 = 50 / 52 of the selected films . answer : a"
Answer: a
Question (physics): a clock shows the time as 10 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 40 minutes
Rationale: "there are 8 hours in between 10 a . m . to 6 p . m . 8 * 5 = 40 minutes . answer : e"
Answer: e
Question (general): in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 23,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 169 %
Rationale: "the percent increase is ( 23947 - 8902 ) / 8902 = 15045 / 8902 = 1.69 so the approximate answer is e"
Answer: e
Question (gain): if the cost price of 24 chocolates is equal to the selling price of 16 chocolates , the gain percent is :
Options: a ) 24 % , b ) 8 % , c ) 50 % , d ) 40 % , e ) none of these
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 16 chocolates = rs . 16 ; s . p . of 16 chocolates = rs . 24 . . ' . gain % = 8 * 100 / 16 = 50 % answer : c"
Answer: c
Question (physics): a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . find out the number of days for which the remaining food will last .
Options: a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36
Rationale: explanation : given that fort had provision of food for 150 men for 45 days hence , after 10 days , the remaining food is sufficient for 150 men for 35 days remaining men after 10 days = 150 - 25 = 125 assume that after 10 days , the remaining food is sufficient for 125 men for x days more men , less days ( indirect proportion ) ( men ) 150 : 125 : : x : 35 ⇒ 150 × 35 = 125 x ⇒ 6 × 35 = 5 x ⇒ x = 6 × 7 = 42 i . e . , the remaining food is sufficient for 125 men for 42 days answer : option b
Answer: b
Question (other): the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 14 and 15 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 345 , d ) 231 , e ) 121
Rationale: "clearly , the numbers are ( 23 * 14 ) and ( 23 * 15 ) . larger number = ( 23 * 15 ) = 345 . answer : c"
Answer: c
Question (physics): during a given week a programmer spends 1 / 4 of his time preparing flow chart , 3 / 8 of his time coding and the rest of the time in debugging the programs . if he works 48 hours during the week , how many hours did he spend debugging the program .
Options: a ) 15 hrs , b ) 16 hrs , c ) 18 hrs , d ) 19 hrs , e ) 17 hrs
Rationale: programmer takes 1 / 4 * 48 = 12 hrs a week to make flowchrt same way . . . . . 18 hrs a week for codin . . . so . . . . for debugging = 48 - ( 12 + 18 ) = 18 hrs answer : c
Answer: c
Question (general): 1 / 2,16 , 4,15 , 3,56 , _ ?
Options: a ) 28 / 3 , b ) 27 / 3 , c ) 26 / 3 , d ) 25 / 3 , e ) 24 / 3
Rationale: "take alternative no . 1 / 2 , 4,3 16 / 4 = 4 15 / 5 = 3 56 / 6 = 28 / 3 hence ans is 28 / 3 answer : a"
Answer: a
Question (physics): there is enough provisions for 600 men in an army camp for 25 days . if there were 250 men less , how long will the provision last ?
Options: a ) 10 days , b ) 40 days , c ) 50 days , d ) 60 days , e ) 80 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 250 * d 2 d 2 = 600 * 25 / 250 = 60 days . answer : d"
Answer: d
Question (physics): in what time will a train 200 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 200 / 40 = 5 sec . answer : e"
Answer: e
Question (other): in a group of 100 cars , 49 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 49 , b ) 47 , c ) 48 , d ) 51 , e ) 53
Rationale: lets assume ac = 51 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 2 tocars with ac and racing stripes . hence ac = 51 - 2 = 49 . the answer is a
Answer: a
Question (gain): at what rate percent on simple interest will rs . 1500 amount to rs . 2000 in 5 years ?
Options: a ) 8.33 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 500 = ( 1500 x 5 xr ) / 100 r = 8.33 % answer : option a"
Answer: a
Question (gain): last year a certain bond price with a face value of 5000 yielded 10 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 7692 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.1 * 5000 / 0.065 - - > selling price = ~ 7692 answer : a ."
