regisss/math_qa huggingface dataset:
Problem: what sum of money will produce rs . 75 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 337 , b ) 500 , c ) 266 , d ) 288 , e ) 536
Rationale: "75 = ( p * 4 * 7 / 2 ) / 100 p = 536 answer : e"
Answer: e
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 16000 , then find his savings ?
Options: a ) 3600 , b ) 3607 , c ) 3200 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 16000 = > x = 3200 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3200 . answer : c"
Answer: c
Problem: a certain fraction has the same ratio to 1 / 33 , as 3 / 4 does to 7 / 11 . what is this certain fraction ?
Options: a ) 1 / 14 , b ) 1 / 18 , c ) 1 / 21 , d ) 1 / 25 , e ) 1 / 28
Rationale: "x / ( 1 / 33 ) = ( 3 / 4 ) / ( 7 / 11 ) x = 3 * 11 * 1 / 33 * 4 * 7 = 1 / 28 the answer is e ."
Answer: e
Problem: a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 38 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 4.0
Rationale: "in the third time interval the average speed of the car was 38 + 5 + 5 = 30 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 48 * 1 / 12 = 4 miles . answer : e ."
Answer: e
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 1 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 1 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 1 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 1 / 7 x 1 / 5 = 1 / 35 answer : a"
Answer: a
Problem: if a and b are distinct positive integers . the units digit of a ^ 2 is equal to the units digit of a , and the units digit of b ^ 2 is equal to the units digit of b . if the units digit of a · b is equal to neither the units digit of a nor the units digit of b , then what is the units digit of a · b ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: there are four digits which when squared give the same units digits : 0 , 1 , 5 , 6 0 ^ 2 = 0 1 ^ 2 = 1 5 ^ 2 = 25 6 ^ 2 = 36 so a and b must take 2 of these values . they are positive integers so 0 is not possible . if one of the digits is 1 , when the other is multiplied by 1 , you will get the same digit . 1 * 5 = 5 so 1 is out of the picture . then you have only two digits left 5 and 6 . so out of a and b , one must be 5 and the other 6 . 5 * 6 = 30 so units digit of their product = 0 answer ( a )
Answer: a
Problem: what is the next number : 3 , 27 , 627 , __
Options: a ) 8847 , b ) 9837 , c ) 11,497 , d ) 15,627 , e ) 19,307
Rationale: "5 ^ 0 + 2 = 3 5 ^ 2 + 2 = 27 5 ^ 4 + 2 = 627 5 ^ 6 + 2 = 15,627 the answer is d ."
Answer: d
Problem: if the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 2 , what is the ratio of apples to cucumbers ?
Options: a ) 6 : 5 , b ) 1 : 4 , c ) 4 : 3 , d ) 2 : 3 , e ) 5 : 4
Rationale: "the ratio of bananas to cucumbers is 1 to 2 which equals 2 to 4 . the ratio of apples to bananas to cucumbers is 5 to 2 to 4 . the ratio of apples to cucumbers is 5 to 4 . the answer is e ."
Answer: e
Problem: what is the least integer greater than 1 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( 1 ) + ( 0.5 ) = 1.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from 1 to 1.5 ) . next , the question asks for the least integer that is greater than 1.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of 1.5 is 2 . final answer : e"
Answer: e
Problem: when 242 is divided by a certain divisor the remainder obtained is 6 . when 698 is divided by the same divisor the remainder obtained is 13 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 23 , e ) none of these
Rationale: "let that divisor be x since remainder is 6 or 13 it means divisor is greater than 13 . now 242 - 6 = 236 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 13 = 685 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 236 + 685 ) + 6 + 13 = x ( k + l ) + 19 when we divide this number by x then remainder will be equal to remainder of ( 19 divided by x ) = 5 hence x = 19 - 5 = 14 hence b"
Answer: b
Problem: in a river flowing at 2 km / hr , a boat travels 56 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 21 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 56 km total time taken = time taken downstream + time taken upstream = ( 56 / 8 ) + ( 56 / 4 ) = 21 hr . answer : option d"
Answer: d
