regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: ( 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: pipe a can fill a tank in 16 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 21
Rationale: "let the pipe b be closed after x minutes . 30 / 16 - x / 24 = 1 = > x / 24 = 30 / 16 - 1 = 14 / 16 = > x = 14 / 16 * 24 = 21 . answer : e"
Answer: e
Problem: what is the units digit of ( 147 ^ 25 ) ^ 50 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 25 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 50 has the form 4 n + 2 , so the units digit is 9 . the answer is e .
Answer: e
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 33 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 65 %
Rationale: "x discount on pony jeans , ( 0.33 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.33 - x ) + 2 * 18 x = 9 - - > x = 0.65 = 65 % answer : e ."
Answer: e
Problem: a train travelling at a speed of 75 mph enters a tunnel 31 / 2 miles long . the train is 1 / 4 mile long . how long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 2.5 min , b ) 3 min , c ) 3.2 min , d ) 3.5 min , e ) 4 min
Rationale: total distance = ( 7 / 2 + 1 / 4 ) miles = 15 / 4 miles time taken = 15 / 4 * 75 hrs = 1 / 20 hrs = 3 min answer b
Answer: b
Problem: the value of log 343 7 is
Options: a ) 1 / 3 , b ) - 3 , c ) - 1 / 3 , d ) 3 , e ) 0.3
Rationale: "solution let log 3437 = n . then , 343 n = 7 = ( 73 ) n = 7 . ‹ = › 3 n = 1 ‹ = › n = 1 / 3 . log 343 7 = 1 / 3 . answer a"
Answer: a
Problem: a watch was sold at a loss of 16 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 700 , b ) 882 , c ) 799 , d ) 778 , e ) 901
Rationale: "84 % 104 % - - - - - - - - 20 % - - - - 140 100 % - - - - ? = > rs . 700 answer : a"
Answer: a
Problem: robin ' s average ( arithmetic mean ) test score on 9 tests is 82 . what must be robin ' s score on a 10 th test for his average score on the 10 tests to be 83 ?
Options: a ) 92 , b ) 82 , c ) 72 , d ) 62 , e ) 52
Rationale: ( 9 * 82 + x ) / 10 = 83 x = ( 10 * 83 ) - ( 9 * 82 ) x = 830 - 738 total score required 830 - 738 = 92 correct answer is a
Answer: a
Problem: the simple form of the ratio 9 / 8 : 3 / 4 is ?
Options: a ) 5 : 8 , b ) 5 : 5 , c ) 5 : 9 , d ) 3 : 2 , e ) 5 : 1
Rationale: "9 / 8 : 3 / 4 = 3 : 2 answer : d"
Answer: d
Problem: a goods train runs at the speed of 72 km / hr and crosses a 210 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 782 , c ) 278 , d ) 310 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 210 ) / 26 = 20 x = 310 m . answer : d"
Answer: d
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 220 , what were her original savings ?
Options: a ) $ 900 , b ) $ 880 , c ) $ 1000 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 220 . so 1 / 4 of her savings is $ 220 . so her original savings are 4 times $ 220 = $ 880 correct answer b"
Answer: b
Problem: i have only 1 $ and 2 $ note . i want to give 95 $ to john . how many maximum number of 2 $ note i need ?
Options: a ) 39 , b ) 95 , c ) 47 , d ) 55 , e ) 76
Rationale: check whether 95 is divisible by 2 then that is maximum no of 2 $ note else check next maximum term before 95 so 94 / 2 = 47 ans is c
Answer: c
Problem: if 10,000 microns = 1 decimeter , and 10,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05
Rationale: given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b
Answer: b
Problem: a train 125 m long crosses a platform 125 m long in 14 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 64 kmph , c ) 54 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 125 + 125 = 250 t = 14 s = 250 / 14 * 18 / 5 = 64 kmph answer : b"
Answer: b
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 12 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 50 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 %
Rationale: let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.12 0.2 x = 0.02 x = 0.1 = 10 % the answer is e .
Answer: e
Problem: what is the compound interest paid on a sum of rs . 3500 for the period of 2 years at 10 % per annum .
Options: a ) 630 , b ) 735 , c ) 825 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3500 = 3500 * ( 21 / 100 ) = 735 answer b"
Answer: b
Problem: a grand father has 3 grand children . age difference of two children among them is 3 . eldest child age is 3 times the youngest child ’ s age and the eldest child age is two year more than the sum of age of other two children . what is the age of the eldest child ?
Options: a ) 22 , b ) 15 , c ) 28 , d ) 26 , e ) 9
Rationale: as the eldest son ' s age is 3 times that of the youngest , eldest son ' s age should be a multiple of 3 . from the given options take 15 as the eldest son ' s age . then youngest son ' s age becomes 5 . but eldest sons age is 2 more than the sum of the remaining two sons . so sum of the remaining two sons is 13 . so the age of the middle son is 13 - 5 = 8 . which satisfies another condition in the question that the difference between the two sons age is 3 . so answer is 15 . answer : b
Answer: b
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 87 . how much was lent at 5 % ?
