regisss/math_qa huggingface dataset:
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) rs . 14,000 , b ) rs . 12,000 , c ) rs . 30,000 , d ) rs . 40,000 , e ) rs . 45,000
Rationale: "explanation : [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer is b"
Answer: b
Problem: shopkeeper rise price by 32 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 0.98 % , b ) 4.98 % , c ) 3.95 % , d ) 6.98 % , e ) 7.98 %
Rationale: "let d initial price be 100 32 % rise now price = 132 / 100 * 100 = 132 10 % discount then price = 132 * 90 / 100 = 118.8 15 % discount then price = 118.8 * 85 / 100 = 100.98 so gain = 100.98 - 100 = 0.98 gain % = gain * 100 / cp = = > 0.98 * 100 / 100 = 0.98 % answer : a"
Answer: a
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 20000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 4000 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 20000 = > x = 4000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 4000 answer : b"
Answer: b
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 17 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 38 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 10 % + 1 part of x ( unknown ) % = 4 parts of 17 % = > x % = 68 % - 30 % = 38 % ans d it is ."
Answer: d
Problem: 8 x 1.6 - 3 x 1.4 / 1.3 = ?
Options: a ) 21.5 , b ) 22 , c ) 15.8 , d ) 12.8 , e ) 25
Rationale: "given expression = ( 12.8 - 4.2 ) / 0.4 = 8.6 / 0.4 = 8.6 / 0.4 = 21.5 answer is a ."
Answer: a
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 3.5 t seconds , then what is the length of the platform ?
Options: a ) 0.5 l , b ) 1.5 l , c ) 2.5 l , d ) 3.5 l , e ) 4.5 l
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 3.5 t ( l + p ) / ( l / t ) = 3.5 t p = 2.5 l the answer is c ."
Answer: c
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1190 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 70 × 9 = 630 . total cost he has to pay = 560 + 630 = 1190 . d )"
Answer: d
Problem: a cycle is bought for rs . 840 and sold for rs . 1220 , find the gain percent ?
Options: a ) 70 % , b ) 45 % , c ) 48 % , d ) 30 % , e ) 40 %
Rationale: "explanation : 840 - - - - 380 100 - - - - ? = > 45 % answer : b"
Answer: b
Problem: for all numbers a and b , the operationis defined by ab = ( a + 2 ) ( b – 3 ) . if 3 x = – 25 , then x =
Options: a ) – 15 , b ) – 2 , c ) - 3 , d ) 6 , e ) 15
Rationale: ( 3 + 2 ) ( x - 3 ) = - 25 . . x - 3 = - 5 . . x = - 2 b
Answer: b
Problem: the ratio of length to width of a rectangular showroom window is 3.3 to 2 . if the width of the window is 8 feet , what is the approximate length of the display in feet ?
Options: a ) 7
b ) 11
c ) 13
d ) 16
e ) 26
Rationale: explanation : letting l be the length of the window , the proportion for the ratio of the length to the width can be expressed in the following equation : 3.3 / 2 = l / 8 26.4 = 2 l 13.2 = l answer : option c
Answer: c
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 170 , what is the least possible value of n ?
Options: a ) 14 , b ) 13 , c ) 15 , d ) 17 , e ) 16
Rationale: 17 , since n needs to be the largest of the prime factors . therefore , the answer is d .
Answer: d
Problem: in a jar there are balls in different colors : blue , red , green and yellow . the probability of drawing a blue ball is 1 / 8 . the probability of drawing a red ball is 2 / 5 . the probability of drawing a green ball is 7 / 10 . if a jar can not contain more than 50 balls , how many yellow balls are in the jar ?
Options: a ) 12 , b ) 15 , c ) 23 , d ) 7 , e ) 5
Rationale: answer of 1 st just add the given probabilities p ( blue ) + p ( red ) + p ( green ) i . e 1 / 8 + 2 / 5 + 3 / 10 = 5 + 16 + 12 / 40 now we know p ( blue ) + p ( red ) + p ( green ) + p ( yellow ) = 1 33 / 40 + p ( yellow ) = 1 p ( yellow ) = 33 / 40 i . e why yellow balls are 7 . d
Answer: d
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 3.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is e
Answer: e
Problem: find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm .
Options: a ) 150 sq . cm
b ) 120 sq . cm
c ) 130 sq . cm
d ) 125 sq . cm
e ) 110 sq . cm
Rationale: let abcd is a rhombus with diagonals ac and bd which intersect each other at o . ac = 24 ⇒ ao = 12 let bo = x and ab = 13 cm ( given ) by pythagorean theorem c 2 = a 2 + b 2 13 2 = 12 2 + x 2 169 = 144 + x 2 x 2 = 169 – 144 x 2 = 25 x = 5 cm bo = 5 cm diagonal bd = 2 x 5 = 10 cm . area = ½ x [ product of diagonals ] = ½ x 24 x 10 area = 120 sq . cm answer is b
Answer: b
Problem: there are 6 different travelers who each have a choice of vacationing at one of 10 different destinations . what is the probability that all 6 travelers will end up vacationing at the same destination ?
Options: a ) 0.1 , b ) 0.001 , c ) 0.0002 , d ) 1.0 e - 05 , e ) 0.0001
Rationale: prob that traveler 1 will choose 1 st place ( any particular place ) out 10 places = 1 / 10 prob that traveler 2 will choose same place out 10 places = 1 / 10 . . . . . . total = 1 / 10 * . . . 1 / 10 ( 6 times ) = 1 / 10 ^ 6 but this can happen for all of the 10 places . so prob = 10 / ( 10 ^ 6 ) = 1 / 10 ^ ( 6 - 1 ) = 0.00001 answer - d
Answer: d
Problem: of the 90 people in a room , 2 / 5 are women . if 2 / 3 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 26 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "women = 2 / 5 * 90 = 36 married = 2 / 3 * 90 = 60 unmarried = 30 max ( un - married women ) = 30 b"
Answer: b
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1 . 5 kmph . a man rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is
Options: a ) 16 hours , b ) 18 hours , c ) 20 hours , d ) 24 hours , e ) 28 hours
Rationale: "upstream = 9 kmph - 1.5 kmph = 7.5 kmph downstream = 9 kmph + 1.5 kmph = 10.5 kmph total time taken = 105 / 7.5 + 105 / 10.5 = 24 hrs answer : d"
Answer: d
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 83 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8300 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 83 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 83 = > total appeared candidates in state b = 83 x 100 = 8300 = > total appeared candidates in state a = total appeared candidates in state b = 8300"
Answer: b
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is :
Options: a ) 16 hours , b ) 18 hours , c ) 20 hours , d ) 24 hours , e ) 26 hours
Rationale: "speed of upstream = 9 - 1.5 = 7.5 kmph speed of down stream = 9 + 1.5 = 10.5 kmph total time = ( 105 / 7.5 ) + ( 105 / 10.5 ) = 24 hrs answer : d"
Answer: d
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 902 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 902 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 902 so , 3 y < 390 = = > y < 130 so , y can take any value which is less than 130 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . e"
Answer: e
Problem: alice is now 10 years older than bob . if in 6 years alice will be twice as old as bob , how old will alice be in 5 years ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: a = b + 10 so b = a - 10 . a + 6 = 2 ( b + 6 ) . a + 6 = 2 ( a - 10 + 6 ) . a + 6 = 2 a - 8 . a = 14 . in 5 years , alice will be 19 years old . the answer is a .
Answer: a
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,800 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,400 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 30 % , b ) 35 % , c ) 25 % , d ) 40 % , e ) 50 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 2800 : 8400 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : c"
Answer: c
Problem: thabo owns exactly 180 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 180 3 x + 60 + x = 180 x = 30 answer ( c . )"
Answer: c
Problem: a school has 7 maths 6 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: total subjects = 7 + 6 + 5 = 18 max subjects by 1 teacher = 3 so , min of teachers required = 18 / 3 = 6 answer : c
Answer: c
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 10 per sq m ?
Options: a ) 6350 , b ) 7357 , c ) 6328 , d ) 6750 , e ) 7560
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 10 = rs . 6750 answer : d"
Answer: d
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.36 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.48 , d ) 44 , e ) 48
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 36 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 36 = 48 cents . answer : e ."