Problem: a certain rectangular crate measures 8 feet by 12 feet by 14 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 6 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . so to maximize the above eqn , radius may be of 9 , 10,12 one of the base area ( 8 x 12 , 14 x 12 or 8 x 14 ) r is maximum for base 14 x 12 and 12 can be maximum value so r = 10 / 2 = 6 a"
Answer: a
Problem: there are 640 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 375 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 640 . hence 3 x + 5 x = 640 solve for x 8 x = 640 x = 80 number of boys 3 x = 3 × 80 = 240 number of girls 5 x = 5 × 80 = 400 e"
Answer: e
Problem: a ratio between two numbers is 5 : 4 and their l . c . m . is 80 . the first number is
Options: a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 5 x and 4 x . then , their l . c . m . is 20 x . ∴ 20 x = 80 ⇔ x = 4 . hence , the first number is 20 . answer c"
Answer: c
Problem: if the simple interest on a sum of money for 3 years at 7 % per annum is rs . 570 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 610.83 , b ) rs . 810.83 , c ) rs . 617 , d ) rs . 618 , e ) rs . 610.83
Rationale: "sum = ( 570 * 100 ) / ( 7 * 3 ) = rs . 2 , 714.29 amount = [ 2 , 714.29 * ( 1 + 7 / 100 ) 3 ] = rs . 3 , 325.12 c . i . = ( 3 , 325.12 - 2 , 714.29 ) = rs . 610.83 . answer : e"
Answer: e
Problem: what is the least number that should be added to 1055 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1055 / 23 ) gives a remainder 20 so we need to add 3 . the answer is c ."
Answer: c
Problem: an entry in an unshaded square is obtained by adding the entries connected to it from the row above ( 11 is one such number ) . write the value of n ?
Options: a ) 10
b ) 11
c ) 12
d ) 9
e ) 8
Rationale: see the values row wise 5 6 n 7 11 6 + n 7 + n 11 + 6 + n 6 + n + 7 + n 60 hence 11 + 6 + n + 6 + n + 7 + n = 60 n = 10 answer : a
Answer: a
Problem: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 65 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 10 , c ) 15 , d ) 20 , e ) 30
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 65 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 65 x 1 ( a = 6 , b = 5 respectively we have = 30 ) . this is the greatest possible value of b x a . imo e ."
Answer: e
Problem: a computer factory produces 3024 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 3024 / ( 28 * 24 * 2 ) = 2.25 answer a"
Answer: a
Problem: a man has rs . 400 in the denominations of one - rupee notes , 5 - rupee notes and 10 rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 90 , e ) 95
Rationale: let number of notes of each denomination be x . then x + 5 x + 10 x = 400 16 x = 400 x = 25 . hence , total number of notes = 3 x = 75 answer : option c
Answer: c
Problem: in a sports club with 30 members , 17 play badminton and 17 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 17 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 17 - x ) + x + 2 = 30 36 - 2 x + x = 30 36 - x = 30 x = 6 so 6 members play both badminton and tennis . b"
Answer: b
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5000 = ?
Options: a ) 392 , b ) 229 , c ) 753 , d ) 750 , e ) 540
Rationale: "d 750 ? = 5000 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 750"
Answer: d
Problem: if x / y = 2 / z , then 5 x ^ 2 =
Options: a ) y / z , b ) 20 y ² / z ² , c ) y ² z ² , d ) 5 y ² / z ² , e ) yz
Rationale: "this question is most easily solved by isolating y in the equation and substituting into the expression 5 x ² : x / y = 2 / z x = 2 y / z if we substitute 2 y / z into the expression for x , we get : 5 ( 2 y / z ) ² = 5 ( 4 y ² / z ² ) = 20 y ² / z ² . the correct answer is choice ( b )"
Answer: b
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 25 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 30 meters . what distance is she from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 55 m east
Rationale: "the net distance is 25 + 30 = 55 meters to the east . the answer is e ."
Answer: e
Problem: in a sample of associates at a law firm , 25 percent are second - year associates , and 75 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?
Options: a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "75 percent are not first - year associates - - > this means 75 percent associates are either two or more than two years already , we know % of second - year associates = 25 % so , % of associates there for more than two years = 75 % - 25 % = 50 % . . = > ( c ) . . is it correct ?"