Answer: a
Question (other): the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people c who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , c = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"
Answer: d
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.1 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 11 / 31 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.4 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 22 hours . total hours = 62 . then the fraction would be 22 / 62 = 11 / 31 . therefore answer d ."
Answer: d
Question (other): in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 6 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 6 ( equiped with cable tv ) i . e . 1 / 6 ( 1 / 5 ) = 1 / 30 therefore only video cassette recorder = 1 / 10 - 1 / 30 = 1 / 15 total = 1 / 5 + 1 / 15 + neither cable tv nor videocassette recorders 1 = 4 / 15 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 4 / 15 = 11 / 15 hence b ."
Answer: b
Question (physics): walking at 3 / 4 of her normal speed , a worker is 8 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let v be her normal speed and let t be her normal time . d = ( 3 / 4 ) v * ( t + 8 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 3 / 4 ) v * ( t + 8 ) t / 4 = 6 t = 24 the answer is b ."
Answer: b
Question (general): the total age of a and b is 14 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 14 , b ) 27 , c ) 21 , d ) 18 , e ) 11
Rationale: "( a + b ) - ( b + c ) = 14 a - c = 14 . c is younger than a by 14 years . answer : a"
Answer: a
Question (general): in a party every person shakes hands with every other person . if there were a total of 171 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 171 n ( n - 1 ) / 2 = 171 â ˆ ´ n = 19 answer : option e
Answer: e
Question (physics): two spherical balls lie on the ground touching . if one of the balls has a radius of 7 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 30 / 7 , b ) 50 / 3 , c ) 70 / 4 , d ) 80 / 5 , e ) 90 / 8
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 3 / 7 = ( r - 10 ) / r 3 r = 7 r - 70 r = 70 / 4 the answer is c ."
Answer: c
Question (general): a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is
Options: a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 140 km
Rationale: explanation : let the journey be x km then , 3 x / 5 + 7 x / 20 + 6.5 = x 12 x + 7 x + 130 = 20 x x = 130 km answer : option d
Answer: d
Question (physics): two trains of length 100 meters and 200 meters are 450 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 450 / 45 = 10 seconds the answer is c ."
Answer: c
Question (physics): a train travels from new york to chicago , a distance of approximately 540 miles , at an average rate of 60 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 10 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 540 / 60 = 9 hours . therefore , the train depart from new york at 7 : 00 - 9 hours = 10 : 00 in the morning , new york time . answer : e ."
Answer: e
Question (physics): a train is 360 meter long is running at a speed of 52 km / hour . in what time will it pass a bridge of 140 meter length .
Options: a ) 24.62 seconds , b ) 34.62 seconds , c ) 44.62 seconds , d ) 54.62 seconds , e ) none of these
Rationale: "explanation : speed = 52 km / hr = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 130 / 9 = 34.62 seconds answer : b"
Answer: b
Question (general): a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 540 ?
Options: a ) 249 , b ) 498 , c ) 676 , d ) 269 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 540 y = 2 x + 2 538 = 2 x x = 269 answer : d . 269"
Answer: d
Question (other): in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 24 per kg so that cost of mixture is rs . 18 per kg ?
Options: a ) 4 : 1 , b ) 2 : 1 , c ) 3 : 1 , d ) 4 : 3 , e ) 4 : 5
Rationale: "( 18 - 24 ) / ( 16 - 18 ) = 6 / 2 = 3 : 1 answer : c"
Answer: c
Question (general): in a class of 25 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) 47 , b ) 45.6 , c ) 44 , d ) 48 , e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 19 * 45 = 1140 average marks of whole class = 1140 / 25 = 45.6 answer : option b"
Answer: b
Question (gain): ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 3 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) 228 , b ) 350 , c ) 27 , d ) 200 , e ) 881
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 3 / 100 ) = 15000 - 450 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 450 + 800 = rs . 350 as this is positive , an overall profit of rs . 350 was made . answer : b"
Answer: b
Question (general): from a total of 5 boys and 3 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 24 , c ) 30 , d ) 120 , e ) 240
Rationale: "answer = c = 30 no of 4 person committees that can be formed = 5 c 2 * 3 c 2 = 30 answer c"
Answer: c
Question (physics): a man , a woman and a boy can together complete a piece of work in 3 days . if a woman alone can do it in 6 days and a boy alone in 18 days , how long will a man take to complete the work ?