Answer: e
Problem: at a certain high school , the senior class is twice the size of the junior class . if 3 / 8 of the seniors and 1 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 4
Rationale: "start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 3 / 8 ) * 200 = 75 and ( 1 / 4 ) * 100 = 25 . 75 + 25 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : d"
Answer: d
Problem: in a school with 604 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 151 , c ) 250 , d ) 350 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 600 - x ) . then , ( 11 3 / 4 × 604 ) ⇔ 11 x + 12 ( 604 - x ) ⇔ x = 7248 - 7097 ⇔ 151 . answer b"
Answer: b
Problem: when the price of an article was reduced by 20 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % 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 20 % , the new price is 0.8 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.8 p ) ( 1.8 n ) = 1.44 np , which is 1.44 times the old revenue , so is 44 % greater . answer : a"
Answer: a
Problem: a 110 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 31
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 110 = 31 answer : e"
Answer: e
Problem: sachin is younger than rahul by 8 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 26 , d ) 27 , e ) 28
Rationale: "if rahul age is x , then sachin age is x - 8 , so ( x - 8 ) / x = 7 / 9 = > 9 x - 72 = 7 x = > 2 x = 72 = > x = 36 so sachin age is 36 - 8 = 28 answer : e"
Answer: e
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length
Options: a ) 12 , b ) 12.1 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 20 = 12.1 sec . answer : option b"
Answer: b
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 25 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 36.25 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 25 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.25 . so his profit is $ 6.25 - $ 4 = $ 2.25 and his profit percent is ( 2.25 / 4 ) * 100 = 56.25 % answer : - d"
Answer: d
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 90 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: ( 110 mph + 90 mph ) / 2 = 100 mph correct answer is : d
Answer: d
Problem: in 30 years , a will be twice as old as b was 30 years ago . if a is now 5 years older than b , the present age of b is ?
Options: a ) 85 yrs , b ) 95 yrs , c ) 93 yrs , d ) 82 yrs , e ) 90 yrs
Rationale: "let b ' s present age = x years then a ' s present age = x + 5 years x + 5 + 30 = 2 ( x - 30 ) x + 35 = 2 x - 60 x = 95 years answer is b"
Answer: b
Problem: a jogger running at 9 kmph along side a railway track is 280 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 40 sec , c ) 36 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 280 + 120 ) m = 400 m . ∴ time taken = ( 400 ⁄ 10 ) sec = 40 sec . answer b"
Answer: b
Problem: what is the square root of 0.16
Options: a ) 0.4 , b ) 0.04 , c ) 0.004 , d ) 4 , e ) 1
Rationale: "explanation : as . 4 * . 4 = 0.16 option a"
Answer: a
Problem: an escalator moves towards the top level at the rate of 7 ft . sec and its length is 180 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 5 sec , b ) 25 sec , c ) 20 sec , d ) 15 sec , e ) 10 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 180 / ( 7 + 2 ) = 20 sec answer : c"
Answer: c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1000 resolutions ?
Options: a ) 1077 m , b ) 804 m , c ) 978 m , d ) 1048 m , e ) 878 v
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1000 resolutions . = 1000 * 2 * 22 / 7 * 22.4 = 104800 cm = 1408 m answer : d"
Answer: d
Problem: a garrison of 2000 men has provisions for 60 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1500 , b ) 1893 , c ) 1979 , d ) 1900 , e ) 1278
Rationale: "2000 - - - - 60 2000 - - - - 45 x - - - - - 20 x * 20 = 2000 * 45 x = 4500 2000 - - - - - - - 1500 answer : a"
Answer: a
Problem: anil grows tomatoes in his backyard which is in the shape of a square . each tomato takes 1 cm 2 in his backyard . this year , he has been able to grow 131 more tomatoes than last year . the shape of the backyard remained a square . how many tomatoes did anil produce this year ?
Options: a ) 4225
b ) 4096
c ) 4356
d ) insufficient data
e ) none of these
Rationale: detailed solution let the area of backyard be x 2 this year and y 2 last year ∴ x 2 - y 2 = 131 = ) ( x + y ) ( x - y ) = 131 now , 131 is a prime number ( a unique one too . check out its properties on google ) . also , always identify the prime number given in a question . might be helpful in cracking the solution . = ) ( x + y ) ( x - y ) = 131 x 1 = ) x + y = 131 x - y = 1 = ) 2 x = 132 = ) x = 66 and y = 65 ∴ number of tomatoes produced this year = 662 = 4356 correct choice ( c )
Answer: c
Problem: when asked what the time is , a person answered that the amount of time left is 1 / 5 of the time already completed . what is the time .
