Cheukting/mathqa huggingface dataset:
Question (physics): a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 7 miles per hour for 2 hours . how many miles in total did she walk ?
Options: a ) 24 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 7 miles per hour and 2 hours - 14 miles total 18 + 20 + 14 = 52 answer : option b ."
Answer: b
Question (general): if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 5 x , then f ( - 1 ) =
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: "f ( - 1 ) = 3 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 2 ( - 1 ) ^ 2 + 5 ( - 1 ) = 3 + 4 - 2 - 5 = 0 the answer is c ."
Answer: c
Question (general): carol spends 1 / 4 of her savings on a stereo and 1 / 5 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 9 / 20 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 5 ) ( 1 / 4 ) s = ( 4 / 5 ) * ( 1 / 4 ) * s = ( 1 / 5 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 5 ) / s = 9 / 20 answer : d"
Answer: d
Question (general): if x is 20 percent greater than 55 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 66 , e ) 108
Rationale: x is 20 % greater than 55 means x is 1.2 times 55 ( in other words 55 + 20 / 100 * 55 = 1.2 * 55 ) therefore , x = 1.2 * 55 = 66 answer : d
Answer: d
Question (general): find the value of 72519 x 9999 = y ?
Options: a ) 354517481 , b ) 457687783 , c ) 246567689 , d ) 725117481 , e ) 565776879
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Question (other): a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 49 / 64 . how many marbles are in the bag ?
Options: a ) 24 , b ) 48 , c ) 60 , d ) 96 , e ) 84
Rationale: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 49 / 64 - - > ( x - 12 ) ^ 2 = 49 / 64 x ^ 2 square rooting u have x - 12 / x = 7 / 8 or x = 96 d"
Answer: d
Question (general): average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?
Options: a ) 41 , b ) 39 , c ) 43 , d ) 45 , e ) 47
Rationale: option ' c '
Answer: c
Question (gain): the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 432 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 3600 , d ) 9766 , e ) 10800
Rationale: p = 432 ( 100 / 5 ) ^ 2 = > p = 10800 answer : e
Answer: e
Question (physics): a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 32 , e ) 36
Rationale: explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 π r 1 st round : speed = π r for 30 seconds . so , total distance travelled = π r / 2 . speed = π r / 2 for 1 minute . so , total distance travelled = π r / 2 . speed = π r / 4 for 2 minutes . so , total distance travelled = π r / 2 . speed = π r / 8 for 4 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 7.5 minutes . 2 nd round : speed = π r / 16 for 8 minutes . so , total distance travelled = π r / 2 . speed = π r / 32 for 16 minutes . so , total distance travelled = π r / 2 . speed = π r / 64 for 32 minutes . so , total distance travelled = π r / 2 . speed = π r / 128 for 64 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c
Answer: c
Question (physics): . a car covers a distance of 1028 km in 4 hours . find its speed ?
Options: a ) 104 , b ) 255 , c ) 266 , d ) 257 , e ) 276
Rationale: "1028 / 4 = 257 kmph answer : d"
Answer: d
Question (gain): the cost price of a radio is rs . 2550 and it was sold for rs . 2130 , find the loss % ?
Options: a ) 18 , b ) 10 , c ) 15 , d ) 66 , e ) 41
Rationale: "2550 - - - - 400 100 - - - - ? = > 15 % answer : c"
Answer: c
Question (general): if x * y = xy – 2 ( x + y ) for all integers x and y , then 4 * ( – 3 ) =
Options: a ) – 14 , b ) – 11 , c ) – 4 , d ) 4 , e ) 16
Rationale: "4 * ( - 3 ) = 4 * ( - 3 ) - 2 ( 4 + ( - 3 ) ) = - 12 - 2 = - 14 option ( a )"
Answer: a
Question (geometry): the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?
Options: a ) t = 16 , b ) t = 32 , c ) t = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Question (physics): an enterprising businessman earns an income of re 5 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 10 th day of business , he earns an income of :
Options: a ) 21 , b ) 22 , c ) 20 , d ) 45 , e ) 30
Rationale: 2 nd day he earns = 3 ( 2 – 5 ) 3 rd day he earns = 3 ( 3 – 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d
Answer: d
Question (general): a student chose a number , multiplied it by 3 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 80 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 3 ⋅ x − 138 = 102 3 x = 240 x = 80 answer a"
Answer: a
Question (physics): two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none
Rationale: solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c
Answer: c
Question (gain): the population of a village is 14300 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?