Options: a ) 228 , b ) 299 , c ) 300 , d ) 500 , e ) 188
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 87 5 x / 100 + 90 â € “ 6 x / 100 = 87 x / 100 = 3 = > x = 300 answer : c"
Answer: c
Problem: what is the lowest positive integer that is divisible by 4 through 7 , inclusive ?
Options: a ) 77 , b ) 270 , c ) 1600 , d ) 840 , e ) 980
Rationale: "the integer should be divisible by : 4 , 5 , 6 and 7 . the least common multiple of these integers is lcm = 4 * 5 * 6 * 7 = 840 answer : d"
Answer: d
Problem: of the people who responded to a market survey , 60 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 3 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 150 , c ) 240 , d ) 360 , e ) 480
Rationale: "ratio = 3 : 1 = > 3 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 60 = > 3 x = 60 = > x = 20 hence total no . of respondents = 60 + 20 = 80 hence a is the answer ."
Answer: a
Problem: the average of 50 numbers id 38 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 11.3 , e ) 37.5
Rationale: "explanation : total of 50 numbers = ( 50 × 38 ) = 1900 ( 50 × 38 ) = 1900 total of 48 numbers = ( 1900 - ( 45 + 55 ) ] = 1800 required average = 180048 = 2256 = 37.5 answer : e"
Answer: e
Problem: when fair coin is tossed 9 times find the probability of getting head at least once .
Options: a ) 1 / 512 , b ) 511 / 512 , c ) 9 / 512 , d ) 503 / 51 , e ) 503 / 510
Rationale: 1 - 1 / 2 ^ 9 = 1 - 1 / 512 = 511 / 512 answer : b
Answer: b
Problem: an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets water in at the rate of 16 litres / min then outlet pipe would take 8 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 21600 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 16 litres / min , or 16 * 60 = 960 liters / hour ; net outflow rate when both pipes operate would be x - 960 liters / hour . capacity of the tank = x * 10 hours = ( x - 960 ) * ( 10 + 8 ) hours 10 x = ( x - 960 ) * 18 - - > x = 2160 - - > capacity = 10 x = 21600 liters . answer : c ."
Answer: c
Problem: in a certain company , a third of the workers do not have a retirement plan . 50 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 156 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,5 * 1 / 3 * x 120 = 13 / 30 x x = 276 276 - 120 = 156 answer d"
Answer: d
Problem: which number need to add to 1782452 to get a number exactly divisible by 92 ?
Options: a ) 44 , b ) 43 , c ) 42 , d ) 41 , e ) 48
Rationale: "1782452 / 92 = 19374 and reminder = 44 . 92 - 44 = 48 so , the next number divisible by 92 is 48 places in front of 1782452 which means 48 + 1782452 = 1782500 48 should be added to 1782452 e"
Answer: e
Problem: a boat takes 19 hours for travelling downstream fro poin a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 180 km , b ) 190 km , c ) 220 km , d ) 230 km , e ) none
Rationale: sol . speed downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed upstream = ( 14 - 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 ⇔ x / 18 + x / 20 = 19 ⇒ x = 180 km . answer a
Answer: a
Problem: city x has a population 7 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 14 : 1 , e ) 18 : 1
Rationale: x = 7 y , y = 2 * z x : y , y : z 7 : 1 , 2 : 1 14 : 2 , 2 : 1 so , x : z = 14 : 1 ( d )
Answer: d
Problem: in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the sixth row ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 6 th row is 1 + 3 ( 5 ) = 16 the answer is b ."
Answer: b
Problem: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 20 feet between each tree . how many trees can be planted if the road is 148 feet long ?
Options: a ) 8
b ) 9
c ) 10
d ) 11
e ) 16
Rationale: let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 20 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 20 feet spaces will be t - 1 . then , the length of sidewalk required for 20 feet spaces will be 20 * ( t - 1 ) it is given that total length of sidewalk is 148 feet . or 20 ( t - 1 ) + t = 148 or 20 t - 20 + t = 148 or 21 t = 168 or t = 8 answer : - a
Answer: a
Problem: 20 balls are numbered 1 to 20 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 7 / 30 , b ) 3 / 14 , c ) 9 / 38 , d ) 4 / 21 , e ) 5 / 26
Rationale: "p ( 1 st ball is even ) = 10 / 20 p ( 2 nd ball is also even ) = 9 / 19 p ( both balls are even ) = 10 / 20 * 9 / 19 = 9 / 38 the answer is c ."