Options: a ) 2 , b ) 9 , c ) 3 , d ) 8 , e ) 6
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 15 x ⇒ x = 2024 − x = 15 x ⇒ x = 20 time is 8 pm answer : d"
Answer: d
Problem: a sum of money at simple interest amounts to rs . 1717 in 1 year and to rs . 1734 in 2 years . the sum is :
Options: a ) rs . 1200 , b ) rs . 1690 , c ) rs . 1600 , d ) rs . 1700 , e ) rs . 1500
Rationale: "s . i . for 1 year = rs . ( 1734 - 1717 ) = rs . 17 . principal = rs . ( 1717 - 17 ) = rs . 1700 . answer : option d"
Answer: d
Problem: if remainder is 8 , quotient is 43 and dividend is 997 then what is divisor ?
Options: a ) 21 , b ) 20 , c ) 23 , d ) 27 , e ) 31
Rationale: we know dividend = divisor * quotient + remainder = = = > 997 = divisor * 43 + 8 = = = = = > 989 / 43 = divisor = = = > divisor = 23 ans - c
Answer: c
Problem: victor gets 80 % marks in examinations . if these are 240 marks , find the maximum marks .
Options: a ) 334 , b ) 300 , c ) 376 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 80 % of m = 240 ⇒ 80 / 100 × m = 240 ⇒ m = ( 240 × 100 ) / 80 ⇒ m = 24000 / 80 ⇒ m = 300 therefore , maximum marks in the examinations are 300 answer : b"
Answer: b
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 10800 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 105.00 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 10800 ⇔ 12 x 2 = 10800 ⇔ x 2 = 900 ⇔ x = 30 . so , length = 90 m and breadth = 120 m . perimeter = [ 2 ( 90 + 120 ) ] m = 420 m . ∴ cost of fencing = rs . ( 0.25 × 420 ) = rs . 105.00 . answer d"
Answer: d
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 60 , what is the greatest possible value of q minus r ?
Options: a ) 52 , b ) 54 , c ) 55 , d ) 56 , e ) 58
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 60 . the greatest multiple of 9 which is less than 60 is 54 . the answer is b ."
Answer: b
Problem: there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 84 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ?
Options: a ) rs 450 , b ) rs 920 , c ) rs 550 , d ) rs . 630 , e ) none of these
Rationale: explanation : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 84 ? 7 x = 126 ? x = 18 therefore original expenditure = rs . ( 35 18 ) = rs . 630 . answer : d
Answer: d
Problem: 27 is a perfect cube . when x is added to the prime factor of 27 , the result is also a perfect cube . what is x ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "27 is 3 * 3 * 3 a 3 + 1 = 4 , 4 = 2 * 2 b 3 + 3 = 6 , 6 = 2 * 3 c 3 + 5 = 8 , 8 = 2 * 2 * 2 d 3 + 7 = 10 , 10 = 2 * 5 e 3 + 11 = 14 , 14 = 2 * 7 c is the only addition that gives a perfect cube ."
Answer: c
Problem: a 480 m long train is running at a speed of 55 km / hr . it crossed a platform of length 620 m in ?
Options: a ) 41.1 sec , b ) 72 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 480 m + 620 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 1100 m time = distance / speed = 1100 x 18 / ( 5 x 55 ) = 72 sec ans is : b"
Answer: b
Problem: if the sum and difference of two numbers are 15 and 10 respectively , then the difference of their square is :
Options: a ) 12 , b ) 150 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 15 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 15 * 10 = 150 . answer : b"
Answer: b
Problem: a batsman scored 100 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 40 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 100 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 100 - 60 = 40 required % = ( 40 / 100 ) × 100 = 40 % answer : option b"
Answer: b
Problem: a shopkeeper sold an article at $ 100 with 45 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 72 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 145 = $ 69 ( approximately ) answer is e"
Answer: e
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 4 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 2 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 3 * 2 = 6 miles . so , the distance between him and walt was 48 - 6 = 42 miles when walt left his house . now , their combined rate to cover this distance was 3 + 4 = 7 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 42 / 7 = 6 hours . total time that lionel was walking is 2 + 6 = 8 hours , which means that he covered in that time interval distance = rate * time = 3 * 8 = 24 miles . answer : d ."