Answer: c
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 10 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 12 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 10 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 10 hence x = 12 . answer is d"
Answer: d
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 300,000 and only 1 % on a company ’ s payroll above $ 300,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 230,000 , d ) $ 400,000 , e ) $ 2 , 200,000
Rationale: "answer : c , ( with different approach ) : the 300 paid is 1 % of the additional amount above 200,000 . let it be x now 1 % of x = 300 therefore x = 30,000 total = 200,000 + x = 230,000"
Answer: c
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 18 , 828.80 , b ) rs . 19 , 828.80 , c ) rs . 18 , 028.80 , d ) rs . 17 , 828.80 , e ) none of these
Rationale: "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : b"
Answer: b
Problem: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability r this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability r of cgd / ( cg ) - > 3 / 19 answer d"
Answer: d
Problem: if a / b = 5 / 4 , then ( 4 a + 3 b ) / ( 4 a - 3 b ) = ?
Options: a ) 7 , b ) 6 , c ) 3 , d ) 5 , e ) 4
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 4 a + 3 b ) / ( 4 a - 3 b ) = ( 4 a / b + 3 ) / ( 4 a / b - 3 ) since a / b = 5 / 4 this implies that = [ ( 4 * 5 ) / 4 + 3 ] / [ ( 4 * 5 ) / 4 - 3 ) ] = ( 5 + 3 ) / ( 5 - 3 ) = 4 option : e"
Answer: e
Problem: total 63 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64
Rationale: "64 players answer : e"
Answer: e
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2012 ) = ?
Options: a ) 2013 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2012 ) = 2013 ans : a"
Answer: a
Problem: what is ( 21 ^ 7 + 21 ) / 21 ?
Options: a ) 82216043 , b ) 83786095 , c ) 84316108 , d ) 85766122 , e ) 86426237
Rationale: ( 21 ^ 7 + 21 ) / 21 = 21 * ( 21 ^ 6 + 1 ) / 21 = 21 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is d .
Answer: d
Problem: if 102 x = 25 , then 10 - x equals :
Options: a ) a ) 3 , b ) b ) 2 , c ) c ) 6 , d ) d ) 9 , e ) e ) 1 / 5
Rationale: "102 x = 25 ( 10 x ) 2 = 52 10 x = 5 1 / 10 x = 1 / 5 10 - x = 1 / 5 answer : e"
Answer: e
Problem: in an examination 35 % of the students passed and 520 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 800 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 520 65 x / 100 = 520 x = 520 * 100 / 65 = 800 answer is c"
Answer: c
Problem: a cube has a volume of 343 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 24 , b ) 48 , c ) 64 , d ) 2744 , e ) 100
Rationale: "volume = 343 = side ^ 3 i . e . side of cube = 7 new cube has dimensions 14 , 14 , and 14 as all sides are twice of teh side of first cube volume = 14 * 14 * 14 = 2744 square feet answer : option d"
Answer: d
Problem: a train crosses a platform of 170 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 70 , b ) 88 , c ) 167 , d ) 197 , e ) 161
Rationale: "length of the train be ‘ x ’ x + 170 / 15 = x + 250 / 20 20 x + 3400 = 15 x + 3750 5 x = 350 x = 70 m answer : a"
Answer: a
Problem: a 6 litre sol is 25 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3 , e ) e . 5.4
Rationale: "25 % of 6 = 1.5 50 % of 6 = 3 shortage is 1.5 so we need to have 1.5 / 50 % to get 50 % alcohol content . = 3 d"
Answer: d
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 40 ps per meter is ?
Options: a ) 287 , b ) 369 , c ) 100 , d ) 279 , e ) 361
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.40 = rs . 100 answer : c"
Answer: c
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2000 , then what is the income of p 1 ?
Options: a ) s . 5000 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 2000 … ( i ) and 4 x – 2 y = 2000 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2000 - > x = 1000 p 1 ’ s income = rs 5 * 1000 = rs . 5000 answer : a"
Answer: a
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 26 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 99
Rationale: "use the options . the options which after getting added to 26 shows a cube of a number could be right . here 64 + 26 = 90 72 + 26 = 98 86 + 26 = 112 98 + 26 + 124 99 + 26 = 125 - - - ( 5 * 5 * 5 ) so we have 99 as the answer ! e"
Answer: e
Problem: in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 320 points , how many points is the third question worth ?
Options: a ) 39 , b ) 24 , c ) 22 , d ) 20 , e ) 18
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 320 10 x = 140 x = 14 3 rd question = x + 8 = 14 + 8 = 22 answer c"
Answer: c
Problem: it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 32 of the dish ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . after 25 days , the dish was 1 / 32 full . the answer is a ."
