regisss/math_qa huggingface dataset:
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 21 / 25 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 42 / 5 ) / 10 = 42 / 50 = 21 / 25 answer d"
Answer: d
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is three times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 27 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 9 : 2 = > for 9 soap , salt = 2 = > for 2 soap , salt = ( 2 / 9 ) * 2 = 4 / 9 so , water : soap : salt = 3 : 2 : 4 / 9 = 27 : 18 : 4 after open container , water : soap : salt = 13.5 : 18 : 4 so , water : salt = 13.5 : 4 = 27 : 8 answer : e"
Answer: e
Problem: at a party , 13 guests brought wine and 14 guests brought beer . if exactly 11 guests brought only one of the two types of drinks , how many guests brought both types of drinks ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 14
Rationale: say x guests brought both drinks . ( 13 - x ) + ( 14 - x ) = 11 - - > x = 8 . answer : d .
Answer: d
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would earn rs . 482 more if the interest were paid half - yearly . calculate the sum .
Options: a ) 2878 , b ) 279 , c ) 279 , d ) 482 , e ) 661
Rationale: p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d
Answer: d
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 75 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 22.5 %
Rationale: "the actual answer is obtained by multiplying 175 % by 70 % and subtracting 100 % from this total . that is : 175 % × 70 % = 122.5 % ; 122.5 % − 100 % = 122.5 % . answer : e"
Answer: e
Problem: farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % the correct answer is ( b ) ."
Answer: b
Problem: the total number of digits used in numbering the pages of a book having 266 pages is
Options: a ) 732 , b ) 990 , c ) 109 , d ) 130 , e ) 690
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 167 ) = ( 9 + 180 + 501 ) = 690 . answer : e"
Answer: e
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 . 1400 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3500 , 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 = 1400 … ( i ) and 4 x – 2 y = 1400 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1400 - > x = 700 p 1 ’ s income = rs 5 * 700 = rs . 3500 answer : d"
Answer: d
Problem: the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs 8,748 , its purchase price was ?
Options: a ) rs 16,000 , b ) rs 18,000 , c ) rs 12,000 , d ) rs 14,000 , e ) none of these
Rationale: "we have p = 8748 , r = - 10 and n = 3 therefore , the purchase price of the machine = p / ( 1 + ( r / 100 ) ) n = 8748 / ( 1 - ( 10 / 100 ) ) 3 = 8748 x ( 100 / 90 ) x ( 100 / 90 ) x ( 100 / 90 ) = 12,000 . answer : c"
Answer: c
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 340,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,416 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 340000 [ 1 ] 0.04 x = 0.80 * 340000 = 272000 [ 2 ] 272000 + 0.09 y = 340000 - - > 0.09 y = 64000 [ 3 ] 272000 / 12 = 22666.67 [ 4 ] 64000 / 12 = 5666.67 [ 5 ] adding [ 4,5 ] we get : 28333.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.416 , ans a"
Answer: a
Problem: a mixture of 150 liters of wine and water contains 10 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 16
Rationale: "number of liters of water in 150 liters of the mixture = 10 % of 150 = 10 / 100 * 150 = 15 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 15 + p ) and total volume of mixture is ( 150 + p ) . ( 15 + p ) = 25 / 100 * ( 150 + p ) 60 + 4 p = 150 + p p = 30 liters . answer : b"
Answer: b
Problem: what is the difference between the local values of 8 in the number 58408 ?
Options: a ) 2992 , b ) 7992 , c ) 2877 , d ) 2077 , e ) 6229
Rationale: explanation : 8000 â € “ 8 = 7992 answer : b
Answer: b
Problem: three numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :
Options: a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7
Rationale: "number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d"
Answer: d
Problem: the area of a parallelogram is 147 sq m and its base is thrice the corresponding height . then the length of the base is ?