Answer: d
Problem: the difference between the local value and the face value of 6 in the numeral 85475641 is
Options: a ) 459 , b ) 954 , c ) 594 , d ) 584 , e ) 458
Rationale: "explanation : ( local value of 6 ) - ( face value of 6 ) = ( 600 - 6 ) = 594 c )"
Answer: c
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 17 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 555 , d ) 664 , e ) 526
Rationale: 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 117 = rs . 526 answer : option e
Answer: e
Problem: 28 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.25 , b ) 38.25 , c ) 33.25 , d ) 12.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 28 = 12.25 answer : d"
Answer: d
Problem: a 35 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 10 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 35 = 10 answer : a"
Answer: a
Problem: car a is 30 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 4.5 , c ) 4.75 , d ) 3.75 , e ) 3.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 30 miles and drive 8 miles ahead so to drive 38 miles it ' ll need 38 / 8 = 3.5 hours . answer : c"
Answer: c
Problem: if a car went the first third of the distance at 80 kmh , the second third at 18 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 34 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 720 ( this number is convenient because it is divisible by 80 , 18 and 48 ) so : 720 = 80 * t 1 = 9 hrs 720 = 18 * t 2 = 40 hrs 720 = 48 * t 3 = 15 hrs t = t 1 + t 2 + t 3 = 64 hrs d = rt ( 720 * 3 ) = r * 64 r = 33.75 answer : a"
Answer: a
Problem: in a group of ducks and cows , the total number of legs are 22 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 22 = > 2 x = 22 = > x = 11 a"
Answer: a
Problem: how long does a train 110 meters long running at the rate of 36 km / hr take to cross a bridge 132 meters in length ?
Options: a ) 24.2 sec , b ) 30.6 sec , c ) 32.6 sec , d ) 28.1 sec , e ) 20.4 sec
Rationale: "distance = length of train + length of bridge = 110 + 132 = 242 speed = 36 km / hr = 36 * 5 / 18 = 10 m / s required time = 242 / 10 = 24.2 seconds answer is a"
Answer: a
Problem: a certain airline ' s fleet consisted of 100 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let x be the number of years . 4 x > 100 - 3 x 7 x > 100 x > 14 + 2 / 7 the answer is b ."
Answer: b
Problem: the price of an article is cut by 10 % . to restore it to the former value , the new price must be increased by
Options: a ) 10 % , b ) 9 1 / 11 % , c ) 11 1 / 9 % , d ) 11 % , e ) none
Rationale: "explanation : let original price = rs . 100 then , new price = rs . 90 increase on rs . 90 = rs . 100 increase % = ( 10 / 90 × 100 ) % = 11 1 / 9 % correct option : c"
Answer: c
Problem: on dividing 23 by a number , the quotient is 5 and the remainder is 3 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7
Rationale: d = ( d - r ) / q = ( 23 - 3 ) / 5 = 20 / 5 = 4 c
Answer: c
Problem: ( 2 ^ 2 + 4 ^ 2 + 6 ^ 2 + . . . . . + 14 ^ 2 ) = ?
Options: a ) 88 , b ) 560 , c ) 99 , d ) 550 , e ) 540
Rationale: = ( 1 x 2 ) ^ 2 + ( 2 x 2 ) ^ 2 , + ( 2 x 3 ) ^ 3 + . . . . . . ( 2 x 7 ) ^ 2 = 2 ^ 2 x ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . . . . . + 7 ^ 2 ) formula is = 1 / 6 n ( n + 1 ) ( 2 n + 1 ) = ( 4 x 1 / 6 x 7 x 8 x 15 ) = ( 4 x 140 ) = 560 answer is b
Answer: b
Problem: a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 2 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 46 , c ) 49 , d ) 54 , e ) 86
Rationale: "n = 4 k + 1 = 5 j + 2 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 5 j + 2 . 1 , 5 , 9 , 13 , 17 = 5 ( 3 ) + 2 the next such number is 17 + 4 * 5 = 37 . 17 + 37 = 54 the answer is d ."
Answer: d
Problem: find large number from below question the difference of two numbers is 100 . on dividing the larger number by the smaller , we get 9 as quotient and the 4 as remainder
Options: a ) 120 , b ) 100 , c ) 112 , d ) 150 , e ) 105
Rationale: "let the smaller number be x . then larger number = ( x + 100 ) . x + 100 = 9 x + 4 8 x = 96 x = 12 large number = 12 + 100 = 112 c"
Answer: c
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.30 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 5.20 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.3 ) = $ 4.2 ( as the charge is 0.3 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 4.2 = 5.2 answer is d ."