Answer: a
Problem: rahim bought 32 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 20
Rationale: "average price per book = ( 1500 + 340 ) / ( 32 + 60 ) = 1840 / 92 = rs . 20 answer : e"
Answer: e
Problem: the average of numbers 0.64204 , 0.64203 , 0.64202 and 0.64201 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642025 , e ) none
Rationale: "answer average = ( 0.64204 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.5681 / 4 = 0.642025 correct option : d"
Answer: d
Problem: there are 16 teams in a tournament . if during the first round , each team plays every other team exactly once , how many games will be played in the first round ?
Options: a ) 15 , b ) 30 , c ) 120 , d ) 240 , e ) 256
Rationale: number of ways to pick 2 teams from a total of 16 = 16 c 2 = 16 ! / 14 ! * 2 ! = 120 . hence c .
Answer: c
Problem: there are 193 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 25 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 110 , d ) 98 , e ) 108
Rationale: you had the answer almost right . the x = 85 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 85 + 25 = 110 c
Answer: c
Problem: 18 balls are numbered 1 to 18 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 2 / 9 , b ) 4 / 17 , c ) 6 / 29 , d ) 8 / 35 , e ) 10 / 43
Rationale: "p ( 1 st ball is even ) = 9 / 18 p ( 2 nd ball is also even ) = 8 / 17 p ( both balls are even ) = 9 / 18 * 8 / 17 = 4 / 17 the answer is b ."
Answer: b
Problem: what is the probability that the sum of two dice will yield a 8 , and then when both are thrown again , their sum will again yield a 8 ? assume that each die has 7 sides with faces numbered 1 to 7 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 49
Rationale: "solution - rolling dices is an independent event . the combinations to get 8 are ( 1,7 ) , ( 7,1 ) , ( 2,6 ) , ( 6,2 ) , ( 3,5 ) , ( 5,3 ) , ( 4 , , 4 ) and total combinations of both dices is 49 . the probability of getting 8 in first attempt is 7 / 49 = 1 / 7 . probability of getting 8 again in second attempt = ( 1 / 7 ) * ( 1 / 7 ) = 1 / 49 . ans e"
Answer: e
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 15 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 277 , c ) 187 , d ) 257 , e ) 150
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 15 sec = 15 * 10 = 150 m . the length of the faster train = 150 m . answer : e"
Answer: e
Problem: a man swims downstream 72 km and upstream 45 km taking 12 hours each time ; what is the speed of the current ?
Options: a ) 1.125 , b ) 1.128 , c ) 1.126 , d ) 1.123 , e ) 1.121
Rationale: "72 - - - 12 ds = 6 ? - - - - 1 45 - - - - 12 us = 3.75 ? - - - - 1 s = ? s = ( 6 - 3.75 ) / 2 = 1.125 answer : a"
Answer: a
Problem: find the simple interest on rs . 850 for 10 months at 7 paisa per month ?
Options: a ) s . 768 , b ) s . 329 , c ) s . 595 , d ) s . 600 , e ) s . 725
Rationale: "explanation : i = ( 850 * 10 * 7 ) / 100 = 595 answer : option c"
Answer: c
Problem: sandy bought 65 books for $ 1480 from one shop and 55 books for $ 920 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 38 , b ) $ 18 , c ) $ 99 , d ) $ 27 , e ) $ 20
Rationale: "average price per book = ( 1480 + 920 ) / ( 65 + 55 ) = 2400 / 120 = $ 20 the answer is e ."
Answer: e
Problem: how many of the positive divisors d of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . d = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Problem: calculate 1307 x 1307 = ?
Options: a ) 1601249 , b ) 1607249 , c ) 1701249 , d ) 1708249 , e ) none
Rationale: "answer 1307 x 1307 = ( 1307 ) 2 = ( 1300 + 7 ) 2 = ( 1300 ) 2 + ( 7 ) 2 + 2 x 1300 x 7 = 1690000 + 49 + 18200 = 1708249 option : d"
Answer: d
Problem: the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 80 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 4 / 63 , e ) none
Rationale: "answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 80 / 1260 = 4 / 63 correct option : d"
Answer: d
Problem: bottle r contains 100 capsules and costs $ 6.30 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.04 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002
Rationale: "cost per capsule in r is 6.30 / 100 = 0.063 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.004 the answer is a"
Answer: a
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 250 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 183
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 250 newborn 250 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 183 is expected to survive . answer : e ."