Options: a ) 5 days , b ) 8 days , c ) 7 days , d ) 9 days , e ) 8 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 wo man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 man alone can finish the work in 9 days . answer : option d"
Answer: d
Question (physics): a cyclist covers a distance of 750 m in 2 min 30 sec . what is the speed in km / hr of the cyclist ?
Options: a ) 9 km / hr , b ) 7 km / hr , c ) 12 km / hr , d ) 15 km / hr , e ) 18 km / hr
Rationale: "speed = { 750 } m / sec = 5 m / sec = { 5 * 18 } km / hr = 18 km / hr ans : e"
Answer: e
Question (physics): a train running at the speed of 70 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 227 m , b ) 150 m , c ) 167 m , d ) 175 m , e ) 187 m
Rationale: "speed = 70 * 5 / 18 = 175 / 9 m / sec length of the train = speed * time = 175 / 9 * 9 = 175 m answer : d"
Answer: d
Question (physics): on my sister ' s birthday , she was 126 cm in height , having grown 5 % since the year before . how tall was she the previous year ?
Options: a ) 124 cm , b ) 120 cm , c ) 116 cm , d ) 112 cm , e ) 110 cm
Rationale: let the previous year ' s height be x . 1.05 x = 126 x = 120 the answer is b .
Answer: b
Question (probability): what is the probability of drawing a ` ` queen ' ' from a deck of 52 cards ?
Options: a ) 2 / 7 , b ) 1 / 13 , c ) 3 / 5 , d ) 2 / 8 , e ) 1 / 7
Rationale: "explanation : total number of cards , n ( s ) = 52 total number of ` ` queen ' ' cards , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 52 = 1 / 13 answer : b"
Answer: b
Question (general): how many multiples of 2 are there between 1 and 58 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "28 multiples of 2 between 1 and 58 exclusive . from 2 * 1 upto 2 * 28 , ( 1,2 , 3,4 , . . . , 28 ) . hence , 28 multiples ! correct option is e"
Answer: e
Question (general): for a certain art exhibit , a museum sold admission tickets to a group of 50 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 38500 , e ) $ 48600
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 50 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 50 - - > x = 27 * 50 and 3 x = 3 * ( 27 * 50 ) = 27 * 150 . therefore , the total revenue from ticket sales that day was 27 * 50 * 6 + 27 * 150 * 10 = $ 48,600 . answer : e ."
Answer: e
Question (general): sum of 3 numbers 264 , if the first number be twice then second and third number be one third of the first , then the second number is
Options: a ) 70 , b ) 71 , c ) 72 , d ) 73 , e ) 74
Rationale: explanation : let the second number is x , then first is 2 x , and third is 1 / 3 ( 2 x ) = > 2 x + x + 2 x / 3 = 264 < = > 11 x / 3 = 264 = > x = 72 answer : option c
Answer: c
Question (general): if n = ( 33 ) ^ 43 + ( 53 ) ^ 33 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 33 ) ^ 53 is the same as that of 3 ^ 53 and the units digit of ( 53 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 53 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 53 is the same as the units digit of 3 ^ 3 , so 7 ( 53 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 53 + ( 53 ) ^ 33 is 7 + 7 = 4 . answer : c ."