Answer: d
Problem: there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 18 , then find the smaller number ?
Options: a ) 30 , b ) 66 , c ) 77 , d ) 88 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 18 3 x = 18 = > x = 6 = > smaller number = 5 x = 30 . answer : a"
Answer: a
Problem: find the area of trapezium whose parallel sides are 18 cm and 12 cm long , and the distance between them is 14 cm ?
Options: a ) 288 cm 2 , b ) 277 cm 2 , c ) 224 cm 2 , d ) 226 cm 2 , e ) 227 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 18 + 12 ) * ( 14 ) = 224 cm 2 answer : c"
Answer: c
Problem: the function f ( x ) = x + 4 is given . solve the equation : [ 3 . f ( x - 2 ) ] / f ( 0 ) + 4 = f ( 2 x + 1 )
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) none of these
Rationale: solution : we calculate f ( 0 ) , f ( x - 2 ) , f ( 2 x + 1 ) , namely f ( 0 ) = 0 + 4 = 4 ; f ( x - 2 ) = x - 2 + 4 = x + 2 ; f ( 2 x + 1 ) = 2 x + 1 + 4 = 2 x + 5 the equation gets this look [ 3 ( x + 2 ) ] / 4 + 4 = 2 x + 5 < = > 3 ( x + 2 ) + 16 = 4 ( 2 x + 5 ) < = > 3 x + 6 + 16 = 8 x + 20 < = > 22 - 20 = 8 x - 3 x < = > 2 = 5 x < = > x = 0.4 answer c
Answer: c
Problem: a 340 - liter solution of kola is made from 80 % water , 6 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 14 % .
Rationale: denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 80 - . 06 ) + 3.2 340 ( 0.14 ) + 3.2 47.6 + 3.2 50.8 ratio : 50.8 / 360 = 0.14 answer : e
Answer: e
Problem: find the largest 6 digit number which is exactly divisible by 88 ?
Options: a ) 998765 , b ) 998907 , c ) 999944 , d ) 999954 , e ) 999990
Rationale: largest 6 digit number is 999999 after doing 999999 ÷ 88 we get remainder 55 hence largest 6 digit number exactly divisible by 88 = 999999 - 55 = 999944 c
Answer: c
Problem: ( 0.12 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.12 ) ( power 2 ) + 0.012 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them
Rationale: "given expression = ( 0.12 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.12 ) ( power 2 ) + ( 0.12 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.12 - 0.1 ) = 0.02 answer is e ."
Answer: e
Problem: if the sum of two numbers is 18 and the sum of their squares is 220 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 52 , d ) 88 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 18 and x 2 + y 2 = 220 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 18 ) 2 - 220 = 324 - 220 = 104 xy = 52 . answer c"
Answer: c
Problem: how many positive integers less than 10,000 are there in which the sum of the digits equals 5 ?
Options: a ) 31 , b ) 51 , c ) 56 , d ) 62 , e ) 93
Rationale: basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a separator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit separators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . answer : c
Answer: c
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 20 percent . the enrollment on january 1 , 1993 , was 50 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: 1.20 x = 50 - - > 6 / 5 * x = 50 - - > x = 50 * 5 / 6 = 250 / 6 = ~ 42 . answer : e .
Answer: e
Problem: if the remainder is 7 when positive integer n is divided by 10 , what is the remainder when n is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 2
Rationale: "assume x is quotient here , n = 10 x + 7 - - - - - - - - - - ( 1 ) and n = 5 x + ? we can also write equation ( 1 ) as : n = ( 10 x + 5 ) + 2 . ie 5 ( 2 x + 1 ) + 1 ie the first term is perfectly divisible by 5 . so , the remainder left is 2 so , answer ( e ) is right choice ."