Answer: e
Problem: if 3 a = 4 b and ab ≠ 0 , what is the ratio of a / 4 to b / 3 ?
Options: a ) 64 / 27 , b ) 9 / 16 , c ) 1 , d ) 6 / 8 , e ) 8 / 6
Rationale: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 3 a = 4 b here ' s one pair : a = 4 and b = 3 what is the ratio of a / 9 to b / 8 ? in other words , what is the value of ( a / 4 ) / ( b / 3 ) ? plug in values to get : ( a / 4 ) / ( b / 3 ) = ( 4 / 4 ) / ( 3 / 3 ) = 1 / 1 = 1 c"
Answer: c
Problem: what is the smallest integer x such that 2 x + 2 is divisible by 33 , 44 , 55 , and 666 ?
Options: a ) x = 53186760 , b ) x = 26593379 , c ) x = 73260 , d ) x = 36629 , e ) x = 6666
Rationale: 33 = 3 * 11 44 = 2 * 2 * 11 55 = 5 * 11 666 = 2 * 3 * 3 * 37 so 2 x + 2 = 2 * 2 * 3 * 3 * 5 * 11 * 37 = 73260 , and x = ( 73260 - 2 ) / 2 = 36629 , which is option d .
Answer: d
Problem: if 12 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 44 days
Rationale: "12 * 80 = 20 * x x = 48 days answer : d"
Answer: d
Problem: 5358 x 81 = ?
Options: a ) 423762 , b ) 433758 , c ) 433298 , d ) 433998 , e ) 437382
Rationale: "d 273258 5358 x 81 = 5358 x ( 80 + 1 ) = 5358 x 80 + 5358 x 1 = 428640 + 5358 = 433998"
Answer: d
Problem: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 126 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 5 , e ) 1 / 5
Rationale: "126 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 126 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 126 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 125 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 125 = r ^ 3 r = 5 d"
Answer: d
Problem: there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 15 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 45 , d ) 60 , e ) 120
Rationale: "each person is one participant of 6 games . so there are in all 6 * 15 = 90 instances of one participant games . but each game has 2 participants so total number of games = 90 / 2 = 45 c"
Answer: c
Problem: tough and tricky questions : probability . medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote . what fraction of a group of 1000 people could be expected to be killed if infected and not treated for 3 full days ?
Options: a ) 37 / 64 , b ) 8 / 27 , c ) 2 / 3 , d ) 19 / 27 , e ) 65 / 81
Rationale: at the end of each day we will have 3 / 4 alive . so after 3 days we will have ( 3 / 4 ) ^ 3 people alive . therefore , fraction of dead people will be 1 - ( 3 / 4 ) ^ 3 = 37 / 64 . the correct answer is a .
Answer: a
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 10800 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 10800 ] – [ 3 1 / 3 % of rs . 10800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 10800 = 1 / 6 % of rs . 10800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 10800 ] = rs . 18 . answer is d ."
Answer: d
Problem: in 1985 a company sold a brand of shoes to retailers for a fixed price per pair . in 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent , while the price per pair increased by 20 percent . if the company ’ s revenue from the sale of the shoes in 1986 was $ 3.0 million , what was the approximate revenue from the sale of the shoes in 1985 ?
Options: a ) $ 2.4 million , b ) $ 2.9 million , c ) $ 3.0 million , d ) $ 3.1 million , e ) $ 3.6 million
Rationale: let the number of pairs of shoes sold in 1985 = n let price per pair of shoe sold in 1985 = p in 1986 , number of pairs of shoes sold decreased by 20 % = . 8 n price per pair increased by 20 % = 1.2 p company ' s revenue from sale of shoes in 1986 = 3 million $ = > . 8 n * 1.2 p = 3 = > . 96 np = 3 = > np = 3 / . 96 = 3.125 million $ answer d
Answer: d
Problem: the ratio of the volumes of two cubes is 3375 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 225 : 121 , b ) 221 : 127 , c ) 225 : 191 , d ) 181 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 3375 : ³ √ 1331 = 15 : 11 ratio of surface areas = 15 ^ 2 : 11 ^ 2 = 225 : 121 answer : option a"
Answer: a
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 2 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 / 4 , b ) 4 , c ) 18 / 19 , d ) 9 , e ) 12
Rationale: yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 2 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 2 lets say x machines are used to attain the desired rate , thus x / 36 + x / 2 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 18 x ) / 36 = 1 / 2 19 x / 36 = 1 / 2 x = 18 / 19 . qa = 18 / 19 ( answer c )
Answer: c
Problem: the difference between compound and simple interest on a particular sum of money for 3 years at 6 and 2 / 3 % p . a is rs . 184 . what is the sum ?