Options: a ) 14 m , b ) 29 m , c ) 49 m , d ) 7 , e ) none
Rationale: b * h = 147 b * h = 147 = > b ^ 2 = 49 m . b = 7 answer : ( d )
Answer: d
Problem: a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?
Options: a ) 22 , b ) 27 , c ) 60 , d ) 88 , e ) 12
Rationale: in 120 days , only 240 m of the tunnel is constructed by 60 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 60 = 60 men . answer : b
Answer: b
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 50 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 48 , c ) 60 , d ) 80 , e ) 90
Rationale: "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 50 vehicles . hence 2 / 3 constitutes 100 speedster convertibls = 100 * 4 / 5 = 80 d"
Answer: d
Problem: if there are 4 peanuts in a box and mary puts 12 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "12 + 4 = 16 correct answer is b ) 16"
Answer: b
Problem: 4 dice are thrown and the sum of the numbers noted is 10 . find the probability that all the numbers lie between 2 and 5 ( both inclusive ) ?
Options: a ) 11 / 79 , b ) 10 / 79 , c ) 12 / 79 , d ) 13 / 79 , e ) 14 / 79
Rationale: sum of numbers noted on 4 dice ( with six faces ) to be 10 will include combinations : ( 1,1 , 2,6 ) ( 1,1 , 3,5 ) ( 1,1 , 4,4 ) ( 1,1 , 5,3 ) ( 1,1 , 6,2 ) ( 1,2 , 1,6 ) ( 1,2 , 2,5 ) ( 1,2 , 3,4 ) ( 1,2 , 4,3 ) ( 1,2 , 5,2 ) ( 1,2 , 6,1 ) ( 1,3 , 1,5 ) ( 1,3 , 2,4 ) ( 1,3 , 3,3 ) ( 1,3 , 4,2 ) ( 1,3 , 5,1 ) ( 1,4 , 1,4 ) ( 1,4 , 2,3 ) ( 1,4 , 3,2 ) ( 1,4 , 4,1 ) ( 1,5 , 1,3 ) ( 1,5 , 2,2 ) ( 1,5 , 3,1 ) ( 1,6 , 1,2 ) ( 1,6 , 2,1 ) ( 2,1 , 1,6 ) ( 2,1 , 2,5 ) ( 2,1 , 3,4 ) ( 2,1 , 4,3 ) ( 2,1 , 5,2 ) ( 2,1 , 6,1 ) ( 2,2 , 1,5 ) ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,2 , 5,1 ) ( 2,3 , 1,4 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,3 , 4,1 ) ( 2,4 , 1,3 ) ( 2,4 , 2,2 ) ( 2,4 , 3,1 ) ( 2,5 , 1,2 ) ( 2,5 , 2,1 ) ( 2,6 , 1,1 ) ( 3,1 , 1,5 ) ( 3,1 , 2,4 ) ( 3,1 , 3,3 ) ( 3,1 , 4,2 ) ( 3,1 , 5,1 ) ( 3,2 , 1,4 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,2 , 4,1 ) ( 3,3 , 1,3 ) ( 3,3 , 2,2 ) ( 3,3 , 3,1 ) ( 3,4 , 1,2 ) ( 3,4 , 2,1 ) ( 3,5 , 1,1 ) ( 4,1 , 1,4 ) ( 4,1 , 2,3 ) ( 4,1 , 3,2 ) ( 4,1 , 4,1 ) ( 4,2 , 1,3 ) ( 4,2 , 2,2 ) ( 4,2 , 3,1 ) ( 4,3 , 1,2 ) ( 4,3 , 2,1 ) ( 4,4 , 1,1 ) ( 5,1 , 1,3 ) ( 5,1 , 2,2 ) ( 5,1 , 3,1 ) ( 5,2 , 1,2 ) ( 5,2 , 2,1 ) ( 5,3 , 1,1 ) ( 6,1 , 1,2 ) ( 6,1 , 2,1 ) - - - - - - - total 79 combinations with all the numbers lie between 2 and 5 are ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,4 , 2,2 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,3 , 2,2 ) ( 4,2 , 2,2 ) - - - - - - total 10 so probability = 10 / 79 answer : b
Answer: b
Problem: a truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100 kms in 50 minutes . the ratio of their speeds is ?
