Cheukting/mathqa huggingface dataset:
Question (physics): in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 58 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 57 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "so 57 days answer a = 57"
Answer: a
Question (physics): joshua and jose work at an auto repair center with 1 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 3 probability of chosing jose second = 1 / 2 total = 1 / 6 probability of chosing jose first = 1 / 3 probability of chosing josh second = 1 / 2 total = 1 / 6 final = 1 / 6 + 1 / 6 = 1 / 3 e"
Answer: e
Question (general): what is the value of n if the sum of the consecutive odd intergers e from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Question (general): the average of first thirteen prime numbers which are odd is ?
Options: a ) 20.15 , b ) 21.15 , c ) 22.15 , d ) 23.15 , e ) 24.15
Rationale: explanation : sum of first 13 prime no . which are odd = 275 average = 275 / 13 = 21.15 answer : b
Answer: b
Question (physics): joseph completes work worth $ 3.25 in hour and his cost to company per hour is $ 2.85 . ray completes worth worth of $ 2.80 in an hour and his cost to company is $ 2.65 per hour . if joseph works for 55000 hours , how many must ray work so that company makes at least as much in total gross profit as in case of joseph ?
Options: a ) 7858 , b ) 8301 , c ) 14667 , d ) 63840 , e ) 146,667
Rationale: joseph : profit / hour = 3.25 - 2.85 = 0.4 : no of hours = 55,000 : gross profit = 55,000 * 0.4 = 22,000 ray : profit / hour = 0.15 : gross profit = 22,000 : no of hours = 22,000 / 0.15 = 220,000 / 1.5 ( only closes is 146,667 ) answer e
Answer: e
Question (physics): a train 250 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 95 , b ) 50 , c ) 12 , d ) 13 , e ) 67
Rationale: "speed of the train relative to man = ( 250 / 10 ) m / sec = ( 25 ) m / sec . [ ( 25 ) * ( 18 / 5 ) ] km / hr = 90 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 90 = = > x = 95 km / hr . answer : option a"
Answer: a
Question (general): of the 200 employees at company x , 50 are full - time , and 150 have worked at company x for at least a year . there are 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 10 , d ) 80 , e ) 100
Rationale: "200 employees 50 are full - time 150 have worked at company x for at least a year 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 200 - 50 = 150 employees not full time 150 - 10 = 140 employees not full time who worked over a year 150 employees have worked at company x for at least a year - 140 employees not full time who worked over a year = 10 full - time employees of company x have worked at the company for at least a year ans c"
Answer: c
Question (geometry): if the volume of two cubes are in the ratio 64 : 8 , the ratio of their edges is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 2 : 1 , e ) none of these
Rationale: "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 64 / 8 = > ( a / b ) 3 = ( 4 / 2 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option d"
Answer: d
Question (gain): population is 24000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 26640 , c ) 36644 , d ) 31944 , e ) 26844
Rationale: "population after 1 st year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26400 population after 2 nd year = 26400 * 10 / 100 = 2640 = = = > 26400 + 2640 = 29040 population after 3 rd year = 29040 * 10 / 100 = 2904 = = = > 29040 + 2904 = 31944 answer : d"
Answer: d
Question (general): a man purchased 3 blankets @ rs . 100 each , 2 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 900 , c ) 278 , d ) 450 , e ) 772
Rationale: "10 * 150 = 1500 3 * 100 + 2 * 150 = 600 1500 – 600 = 900 answer : b"
Answer: b
Question (general): find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case .