Answer: e
Problem: on a sum of money , the simple interest for 2 years is rs . 330 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 6.06 % , d ) 10.5 % , e ) 11.5 %
Rationale: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 330 = 10 ( r ã — si ) / ( 2 ã — 100 ) = 10 ( r ã — 330 ) / ( 2 ã — 100 ) = 10 r = 6.06 % answer : option c"
Answer: c
Problem: the average age of 30 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 41 , e ) 36
Rationale: "total age of 50 students = 30 * 10 = 300 total age of 51 persons = 31 * 11 = 341 age of teacher = 341 - 300 = 41 years answer is d"
Answer: d
Problem: what must be added to each term of the ratio 7 : 11 , so as to make it equal to 3 : 4 ?
Options: a ) 8 , b ) 7.5 , c ) 6.5 , d ) 5 , e ) 6
Rationale: "solution : let x be added to each term . according to question , ( 7 + x ) / ( 11 + x ) = 3 / 4 ; or , 33 + 3 x = 28 + 4 x ; or , x = 5 . answer : option d"
Answer: d
Problem: jaime earned enough money by selling seashells at 22 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 11 , c ) 17 , d ) 25 , e ) 30
Rationale: "let ' s test answer a : 5 seashells . . . with 5 seashells , jamie would have 5 ( 22 ) = 110 cents . this would allow him to buy 2 books for 110 cents total , so this is the correct answer . a"
Answer: a
Problem: the water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 4500 , d ) 1200 , e ) 5625
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 20 * 1 / 2 = 600 feet ^ 3 of water must be removed , which equals to 600 * 7.5 = 4500 gallons . answer : c ."
Answer: c
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 57 ?
Options: a ) 3944 , b ) 920 , c ) 7290 , d ) 3876 , e ) 3729
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 57 = rs . 3876 . answer : option d"
Answer: d
Problem: 3 friends alice , bond and charlie divide $ 1105 amongs them in such a way that if $ 10 , $ 20 and $ 15 are removed from the sums that alice , bond and charlie received respectively , then the share of the sums that they got will be in the ratio of 11 : 18 : 24 . how much did charlie receive ?
Options: a ) $ 495 , b ) $ 510 , c ) $ 480 , d ) $ 375 , e ) $ 360
Rationale: explanatory answer let the sums of money received by a , b and c be x , y and z respectively . then x - 10 : y - 20 : z - 15 is 11 a : 18 a : 24 a when $ 10 , $ 20 and $ 15 are removed , we are removing a total of $ 45 from $ 1105 . therefore , 11 a + 18 a + 24 a = 1105 - 45 = 1060 i . e . , 53 a = 1060 or a = 20 . we know that z - 15 = 24 a = 24 * 20 = 480 therefore , z = 480 + 15 = $ 495 correct choice is ( a )
Answer: a
Problem: mother , her daughter and her grand child weighs 150 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 42 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 150 kg daughter + child = 60 kg mother = 150 - 60 = 90 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 90 = 18 kg so now daughter = 120 - ( mother + child ) = 150 - ( 90 + 18 ) = 42 kg answer : c"
Answer: c
Problem: in a weight - lifting competition , the total weight of joe ' s two lifts was 900 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 400
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 900 pounds . we sum the two variables to obtain : f + s = 900 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 900 3 f = 1,200 f = 400 answer is e ."
Answer: e
Problem: the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 14 and 16 . the larger of the two numbers is
Options: a ) 276 , b ) 299 , c ) 312 , d ) 400 , e ) none
Rationale: "solution clearly , the numbers are ( 25 x 14 ) and ( 25 x 16 ) . larger number = ( 25 x 16 ) = 400 . answer d"
Answer: d
Problem: in what time will a train 180 meters long cross an electric pole , if its speed is 154 km / hr
Options: a ) 5 seconds , b ) 4.3 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 154 * ( 5 / 18 ) = 42 m / sec time = distance / speed = 180 / 42 = 4.3 seconds option b"
Answer: b
Problem: a miniature roulette wheel is divided into 9 equal sectors , each bearing a distinct integer from 1 to 9 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun four times , approximately what is the probability that the product of the four winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 80 % , d ) 90 % , e ) 95 %
Rationale: "the only way to have an odd product is if all 4 integers are odd . p ( odd product ) = 5 / 9 * 5 / 9 * 5 / 9 * 5 / 9 = 625 / 6561 p ( even product ) = 1 - 625 / 6561 = 5936 / 6561 which is about 90 % the answer is d ."
Answer: d
Problem: an article is bought for rs . 575 and sold for rs . 675 , find the gain percent ?