Options: a ) 13000 , b ) 13500 , c ) 14000 , d ) 14500 , e ) 15000
Rationale: "p = ( 184 * 10 ^ 6 ) / ( 6 2 / 3 * 6 2 / 3 * ( 300 * 6 2 / 3 ) ) = = > 13500 answer b"
Answer: b
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 36 , what is the measure of side xy ?
Options: a ) 4 , b ) 4 √ 2 , c ) 12 , d ) 8 √ 2 , e ) can not be determined from the information provided
Rationale: "ans c . . 12 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 36 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 12"
Answer: c
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 40 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 88 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 40 / 5 = 8 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 8 = 88 secs . answer : b"
Answer: b
Problem: the sum of two numbers is 12 and the product of the numbers is 35 . find sum of the squares of that numbers .
Options: a ) 84 , b ) 87 , c ) 96 , d ) 79 , e ) 74
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 12 ab = 35 so , 12 ^ 2 = a ^ 2 + b ^ 2 + 2 * 35 144 = a ^ 2 + b ^ 2 + 70 a ^ 2 + b ^ 2 = 74 ans e
Answer: e
Problem: the balance of a trader weighs 20 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 4 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 80 gms because it weighs 20 % less . say , the cost price is $ 80 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 80 + ( 30 / 100 ) * 80 = $ 104 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 104 , the mark up is simply 4 % . ans : a
Answer: a
Problem: it takes 2 workers a total of 12 hours to build a giant machine with each worker working at the same rate . if 3 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 2 : 00 pm , at what time will the machine be complete ?
Options: a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30
Rationale: 2 workers build 1 / 12 of a machine in one hour . 1 worker builds 1 / 24 of a machine in one hour . in the first 3 hours , 3 workers build 3 * ( 1 / 24 ) * 3 = 9 / 24 of a machine from 2 : 00 to 3 : 00 , 4 workers build another 4 / 24 . the total is 13 / 24 . from 3 : 00 to 4 : 00 , 5 workers build another 5 / 24 . the total is 18 / 24 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 24 . the total is 24 / 24 . the machine is complete at 5 : 00 . the answer is c .
Answer: c
Problem: find the number , difference between number and its 3 / 5 is 50 .
Options: a ) 120 , b ) 123 , c ) 124 , d ) 125 , e ) 359
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 50 , = > ( 2 / 5 ) x = 50 = > 2 x = 50 * 5 , = > x = 125 option d"
Answer: d
Problem: in a coconut grove , ( x + 3 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 3 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above
Rationale: "( x + 3 ) × 60 + x × 120 + ( x − 3 ) × 180 / ( x + 3 ) + x + ( x − 3 ) = 100 ⇒ 360 x − 360 / 3 x = 100 ⇒ 60 x = 360 ⇒ x = 6 answer d"
Answer: d
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much w does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) w = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Problem: a 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 210 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 290 ) / 9 = 500 / 9 x + 290 = 500 x = 210 . b"
Answer: b
Problem: find the average of all prime numbers between 4 and 15 .
Options: a ) 30 , b ) 4 , c ) 9 , d ) 8 , e ) none
Rationale: sol . there are four prime numbers between 4 and 15 . they are 5 , 7 , 11 , 13 â ˆ ´ required average = [ 5 + 7 + 11 + 13 / 4 ] = 36 / 4 = 9 answer c
Answer: c
Problem: 100 people are attending a newspaper conference . 40 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 21 , b ) 24 , c ) 28 , d ) 30 , e ) 32
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 40 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 40 + { editors } - x + 2 x - - > x = 60 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 60 - 39 = 21 . answer : a ."
Answer: a
Problem: a milkman purchases the milk at rs . x per litre and sells it at rs . 2 x per litre still he mixes 2 litres water with every 6 litres of pure milk . what is the profit percentage ?