Answer: c
Problem: how long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 17.4 sec
Rationale: "e 17.4 sec d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer is e"
Answer: e
Problem: the probability that a number selected at random from first 50 natural numbers is a composite number is
Options: a ) 21 / 25 , b ) 17 / 25 , c ) 4 / 25 , d ) 8 / 25 , e ) 10 / 25
Rationale: "the number of exhaustive events = 50 c 1 = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . therefore , required probability = 34 / 50 = 17 / 25 . answer : b"
Answer: b
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 15 minutes ?
Options: a ) 15 , b ) 66 , c ) 22.5 , d ) 52 , e ) 42
Rationale: "90 * 15 / 60 = 22.5 kmph answer : c"
Answer: c
Problem: 225 , or 15 ^ 2 , is the first perfect square that begins with two 2 s . what is the sum of the digits of the next perfect square to begin with two 2 s ?
Options: a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: because 16 ^ 2 = 256 , y the next perfect square to begin with two 2 s can not be 3 - digit . let ' s try 4 - digit . 40 ^ 2 = 1600 and 50 ^ 2 = 2500 . so , if there is a 4 - digit perfect square to begin with two 2 s it must be between 41 ^ 2 and 49 ^ 2 . test the middle number 45 ^ 2 = 2025 . test larger number : 46 ^ 2 = 2116 . test next number : 47 ^ 2 = 2209 . bingo ! the sum of the digits = 2 + 2 + 0 + 9 = 13 . answer : c .
Answer: c
Problem: what is the angle between the two hands of a clock when time is 8 : 30
Options: a ) 15 degree , b ) 45 degree , c ) 55 degree , d ) 75 degree , e ) 65 degree
Rationale: "use the formula i . e 1 / 2 ( 60 h - 11 m ) / / h - hour and m - minute 1 / 2 ( 60 * 8 - 11 * 30 ) 1 / 2 ( 150 ) 75 degree answer : d"
Answer: d
Problem: two trains are moving at 80 kmph and 70 kmph in opposite directions . their lengths are 150 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 6 sec , b ) 7 sec , c ) 7 2 / 2 sec , d ) 8 sec , e ) 9 sec
Rationale: 70 + 80 = 150 * 5 / 18 = 125 / 3 mps d = 150 + 100 = 250 m t = 250 * 3 / 125 = 6 sec answer : a
Answer: a
Problem: if x > 0 , x / 50 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 25 = 2 + 4 = 6 6 is 6 % of 100 . answer : a
Answer: a
Problem: the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012
Rationale: let the commodity p costs 40 paise more than the commodity q after n years . price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 = > n = 2.5 / . 25 = 10 = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 answer : d
Answer: d
Problem: a train 110 m long running at 52 kmph crosses a platform in 30 sec . what is the length of the platform ?
Options: a ) 287 , b ) 398 , c ) 323 , d ) 245 , e ) 267
Rationale: "d = 52 * 5 / 18 = 30 = 433 â € “ 110 = 323 answer : c"
Answer: c
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 1 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 1 then x = 1 / 1000 = 0.001 . the answer is c"
Answer: c
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 90 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 2.5 hours for the trip . dan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is d ."
Answer: d
Problem: a and b began business with rs . 2000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .
Options: a ) 175 , b ) 288 , c ) 277 , d ) 877 , e ) 361
Rationale: "( 2 * 8 + 1 * 4 ) : ( 4 * 8 + 5 * 4 ) 5 : 13 5 / 18 * 630 = 175 answer : a"
Answer: a
Problem: a fair coin is tossed 9 times . what is the probability of getting more heads than tails in 9 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Problem: if 18 bindres bind 900 books in 10 days , how many binders will be required to bind 660 books in 12 days ?
Options: a ) 71 , b ) 12 , c ) 18 , d ) 11 , e ) 29
Rationale: explanation : let the required no of binders be x . less books , less binders ( direct proportion ) more days , less binders ( indirect proportion ) \ inline \ fn _ jvn \ left . \ begin { matrix } books \ : 900 : 600 \ \ days \ : \ : 12 : 10 \ end { matrix } \ right \ } : : 18 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn ( 900 \ times 12 \ times x ) = ( 600 \ times 10 \ times 18 ) \ inline \ fn _ jvn \ leftrightarrow x = \ inline \ fn _ jvn \ frac { 600 \ times 10 \ times 18 } { 900 \ times 12 } = 11 answer : d
Answer: d
Problem: if a ã — b = 2 a - 3 b + ab , then 1 ã — 2 + 2 ã — 1 is equal to :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : 1 ã — 2 + 2 ã — 1 = ( 2 ã — 1 - 3 ã — 2 + 1 ã — 2 ) + ( 2 ã — 2 - 3 ã — 1 + 2 ã — 1 ) = ( 2 - 6 + 2 + 4 - 3 + 2 ) = 1 . answer : a
Answer: a
Problem: when a train travels at a speed of 80 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 25 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 80 km / h 50 km / h - - - - > x + 15 distance is equal so 80 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 80 x = 50 x + 750 so the would be in km and x = 25 answer : a"
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 4 seconds . find the length of the train .