Options: a ) 17.39 % , b ) 33 1 / 6 % , c ) 33 1 / 3 % , d ) 38 1 / 3 % , e ) 33 2 / 3 %
Rationale: "575 - - - - 100 100 - - - - ? = > 17.39 % answer : a"
Answer: a
Problem: a cycle is bought for rs . 900 and sold for rs . 1150 , find the gain percent ?
Options: a ) 15 , b ) 20 , c ) 27.77 , d ) 40 , e ) 12
Rationale: "900 - - - - 250 100 - - - - ? = > 27.77 % answer : c"
Answer: c
Problem: an employer pays rs . 20 for each day a worker works and for felts rs . 3 for each day is ideal at the end of sixty days a worker gets rs . 280 . for how many days did the worker remain ideal ?
Options: a ) 10 , b ) 40 , c ) 30 , d ) 20 , e ) 50
Rationale: suppose a worker remained ideal for x days then he worked for 60 - x days 20 * ( 60 - x ) - 3 x = 280 1200 - 23 x = 280 23 x = 920 x = 40 answer is b .
Answer: b
Problem: a train usually travels at a speed of 72 kmph crossing a pole in 7 sec , what would be the length of the train ?
Options: a ) 140 m , b ) 142 m , c ) 146 m , d ) 152 m , e ) 158 m
Rationale: explanation : d = 72 * 5 / 18 * 7 = 140 m answer : option a
Answer: a
Problem: a man received a cheque . the amount in rs . has been transposed for paise and vice versa . after spending rs . 5 and 42 paise , he discovered he now had exactly 6 times the value of the correct cheque amount . what amount he should have received ?
Options: a ) rs 5.30 , b ) rs 6.44 , c ) rs 60.44 , d ) rs 16.44 , e ) none of these
Rationale: explanation : option 4 : - on reversal will be 44 rs 16 ps , after spending 5 rs 42 ps , remaining will be around 40 rs which is not 6 times 16 rs 44 ps . option 3 : - on reversal will lead a smaller value . hence we can eliminate that as well . option 1 : - on reversal is 30 rs 5 paise , after spending 5 rs 42 ps , remaining will be 24 rs 63 paise , 24 rs 63 ps is not 6 times 5 rs 30 paise . option 2 on reversal is 44 rs 06 paise , after spending 5 rs 42 ps , remaining will be 38 rs 64 ps , which is 6 times 6 rs 44 paise . hence rs 6.44 is the answer . we need not even consider option 4 and option 3 as reversed number itself is not 6 times the original number . option 1 when reversed is odd , and when even ( 5 rs 42 ps ) is subtracted from odd , we get a odd number , and an odd number can not be 6 times another number answer : b
Answer: b
Problem: if 30 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 20 %
Rationale: "30 % of ( x - y ) = 20 % of ( x + y ) 30 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 5 y required percentage = y / x * 100 = y / 5 y * 100 = 20 % answer is e"
Answer: e
Problem: the digit in units place of the product 81 x 82 x . . . . . x 89 is
Options: a ) 0 , b ) 2 , c ) 6 , d ) 8 , e ) 9
Rationale: sol . required digit = unit digit in ( 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 ) = 0 . answer a
Answer: a
Problem: alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 5800 gain = 5800 - 5500 = $ 300 gain % = 300 / 5500 * 100 = 5.45 % answer is a"
Answer: a
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 380 m long platform ?
Options: a ) 50 , b ) 27 , c ) 29 , d ) 47 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 380 ) / 36 * 5 / 18 = 50 min . answer : a"
Answer: a
Problem: find the value of 3 + 2 • ( 8 – 3 )
Options: a ) ( a ) 25 , b ) ( b ) 13 , c ) ( c ) 17 , d ) ( d ) 24 , e ) ( e ) 15
Rationale: "3 + 2 • ( 8 – 3 ) = 3 + 2 ( 5 ) = 3 + 2 × 5 = 3 + 10 = 13 answer : ( d )"
Answer: d
Problem: if the height of a cone is increased by 160 % then its volume is increased by ?
Options: a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 160
Rationale: "160 % answer : e"
Answer: e
Problem: if x is an integer and 2.134 × 10 ^ x is less than 210,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "21340 * 10 ^ - 4 * 10 ^ x < 210,000 , x = 4 because the next zero on the right side will make 21,340 > 210,000 answer d ,"
Answer: d