Options: a ) 2 : 3 , b ) ratio 1 : 5 , c ) ratio 1 : 10 , d ) ratio 9 : 13 , e ) ratio 7 : 15
Rationale: "ratio of speeds = ( 200 / 60 ) 18 / 5 : 60 * 100 / 50 = 12 : 120 = 1 : 10 answer is c"
Answer: c
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 9 kgs more for rs . 900 , what is the reduced price for kg ?
Options: a ) 72 , b ) 27 , c ) 40 , d ) 30 , e ) 20
Rationale: "900 * ( 30 / 100 ) = 270 - - - - 9 ? - - - - 1 = > rs . 30 answer : d"
Answer: d
Problem: in how many ways 6 boys and 4 girls can be seated in a row so that they are alternative ?
Options: a ) 14420 , b ) 12620 , c ) 17280 , d ) 21200 , e ) 24560
Rationale: "6 boys can be seated in 6 ! 4 girls can be seated in 4 ! required number = 6 ! 4 ! = 17280 answer is c"
Answer: c
Problem: total dinning bill of 7 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.84
Rationale: "dinner bill of 7 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 7 = $ 21.84 answer : a"
Answer: a
Problem: city x has a population 3 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "x = 3 y , y = 2 * z x : y , y : z 3 : 1 , 2 : 1 6 : 2 , 2 : 1 so , x : z = 6 : 1 ( d )"
Answer: d
Problem: in how many ways can 22 books on english and 20 books on hindi be placed in a row on a shelf so that two books on hindi may not be together ?
Options: a ) 4586 , b ) 5896 , c ) 2415 , d ) 1771 , e ) 1881
Rationale: "in order that two books on hindi are never together , we must place all these books as under : h e h e h e h … . . h e h where h denotes the position of hindi book and e that of english book . since there are 22 books on english , the number of places marked e are 23 . now , 20 places out of 23 can be chosen in 23 c 20 = 23 c 3 = 23 * 22 * 21 3 * 2 * 1 = 1771 ways . hence the number of ways = 1771 ways answer : d"
Answer: d
Problem: what is the dividend ? the divisor is 800 , the quotient is 594 , and the remainder is - 968 .
Options: a ) 6623 , b ) 43036 , c ) 51515 , d ) 474232 , e ) 2025
Rationale: dividend = ? ? = d * q + r ? = 800 * 594 + - 968 ? = 475,200 + - 968 ? = 474,232
Answer: d
Problem: working independently , tina can do a certain job in 12 hours . working independently , ann can do the same job in 9 hours . if tina works independently at the job for 8 hours and then ann works independently , how many hours will it take ann to complete the remainder of the jobs ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 , d ) 2 , e ) 3
Rationale: work done by tina in 1 hr = 1 / 12 work done by tina in 8 hr = 1 / 12 * 8 which is 2 / 3 now , the remaining work is 1 / 3 which is completed by ann in 1 / 3 * 9 which is 3 hr answer : e
Answer: e
Problem: sum of 24 odd numbers is ?
Options: a ) 572 , b ) 573 , c ) 574 , d ) 575 , e ) 576
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 24 odd numbers = 24 ^ 2 = 576 answer : e"
Answer: e
Problem: set x consists of all two - digit primes and set y consists of all positive odd multiples of 9 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 9 , 27 , 45 , . . . . . . . . . . . . . . . , 63 , 81 , 99 } combining two sets , say set z set z = { 9 , 11 , 13 , 17 , 27 , . . . . . . . . . . . . . . . . . . . , 63 , 81 , 83 , 89 , 97,99 } range = max value - min value range ( z ) = 99 - 9 = 90 oa c is the answer ."
Answer: c
Problem: the duplicate ratio of 6 : 4 is ?