Options: a ) 170 , b ) 172 , c ) 174 , d ) 176 , e ) 178
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 31 , 5 ) + 4 = 174 . answer : c"
Answer: c
Question (geometry): an artist wishes to paint a circular region on a square poster that is 3 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) sqrt ( 4.5 / pi ) , d ) 2 / sqrt ( pi ) , e ) pi / 2
Rationale: "area of the poster is 3 x 3 = 9 1 / 2 the area = 4.5 pi * r ^ 2 = 4.5 r ^ 2 = 4.5 / pi r = sqrt ( 4.5 / pi ) answer ( c )"
Answer: c
Question (physics): two trains 120 m and 150 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 14.8 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 9.27 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 150 = 270 m . required time = 270 * 9 / 250 = 9.27 = 9.27 sec . answer : e"
Answer: e
Question (physics): a 160 meter long train crosses a man standing on the platform in 8 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 94 kmph , c ) 92 kmph , d ) 86 kmph , e ) 72 kmph
Rationale: "s = 160 / 8 * 18 / 5 = 72 kmph answer : e"
Answer: e
Question (physics): 18 beavers , working together in a constant pace , can build a dam in 12 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 18 .
Rationale: "total work = 18 * 12 = 216 beaver hours 12 beaver * x = 216 beaver hours x = 216 / 12 = 18 answer : e"
Answer: e
Question (general): a batsman makes a score of 87 runs in the 17 th inning and thus increases his avg by 3 . find his average after 17 th inning .
Options: a ) 12 , b ) 39 , c ) 43 , d ) 52 , e ) 34
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) . : . 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . ans : b"
Answer: b
Question (physics): a company produces 120000 bottles of water everyday . if a case can hold 12 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 10000
Rationale: number of bottles that can be held in a case = 12 number of cases required to hold 120000 bottles = 120000 / 12 = 10000 cases . so the answer is e = 10000
Answer: e
Question (other): at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 15 th highest price and the 22 nd lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: "there were 14 items sold at a higher price than the radio and 21 items sold at a lower price than the radio . including the radio , there were 14 + 21 + 1 = 36 items sold . the answer is c ."
Answer: c
Question (gain): the cash difference between the selling prices of an book at a profit of 4 % and 6 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 50 : 53 , b ) 58 : 53 , c ) 52 : 53 , d ) 42 : 36 , e ) 38 : 53
Rationale: "c 52 : 53 let c . p . of the book be $ x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53"
Answer: c
Question (gain): in town x , 120 percent of the population are employed , and 80 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 33 % , d ) 40 % , e ) 52 %
Rationale: "total employed people 12 % , out of which 80 are employed males , hence 40 % are employed females . ( employed females ) / ( total employed people ) = 40 / 120 = 1 / 3 = 33 % answer : c ."
Answer: c
Question (general): if an average hard drive had a capacity of 0.1 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536
Rationale: "0.1 * 2 ^ 10 = 0.1 * 1024 = 102.4 the answer is d ."
Answer: d
Question (general): ( x + 3 ) is a factor in x ^ 2 - mx - 15 . what is the value of m ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 15 = 0 ( x - 5 ) ( x + 3 ) = 0 x = 5 or x = - 3 substituting both values for x in the equation we find : x ^ 2 - mx - 15 = > ( - 3 ) ^ 2 - m ( - 3 ) = 15 = > 9 + 3 m = 15 = > 3 m = 15 - 9 = 6 = > m = 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 15 - 5 m = 15 - 25 = - 10 m = 2 ao , ans b"
Answer: b
Question (physics): a small water pump would take 3 hours to fill an empty tank . a larger pump would take 1 / 4 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 13 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 3 , e ) 1 / 7
Rationale: rate of the small pump is 1 / 3 tank / hour rate of the larger pump is 1 / ( 1 / 4 ) or 4 tank / hour ; combined rate of the two pumps is 1 / 3 + 4 = 13 / 3 tank / hour , together they will fill the empty tank in 1 / ( 13 / 3 ) = 3 / 13 hours ( time = job / rate ) . answer : a
Answer: a
Question (general): by approximately what percent is x greater than 4 / 7 if ( 1 / 7 ) ( x ) = 1 ?