Options: a ) 18911 , b ) 18788 , c ) 19898 , d ) 14000 , e ) 14400
Rationale: formula : ( after = 100 denominator ago = 100 numerator ) 14300 × 115 / 100 × 115 / 100 = 18911 a
Answer: a
Question (general): what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: "first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b ."
Answer: b
Question (general): if x / 5 + 9 / x = 14 / 5 , what are the values of 3 x - 7 ?
Options: a ) 8 and 9 , b ) 8 and 20 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 29
Rationale: i got the same thing b is the answer 8 or 20
Answer: b
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 23 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 3 : 1 , d ) 1 : 3 , e ) 1 : 4
Rationale: "speed = x and y resp length of first = 27 x length of second train = 17 y related speed = x + y time taken to cross each other = 23 s 27 x + 17 y / x + y = 23 27 x + 17 y = 23 ( x + y ) 4 x = 6 y x / y = 6 / 4 = 3 / 2 answer b"
Answer: b
Question (geometry): a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of the water above the ground ?
Options: a ) 0 feet
b ) 1 feet
c ) 2 feet
d ) 3 feet
e ) 4 feet
Rationale: 36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d
Answer: d
Question (other): the ratio of two speeds of two trains is 3 to 4 . if each of the trains slows its speed 5 km / hr , what will be the ratio of these two train speeds ?
Options: a ) 3 / 4 , b ) 8 / 9 , c ) 18 / 19 , d ) 23 / 24 , e ) it can not be determined from the information given
Rationale: 3 / 4 = 3 x / 4 x we need to find out ( 3 x + 5 ) / ( 4 x + 5 ) off course we can not solve this to arrive at any rational number hence e .
Answer: e
Question (gain): shopkeeper rise price by 33 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 1.745 % , b ) 4.745 % , c ) 3.745 % , d ) 6.745 % , e ) 7.745 %
Rationale: "let d initial price be 100 33 % rise now price = 133 / 100 * 100 = 133 10 % discount then price = 133 * 90 / 100 = 119.7 15 % discount then price = 119.7 * 85 / 100 = 101.745 so gain = 101.745 - 100 = 1.745 gain % = gain * 100 / cp = = > 1.745 * 100 / 100 = 1.745 % answer : a"
Answer: a
Question (other): in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13 . if the shop carries 352 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )"
Answer: b
Question (general): a box contain the number of balls which is as much times greater than 15 as much times lesser than 240 . the no . of ball is ?
Options: a ) 48 , b ) 75 , c ) 60 , d ) 54 , e ) 45
Rationale: "answer let the number be x . x / 15 = 240 / x x ^ 2 = 240 * 15 = 3600 x = √ 3600 = 60 correct option : c"
Answer: c
Question (gain): when the price of an article was reduced by 25 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 35 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 25 % , the new price is 0.75 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.75 p ) ( 1.8 n ) = 1.35 np , which is 1.35 times the old revenue , so is 35 % greater . answer : a"
Answer: a
Question (general): 5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?
Options: a ) 30 , b ) 34 , c ) 40 , d ) 50 , e ) 60
Rationale: explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b
Answer: b
Question (gain): one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a ."
Answer: a
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 black card and the second card is a king or queen ?
Options: a ) 1 / 52 , b ) 1 / 13 , c ) 1 / 26 , d ) 3 / 26 , e ) 17 / 26
Rationale: "p ( black card ) = 1 / 2 p ( king or queen ) = 2 / 13 p ( black card then a king / queen ) = 1 / 2 * 2 / 13 = 1 / 13 the answer is b ."
Answer: b
Question (general): a man whose bowling average is 22.2 , takes 4 wickets for 36 runs and thereby decreases his average by 1.2 . the number of wickets , taken by him before his last match is :
Options: a ) 14 , b ) 22 , c ) 38 , d ) 40 , e ) 50
Rationale: "explanation : let the number of wickets taken before the last match is x . then , ( 22.2 x + 36 ) / ( x + 4 ) = 21 = > 22.2 x + 36 = 21 x + 84 = > 1.2 x = 48 = > x = 48 / 1.2 = 40 answer : d"
Answer: d
Question (physics): a can give b 100 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 10.22 meters , b ) 11.22 meters , c ) 22.22 meters , d ) 33.22 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 880 meters . therefore , b runs 900 meters while c runs 880 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 880 ) / 900 = 977.778 meters thus , b can give c ( 1000 - 977.77 ) = 22.22 meters start answer : c"
Answer: c
Question (physics): a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 60 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 450 × 2 / 15 ) sec = 60 sec answer : e"
Answer: e
Question (geometry): a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?