Answer: c
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 200 questions and secures 240 marks , the number of questions he attempts incorrectly , is :
Options: a ) 135 , b ) 200 , c ) 140 , d ) 112 , e ) 48
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 200 â € “ x ) . 4 x â € “ ( 200 â € “ x ) = 240 or 5 x = 440 or x = 88 . number of incorrect answers = 200 - 88 = 112 answer : d"
Answer: d
Question (physics): a train moves with a speed of 216 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 38.8 , e ) 60
Rationale: solution speed = 216 kmph = ( 216 x 5 / 18 ) m / sec = 60 m / sec . answer e
Answer: e
Question (general): find the least number must be subtracted from 105829 so that remaining no . is divisible by 21 ?
Options: a ) 7 , b ) 10 , c ) 20 , d ) 32 , e ) 35
Rationale: "on dividing 105829 by 21 we get the remainder 10 , so 10 should be subtracted answer is b"
Answer: b
Question (gain): a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . what will be a ' s share in the total profit of rs . 27000 earned at the end of 2 years from the starting of the business ?
Options: a ) rs . 7500 , b ) rs . 9000 , c ) rs . 9500 , d ) rs . 10,800 , e ) none
Rationale: solution a : b : c = ( 20000 × 24 ) : ( 15000 × 24 ) : ( 20000 × 18 ) = 4 : 3 : 3 a ' s share = rs . ( 27000 × 4 / 10 ) = rs . 10800 . answer d
Answer: d
Question (general): the average age of 50 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .
Options: a ) 30 , b ) 65 , c ) 60 , d ) 55 , e ) 56
Rationale: "explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 50 ) = 65 years answer : b"
Answer: b
Question (general): the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 60 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 400 , d ) $ 720 , e ) $ 600
Rationale: "c for cost . p price per person . c = 3 * p c = 4 * p - 240 substituting the value of p from the first equation onto the second we get p = 240 . plugging in the value of p in the first equation , we get c = 720 . which leads us to answer choice d"
Answer: d
Question (general): twice the larger of two numbers is 3 more than 5 times the smaller , and the sum of 4 times the larger and 3 times the smaller is 71 . what are the numbers ?
Options: a ) 21 , 12 , b ) 9 , 0 , c ) 15 , 6 , d ) 10 , 1 , e ) 14 , 5
Rationale: the larger number : x the smaller number : y twice the larger : 2 x three more than five times the smaller : 5 y + 3 relationship between ( ` ` is ' ' ) : 2 x = 5 y + 3 four times the larger : 4 x three times the smaller : 3 y relationship between ( ` ` sum of ' ' ) : 4 x + 3 y = 71 now i have two equations in two variables : 2 x = 5 y + 3 4 x + 3 y = 71 i will solve , say , the first equation for x : x = ( 5 / 2 ) y + ( 3 / 2 ) then i ' ll plug the right - hand side of this into the second equation in place of the ` ` x ' ' : 4 [ ( 5 / 2 ) y + ( 3 / 2 ) ] + 3 y = 71 10 y + 6 + 3 y = 71 13 y + 6 = 71 13 y = 65 y = 65 / 13 = 5 now that i have the value for y , i can solve for x : x = ( 5 / 2 ) y + ( 3 / 2 ) x = ( 5 / 2 ) ( 5 ) + ( 3 / 2 ) x = ( 25 / 2 ) + ( 3 / 2 ) x = 28 / 2 = 14 answer : e
Answer: e
Question (general): if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Question (physics): 800 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 10 , b ) 8 , c ) 16 , d ) 11 , e ) 15
Rationale: "800 * 20 = 1200 * x x = 16 . answer : c"
Answer: c
Question (gain): the list price of an article is rs . 70 . a customer pays rs . 59.22 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 6 %
Rationale: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.22 x = 6 %"
Answer: e
Question (physics): a train crosses a platform of 200 m in 15 sec , same train crosses another platform of length 300 m in 20 sec . then find the length of the train ?
Options: a ) 100 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 152 m
Rationale: "length of the train be ‘ x ’ x + 200 / 15 = x + 300 / 20 4 x + 800 = 3 x + 900 x = 100 m answer : a"
Answer: a