Options: a ) 1125 % , b ) 956 % , c ) 417 % , d ) 3788 % , e ) 219 %
Rationale: what percent is x greater than 4 / 7 if ( 1 / 7 ) ( x ) = 1 ? = > x = 7 % change = [ ( 7 - 4 / 7 ) / ( 4 / 7 ) ] * 100 = ( 49 / 4 - 1 ) * 100 = 45 * 25 = 1125 % ans , a
Answer: a
Question (general): when 1 / 10 percent of 3,000 is subtracted from 1 / 10 of 3,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 397 , e ) 500
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 3,000 ? 2 ) what is 1 / 10 of 3,000 ? to calculate 1 / 10 percent of 3,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 3,000 = 1 / 1,000 x 3,000 = 3 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 3,000 . to do this we simply multiply 1 / 10 by 3,000 . 1 / 10 x 3,000 = 300 the answer to part 1 is 3 , and the answer to part 2 is 300 . their difference is 300 – 3 = 397 . answer d ."
Answer: d
Question (general): how many multiples of 5 are there between 10 and 89 , 10 and 89 inclusive ?
Options: a ) 17 , b ) 16 , c ) 18 , d ) 19 , e ) 20
Rationale: "5 multiples are . . . 10,15 , 20,25 , 30,35 , 40,45 , 50,55 , 60,65 , 70,75 , 80,85 , . . . , . . . , the answer is = 16 answer is b"
Answer: b
Question (physics): a worker can load one truck in 5 hours . a second worker can load the same truck in 8 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.5 , b ) 2.7 , c ) 2.9 , d ) 3.1 , e ) 3.3
Rationale: "the workers fill the truck at a rate of 1 / 5 + 1 / 8 = 13 / 40 of the truck per hour . then the time to fill one truck is 40 / 13 which is about 3.1 hours . the answer is d ."
Answer: d
Question (general): if 4 a = 5 b and ab ≠ 0 , what is the ratio of a / 5 to b / 4 ?
Options: a ) 125 / 64 , b ) 25 / 16 , c ) 1 , d ) 4 / 5 , e ) 64 / 125
Rationale: a nice fast approach is the first find a pair of numbers that satisfy the given equation : 4 a = 5 b here ' s one pair : a = 5 and b = 4 what is the ratio of a / 5 to b / 4 ? in other words , what is the value of ( a / 5 ) / ( b / 4 ) ? plug in values to get : ( a / 5 ) / ( b / 4 ) = ( 5 / 5 ) / ( 4 / 4 ) = 1 / 1 = 1 c
Answer: c
Question (general): what number is that , to which if 1 , 5 , and 13 , be severally added , the first sum shall be to the second , as the second to the third ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: solution let x = the number required . by the conditions , x + 1 : x + 5 = a + 5 : x + 13 subtracting terms , ( art . 385,2 . ) x + 1 : 4 = x + 5 : 8 therefore 8 x + 8 = 4 x + 20 . and x = 3 . answer c
Answer: c
Question (general): the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 40 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 55 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 40 percent is reduced which means the new price is merely 60 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 5 ) p = 9 / 20 p is the new price after both deduction which is 45 percent of the original value p . this implies this entire series of deduction is worth having discounted 55 % of p . so answer is b = 55 %"
Answer: b
Question (general): 2.505 / 10.02 =
Options: a ) 0.35 , b ) 0.3505 , c ) 0.25 , d ) 0.351 , e ) 0.3527
Rationale: "2.505 / 10.02 2505 / 1002 = 2.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.25 . answer : c"
Answer: c
Question (physics): 1000 boys have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: explanation : 1000 * 15 = 1200 * x x = 12.5 b
Answer: b
Question (other): in a certain neighborhood , there are half as many beige houses as white houses , and 6 times as many white houses as brown houses . what is the ratio of the number of brown houses to the number of beige houses ?
Options: a ) 1 : 3 , b ) 1 : 9 , c ) 2 : 5 , d ) 5 : 3 , e ) 6 : 1
Rationale: the ratio of beige : white : brown = 3 : 6 : 1 the answer is a .
Answer: a
Question (geometry): the surface area of a sphere is 4 π r ^ 2 , where r is the radius of the sphere . if the surface area of sphere a is eight times as large as the surface area of sphere b , then the radius of sphere a is how many times the radius of sphere b ?