Options: a ) a ) 4 inches
b ) b ) 6 inches
c ) c ) 5 inches
d ) d ) 8 inches
e ) e ) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c
Answer: c
Question (general): find the greatest number which leaves the same remainder when it divides 25 , 50 and 120 .
Options: a ) 18 , b ) 5 , c ) 12 , d ) 16 , e ) none of these
Rationale: "120 - 50 = 70 50 - 25 = 25 120 - 25 = 95 the h . c . f of 25 , 70 and 95 is 5 . answer : b"
Answer: b
Question (general): o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 11.6 ) + e ( – 10.4 ) + o ( – 9.2 ) + e ( 9.5 ) is :
Options: a ) - 3 , b ) - 1 , c ) 0 , d ) 1 , e ) 3
Rationale: "o ( 11.6 ) + e ( – 10.4 ) + o ( – 9.2 ) + e ( 9.5 ) = 13 + ( - 10 ) + ( - 11 ) + 8 = 0 the answer is c ."
Answer: c
Question (general): what is the smallest positive integer k such that the product of 2205 x k is a perfect square ?
Options: a ) 5 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 2205 = 3 ^ 2 * 7 ^ 7 * 5 , so if k = 5 then 2205 k = ( 3 * 7 * 5 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Question (general): the function f ( p ) represents the number of ways that prime numbers can be uniquely summed to form a certain number p such that p = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d
Answer: d
Question (physics): in what time will a train 175 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.58 sec , b ) 2.91 sec , c ) 4.37 sec , d ) 2.9 sec , e ) 1.8 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 175 / 40 = 4.37 sec . answer : c"
Answer: c
Question (general): a student chose a number , multiplied it by 5 , then subtracted 275 from the result and got 135 . what was the number he chose ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "let x be the number he chose , then 5 ⋅ x − 275 = 135 5 x = 410 x = 82 correct answer b"
Answer: b
Question (general): in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
Options: a ) 36 , b ) 34 , c ) 32 , d ) 30 , e ) 28
Rationale: "let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a ."
Answer: a
Question (physics): susan drives from city a to city b . after two hours of driving she noticed that she covered 80 km and calculated that , if she continued driving at the same speed , she would end up been 15 minutes late . so she increased her speed by 10 km / hr and she arrived at city b 36 minutes earlier than she planned . find the distance between cities a and b .
Options: a ) 223 , b ) 376 , c ) 250 , d ) 378 , e ) 271
Rationale: let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 − 1560 x 40 − 1560 hr . the rest of the distance is ( x − 80 ) ( x − 80 ) km . v = 40 + 10 = 50 v = 40 + 10 = 50 km / hr . so , she covered the distance between a and b in 2 + x − 80502 + x − 8050 hr , and it was 36 min less than planned . therefore , the planned time was 2 + x − 8050 + 36602 + x − 8050 + 3660 . when we equalize the expressions for the scheduled time , we get the equation : x 40 − 1560 = 2 + x − 8050 + 3660 x 40 − 1560 = 2 + x − 8050 + 3660 x − 1040 = 100 + x − 80 + 3050 x − 1040 = 100 + x − 80 + 3050 x − 104 = x + 505 x − 104 = x + 505 5 x − 50 = 4 x + 2005 x − 50 = 4 x + 200 x = 250 x = 250 so , the distance between cities a and b is 250 km . answer : c
Answer: c
Question (physics): a train running at the speed of 40 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 100 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 197 m
Rationale: "speed = 40 * 5 / 18 = 100 / 9 m / sec length of the train = speed * time = 100 / 9 * 9 = 100 m answer : a"
Answer: a
Question (general): what is the remainder if 7 ^ 16 is divided by 100 ?
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: "7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d"
Answer: d
Question (general): a large box contains 17 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 350 , c ) 425 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 17 * 25 = 425 correct answer c"
Answer: c
Question (general): what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?
Options: a ) 12 , b ) 18 , c ) 15 , d ) 6 , e ) 9
Rationale: explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d
Answer: d
Question (other): jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 6 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 30 : 2 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 6 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 30 : 18 : 2 i . e . u : b = 30 : 2 answer : option b"
Answer: b
Question (physics): a man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 3 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 3 * 15 / 60 = 15 / 20 miles and the man walks the distance mm , which is 3 * 9 / 60 = 9 / 20 mile . the difference of 15 / 20 - 9 / 20 = 3 / 10 miles ( mw ) will be covered by the man in ( 3 / 10 ) / 9 = 1 / 30 of an hour , which is 2 minutes . answer b .
Answer: b