Options: a ) 166.69 % , b ) 166.66 % , c ) 166.76 % , d ) 136.66 % , e ) 566.66 %
Rationale: let the cost price of 1 litre pure milk be re . 1 , then \ inline \ begin { bmatrix } 6 & litres ( milk ) & \ rightarrow & cp = rs . 6 \ \ 2 & litres ( water ) & \ rightarrow & cp = rs . 0 \ end { bmatrix } \ rightarrow cp = rs . 6 only and 8 litre mixture \ rightarrow sp \ rightarrow 8 x 2 = rs . 16 profit % = % answer : b
Answer: b
Problem: a and b can do a work in 12 days , b and c in 15 days , c and a in 20 days . if a , b and c work together , they will complete the work in :
Options: a ) 5 days , b ) 7 5 / 6 days , c ) 10 days , d ) 15 2 / 3 days , e ) none of these
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 12 , ( b + c ) ' s 1 day ' s work = 1 / 15 ; ( a + c ) ' s 1 day ' s work = 1 / 20 adding , we get : 2 ( a + b + c ) ' s 1 day ' s work = ( 1 / 12 + 1 / 15 + 1 / 20 ) = 12 / 60 = 1 / 5 ( a + b + c ) ' s 1 day ' s work = 1 / 10 so , a , b and c together can complete the work in 10 days . correct option : c"
Answer: c
Problem: a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 266666.7 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: 3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 10 % total = 45 + 30 + 10 = 85 % remaining = 100 - 85 = 15 % 15 % = 40000 100 % = 40000 * 100 / 15 = $ 266666.7 answer is a
Answer: a
Problem: how many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14 ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "250 / 15 = 16 ( plus remainder ) so there are 16 multiples of 15 250 / 14 = 17 ( plus remainder ) so there are 17 multiples of 14 we need to subtract 1 because 15 * 14 is a multiple of both so it was counted twice . the total is 16 + 17 - 1 = 32 the answer is c ."
Answer: c
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 240 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 48 sec , e ) none of these
Rationale: speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 240 = 600 meter time taken to cross the platform = 600 / ( 25 / 2 ) = 600 ã — 2 / 25 = 48 seconds answer : d
Answer: d
Problem: a train 300 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 48 , c ) 29 , d ) 27 , e ) 21
Rationale: "s = ( 300 + 300 ) / 45 = 600 / 45 * 18 / 5 = 48 answer : b"
Answer: b
Problem: how long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length ?
Options: a ) 28 , b ) 41.25 , c ) 55 , d ) 18 , e ) 12
Rationale: "t = ( 660 + 165 ) / 72 * 18 / 5 t = 41.25 answer : b"
Answer: b
Problem: how many integers from 101 to 700 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 6 = 6 7 is not possible here because it would result in a number greater than 7 ( i . e 707 , 717 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 6 * 10 = 60 answer is b ."
Answer: b
Problem: what sum of money put at c . i amounts in 2 years to rs . 8800 and in 3 years to rs . 9261 ?
Options: a ) 7945 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8800 - - - - 461 100 - - - - ? = > 5.238 % x * 105.238 / 100 * 105.238 / 100 = 8800 x * 1.1075 = 8800 x = 8800 / 1.1075 = > 7945.70 answer : a"
Answer: a
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 63 = x ?
Options: a ) 1 , b ) 5 , c ) 3 , d ) 6 , e ) 7
Rationale: c ) 3
Answer: c
Problem: if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` gone ' ' would be
Options: a ) 3569 , b ) 1552 , c ) 4573 , d ) 4735 , e ) 5235
Rationale: g - 4 o - 7 n - 3 e - 5 so for mango the code is 4735 answer : d
Answer: d
Problem: if henry were to add 4 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 32 , b ) 40 , c ) 64 , d ) 80 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 4 galls 1 / 8 * x = 4 gallons x = 32 gallons answer a"
Answer: a
Problem: a train 120 m long crosses a platform with a speed of 60 kmph in 15 sec ; find the length of the platform ?
Options: a ) 110 , b ) 130 , c ) 120 , d ) 125 , e ) 135
Rationale: d = 120 + x t = 15 s = 120 + x / 15 * 18 / 5 = 60 kmph . = > ( 120 + x ) * 18 = 4500 = > 120 + x = 250 = > x = 130 m answer : b
Answer: b
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 5 % p . a . in 5 years . what is the sum ?