Options: a ) 2
b ) 2 √ 2
c ) 4
d ) 2 π
e ) π · √ 8
Rationale: r 1 : radius of sphere a r 2 : radius of sphere b as per question , 4 π r 1 ^ 2 = 8 ∗ 4 π r 2 ^ 2 or r 12 = 8 ∗ r 2 ^ 2 or r 1 = 2 √ 2 r 2 . hence , b
Answer: b
Question (gain): a man buy a book in rs 50 & sale it rs 50 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 0 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 50 profit = 50 - 50 = 0 % = 0 / 50 * 100 = 0 % answer : b"
Answer: b
Question (physics): a train passes a station platform in 50 sec and a man standing on the platform in 20 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 550 , b ) 400 , c ) 700 , d ) 600 , e ) 850
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 20 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 50 = 20 = > x = 600 m . answer : d"
Answer: d
Question (general): certain stocks in january were 40 % less than they were in february and 15 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?
Options: a ) 50.81 % , b ) 15.11 % , c ) 20.7 % , d ) 48.8 % , e ) 40 %
Rationale: "let stocks value in feb = 100 = > in jan = 60 and march = 60 * 100 / 115 = 51.2 % thus , percent decrease in stocks from feb to march = 100 - 51.2 = 48.8 % hence answer is d"
Answer: d
Question (physics): the length of the bridge , which a train 150 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 150 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 225 m answer : b"
Answer: b
Question (gain): fresh grapes contain 85 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 100 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 85 = 15 % of whole weight ) , so 20 * 0.75 = x * 0.15 - - > x = 100 . answer : c
Answer: c
Question (general): the average age of a family of 6 members is 24 years . if the age of the youngest member is 8 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 16 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 24 = 144 8 yrs back their ages were = 6 x 8 = 48 ages at the birth of youngest member = 144 - 48 = 96 therefore , avg age at the birth of youngest member = 96 / 6 = 16 . answer : b"
Answer: b
Question (gain): tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 45 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 760 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 15 tickets = 20 * 15 = 300 revenue generated from sales of 45 tickets = 120 + 340 + 300 = 760 $ answer b
Answer: b
Question (physics): a car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let t be the total time of the trip . 35 * 4 + 44 ( t - 4 ) = 38 t 6 t = 176 - 140 t = 6 the answer is a ."
Answer: a
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 276 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 50 / 3 3 x + 900 = 1950 = > x = 350 m . answer : b"
Answer: b
Question (general): what is the decimal equivalent of ( 1 / 4 ) ^ 5 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.0001 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 5 = 1 / 1024 = 0.0001 answer : c"
Answer: c
Question (general): a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 800 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 800 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 e"
Answer: e
Question (gain): a reduction of 35 % in the price of apples would enable a man to obtain 42 more for rs . 20 , what is reduced price per dozen ?
Options: a ) 1.7 , b ) 3.5 , c ) 6.3 , d ) 7.1 , e ) 10.4
Rationale: "a 20 * ( 35 / 100 ) = 6 - - - 42 ? - - - 12 = > rs . 1.7"
Answer: a
Question (general): what is the units digit of ( 52 ^ 5 ) ( 37 ^ 3 ) ( 71 ^ 9 ) ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "the units digit of 52 ^ 5 is the units digit of 2 ^ 5 which is 2 . the units digit of 37 ^ 3 is the units digit of 7 ^ 3 which is 3 . the units digit of 71 ^ 9 is the units digit of 1 ^ 9 which is 1 . the units digit of 2 * 3 * 1 is 6 . the answer is c ."
Answer: c
Question (physics): how many seconds will a 220 metre long train take to cross a man running with a speed of 8 km / hr in the direction of the moving train if the speed of the train is 80 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 11 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 80 - 8 ) km / hr = 72 km / hr = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken to pass the man = ( 220 / 20 ) sec = 11 sec . answer : d"
Answer: d