Options: a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Rationale: "36 ^ 2 : 4 ^ 2 = 36 : 16 = 9 : 4 answer : b"
Answer: b
Problem: find 4 + 7 + 10 + 13 + 16 + . . . up to 20 terms
Options: a ) 650 , b ) 640 , c ) 630 , d ) 620 , e ) 610
Rationale: a = 4 d = 7 – 4 = 3 sum of first 20 terms , s 20 answer is a
Answer: a
Problem: there are 10 slate rocks , 11 pumice rocks , and 4 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 3 / 20 , b ) 5 / 26 , c ) 7 / 34 , d ) 9 / 37 , e ) 11 / 49
Rationale: "10 / 25 * 9 / 24 = 3 / 20 the answer is a ."
Answer: a
Problem: if 100 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 125 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 350 , d ) 35 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 200 % of 10 is 20 . . . . ( 70 * 100 ) / 20 = 350 . . . . ans : c"
Answer: c
Problem: a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor .
Options: a ) 233 , b ) 877 , c ) 279 , d ) 176 , e ) 291
Rationale: "explanation : area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d ) 176"
Answer: d
Problem: 5 % of men have unlisted phone numbers and 4 % of women have unlisted phone numbers . population ratio of men : women in the city of gpuzzles is 4 : 3 . if we select randomly 100 people from the phone directory , can you tell us how many people selected will definitely have unlisted phone numbers ?
Options: a ) 0 % , b ) 1 % , c ) 2 % , d ) 3 % , e ) 4 %
Rationale: solution : 0 % explanation : in the number is in the phone directory , it means the number is listed and therefore if we pick any number from phone directory than number is surely listed . answer a
Answer: a
Problem: how many different values of positive integer x , for which | x + 7 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer a i opted to put the random value option . i used 0 , 7 , - 7 and the the extreme of 30 and - 30 . . i was able to solve it in 1 : 09 b"
Answer: b
Problem: you buy a piece of land with an area of â ˆ š 100 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 10 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 100 . answer c"
Answer: c
Problem: find the cost of fencing around a circular field of diameter 14 m at the rate of rs . 2.50 a meter ?
Options: a ) 288 , b ) 110 , c ) 772 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 7 = 44 44 * 2.5 = rs . 110 answer : b"
Answer: b
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many y acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn y = 4 * 94 = 376 correct option - c"
Answer: c
Problem: 10 play kabadi , 15 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 25 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 15 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 15 + 5 = 20 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 20 - 5 = 25 answer : a"
Answer: a
Problem: a tailor trims 7 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 45 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let the original side of the square be x . ( x - 14 ) * ( x - 10 ) = 45 = 5 * 9 x = 19 the answer is d ."
Answer: d
Problem: $ 500 will become $ 1000 in 5 years find the rate of interest ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: si = simple interest = a - p = 1000 - 500 = $ 500 r = 100 si / pt = 100 * 500 / 500 * 5 = 20 % answer is b
Answer: b
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 3.0 = ?
Options: a ) - 0.71 , b ) 1.0 , c ) 1.07 , d ) - 1.42 , e ) 2.71
Rationale: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 3.0 = - 1.42 answer d"
Answer: d
Problem: the number 523 rbc is divisible by 7 , 89 . then what is the value of r * b * c
Options: a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280
Rationale: lcm of 7 , 8 and 9 is 504 , thus 523 rbc must be divisible by 504 . 523 rbc = 523000 + rbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + rbc = k * 504 . k = 1 rbc = 152 - - > r * b * c = 10 k = 2 rbc = 656 - - > r * b * c = 180 as rbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d .
Answer: d
Problem: a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . what is the market value of each share ?