Options: a ) 66.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 4 = 66.67 meter . answer : a"
Answer: a
Problem: the average marks of a class of 30 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 82.5 , b ) 52.9 , c ) 52.2 , d ) 52.5 , e ) 52.7
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1200 + 3000 = 4200 average marks of all the students = 4200 / 80 = 52.5 answer : d"
Answer: d
Problem: 75 men working 8 hours per day dig 50 m deep . how many extra men should be put to dig to a depth of 70 m working 6 hours per day ?
Options: a ) 75 , b ) 45 , c ) 55 , d ) 65 , e ) 35
Rationale: ( 75 * 8 ) / 50 = ( x * 6 ) / 70 = > x = 140 140 â € “ 65 = 65 answer : d
Answer: d
Problem: on a certain date , pat invested $ 5,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 20,000 , in how many years , the total value of the investment plus interest will increase to $ 30,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 5,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 5 , 000.00 took to double 10 , 000.00 . again , 10 , 000.00 took to double 20 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 20 , 000.00 takes the same ( 72 / x ) no of years to double 30 , 000.00 . 72 / x = 6 years . so altogather : 5,000 - 10,000 = 6 years 10,000 - 20,000 = 6 years 20,000 - 30,000 = 3 years answer a 15 years .
Answer: a
Problem: a clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 50 percent of what the collector had paid . the shop then sold the clock again at a profit of 80 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 100 , for how much did the shop sell the clock the second time ?
Options: a ) $ 270 , b ) $ 250 , c ) $ 240 , d ) $ 220 , e ) $ 200
Rationale: original price = x sold to collector at 1.2 x re - buy price = 1.2 x * 0.5 = 0.6 x therefore , x - 0.6 x = 100 ; x = 250 second selling price = 1.8 * 0.6 * 250 = 270 answer : a
Answer: a
Problem: the average of first six prime numbers greater than 3 is ?
Options: a ) 16 , b ) 10 , c ) 12 , d ) 19 , e ) 17.8
Rationale: "5 + 7 + 11 + 13 + 17 + 19 = 72 / 6 = 12 answer : c"
Answer: c
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and 2 y percent of x equals 100 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 140 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and 2 y / 100 of x = 100 2 y / 100 * 4 y = 5000 y = 35 and x = 140 answer - c"
Answer: c
Problem: nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days they completed 1 / 3 part of work . than how many more employees should nhai hire to finish it in time working 10 hours a day ?
Options: a ) 22 , b ) 60 , c ) 28 , d ) 11 , e ) 218
Rationale: "here 2 km is immaterial . the given problem can be written in a tabular form like below . we can apply chain rule now . total men required to complete the remaining work = 100 × 2525 × 810 × 2313100 × 2525 × 810 × 2313 = 160 so additional men required = 160 - 100 = 60 answer : b"
Answer: b
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1680 ?
Options: a ) 1500 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771
Rationale: "1680 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1500 . answer : a"
Answer: a
Problem: if x : y = 1 : 2 , find the value of ( 2 x + 3 y ) : ( x + 4 y )
Options: a ) 5 : 6 , b ) 7 : 8 , c ) 8 : 9 , d ) 9 : 10 , e ) 11 : 12
Rationale: "x : y = 1 : 2 means x / y = 1 / 2 now , ( 2 x + 3 y ) : ( x + 4 y ) = ( 2 x + 3 y ) / ( x + 4 y ) [ divide numerator and denominator by y . ] = [ ( 2 x + 3 y ) / y ] / [ ( x + 4 y ) / 2 ] = [ 2 ( x / y ) + 3 ] / [ ( x / y ) + 4 ] , put x / y = 1 / 2 we get = [ 2 ( 1 / 2 ) + 3 ) / ( 1 / 2 + 4 ) = ( 1 + 3 ) / [ ( 1 + 8 ) / 2 ] = 4 / ( 9 / 2 ) = 4 / 1 × 2 / 9 = 8 / 9 therefore the value of ( 2 x + 3 y ) : ( x + 4 y ) = 8 : 9 answer is c"
Answer: c
Problem: what number has a 5 : 1 ratio to the number 13 ?
Options: a ) 22 , b ) 50 , c ) 88 , d ) 65 , e ) 12
Rationale: "5 : 1 = x : 13 x = 65 answer : d"
Answer: d
Problem: three cubes of metal whose edges are 5 , 10 and 15 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 28 , b ) 77 , c ) 66 , d ) 16.5 , e ) 99
Rationale: "53 + 103 + 153 = a 3 = > a = 16.5 answer : d"
Answer: d