Options: a ) 12021 , b ) 14520 , c ) 16065 , d ) 18925 , e ) 12887
Rationale: "principal = ( 100 * 4016.25 ) / ( 5 * 5 ) = rs . 16065 . answer : c"
Answer: c
Problem: a man rows his boat 84 km downstream and 48 km upstream , taking 2 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 5 kmph , c ) 9 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 84 / ( 2 ) = 42 kmph speed upstream = d / t = 48 / ( 2 ) = 24 kmph the speed of the stream = ( 42 - 24 ) / 2 = 9 kmph answer : c"
Answer: c
Problem: ratio between length and breath of a rectangle is 25 : 16 . the area of the rectangle is same with a square whose side is 200 . find the breadth and length of the rectangle ?
Options: a ) 150,200
b ) 140,300
c ) 100,300
d ) 160,250
e ) 100,200
Rationale: let length l = 25 x and breadth b = 16 x area of the square = 200 ^ 2 = 40000 16 x * 25 x = 40000 400 x ^ 2 = 40000 x ^ 2 = 100 x = 10 length = 25 * 10 = 250 breadth = 16 * 10 = 160 answer : d
Answer: d
Problem: what number has a 20 : 1 ratio to the number 10 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120
Rationale: "20 : 1 = x : 10 x = 10 * 20 x = 150 answer : c"
Answer: c
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 146 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 146 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Problem: mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.3 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.12 , e ) $ 2.30
Rationale: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 30 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 30 - cent increment ) and the the difference in sequential prices of the pots is 30 cents , the largest pot probably has a price that is a 30 - cent increment . from the answer choices , i would then test answer d if . . . . the largest pot = $ 2.125 the other 5 pots are . . . . 0.625 0.925 1.225 1.525 1.825 2.125 total = $ 8.25 so this must be the answer . d"
Answer: d
Problem: what quantity of water should taken out to concentrate 15 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: required answer is = 15 ( 60 - 40 ) / 60 = 5 liters answer is a
Answer: a
Problem: what is the remainder when 9 ^ 19 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "9 ^ 0 = 1 9 ^ 1 = 9 9 ^ 2 = 81 9 ^ 3 = 729 9 ^ 4 = . . . 1 9 ^ 5 = . . . . . 9 and so on in a distinct last - digit pattern of 9,1 , 9,1 . . . after ignoring the first last - digit of 1 19 / 2 = 9 ( with a remainder of 1 ) so the last number is a 9 . alternatively , 19 is an odd number and hence the last digit is a 9 when 9 ^ 19 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 5 hours ?
Options: a ) 675 , b ) 750 , c ) 1,125 , d ) 5,900 , e ) 7,500
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 5 hours ) = 1125 cans . the answer is c ."
Answer: c
Problem: a trained covered x km at 65 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22 , b ) 99 , c ) 26 , d ) 66 , e ) 887
Rationale: "total time taken = x / 65 + 2 x / 20 hours = 3 x / 26 hours average speed = 3 x / ( 3 x / 26 ) = 26 kmph answer : c"
Answer: c
Problem: what is the remainder when 2676 * 1487 * 4459 is divided by 12
Options: a ) 3 , b ) 8 , c ) 12 , d ) 9 , e ) 27
Rationale: "2679 / 12 = = > remainder = 3 1487 / 12 = = > remainder = 11 4459 / 12 = = > remainder = 7 = 3 * 11 * 7 = 231 / 12 = = > remainder = 3 answer : a"
Answer: a
Problem: ms . lopez deposits $ 140 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 169.40 , d ) $ 122.00 , e ) $ 140.00
Rationale: using formula - a = p ( 1 + r / n ) ^ nt given p = 140 n = 2 t = 1 r = 0.2 substituting value in formula a = 140 ( 1 + 0.2 / 2 ) ^ 2 a = 169.40 $ = c
Answer: c
Problem: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 286 , b ) 278 , c ) 255 , d ) 180 , e ) 287
Rationale: "speed = ( 72 * 5 / 18 ) m / sec = ( 20 ) m / sec length of the train = ( speed x time ) = ( 20 * 9 ) m = 180 m . answer : d"
Answer: d