Options: a ) rs . 12 , b ) rs . 18 , c ) rs . 15 , d ) rs . 21 , e ) rs . 25
Rationale: "explanation : face value of each share = rs . 20 dividend per share = 9 % of 20 = 9 × 20 / 100 = 9 / 5 he needs to have an interest of 12 % on his money ie , money paid for a share 9 × 12 / 100 = 9 / 5 money paid for a share = 9 / 5 × 100 / 12 = 15 ie , market value of the share = rs . 15 answer : option c"
Answer: c
Problem: what is the smallest no . which must be added to 27452 so as to obtain a sum which is divisible by 9 ?
Options: a ) 7 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "for 27452 , 2 + 7 + 4 + 5 + 2 = 20 . 7 must be added to 27452 to make it divisible by 9 . now , 2 + 7 + 4 + 5 + 9 = 27 = > 27 is a multiple of 9 and hence 27452 is also divisible by 9 a"
Answer: a
Problem: find the average of first 4 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21
Rationale: "average = ( 5 + 10 + 15 + 20 ) / 4 = 12.5 answer is c"
Answer: c
Problem: the sale price sarees listed for rs . 400 after successive discount is 10 % and 8 % is ?
Options: a ) 338 , b ) 277 , c ) 331.2 , d ) 882 , e ) 212
Rationale: "400 * ( 90 / 100 ) * ( 92 / 100 ) = 331.2 answer : c"
Answer: c
Problem: the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is
Options: a ) 344 , b ) 387 , c ) 308 , d ) 299 , e ) 882
Rationale: "explanation : other number = \ inline \ fn _ jvn \ left ( \ frac { 11 \ times 7700 } { 275 } \ right ) = 308 answer : c ) 308"
Answer: c
Problem: what is the smallest positive integer x , such that 2160 x is a perfect cube ?
Options: a ) 100 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: "take out the factors of 2160 that will come 6 ^ 3 * 10 . for perfect cube you need every no . raise to the power 3 . for 2160 to be a perfect cube , you need two 2 and two 5 that means 100 a is the answer ."
Answer: a
Problem: a batch of cookies was divided amomg 6 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 5 / 7 , e ) 9 / 7
Rationale: this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 6 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 6 ) = 5 / 12 x = 5 / 7 answer : d
Answer: d
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 28160 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "28160 = 1 * 5 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c ."
Answer: c
Problem: two numbers have a h . c . f of 12 and a product of two numbers is 2460 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 205 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2460 / 12 = 205 . answer : c"
Answer: c
Problem: if a - b = 9 and a ^ 2 + b ^ 2 = 281 , find the value of ab
Options: a ) 100 , b ) 12 , c ) 15 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 281 - 81 = 200 = > ab = 100 answer : a"
Answer: a
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 16 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 22 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 16 - 6 = 10 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 10 + 12 = 22 . answer : c"
Answer: c
Problem: a train is moving at 6 / 7 of its usual speed . the train is 15 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 15 minutes represents 1 / 6 of the usual time . the usual time is 1.5 hours . the answer is b ."
Answer: b
Problem: exactly 3 / 5 of the people in the room are under the age of 21 , and exactly 5 / 13 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 60 , e ) 42
Rationale: "the total number of the people in the room must be a multiple of both 5 and 14 ( in order 3 / 5 and 5 / 14 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 5 and 14 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 5 * 70 = 42 people in the room under the age of 21 . answer : e ."
Answer: e
Problem: there are 2 sections a and b in a class , consisting of 60 and 70 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 70.76 kg , d ) 69.15 kg , e ) 70.89 kg
Rationale: "total weight of 60 + 70 students = 60 * 60 + 70 * 80 = 3600 + 5600 average weight of the class is = 9200 / 130 = 70.76 kg answer is c"
Answer: c
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 80 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 44 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 80 % more ie . , 180 recliners hence her sales tields 180 * 80 = $ 14400 increase in sales = 14400 - 10000 = $ 4400 so % increase = 4400 * 100 / 10000 = 44 % e is the answer"
Answer: e
Problem: in a family 19 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 31 , c ) 9 , d ) 31 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 19 + 12 = 31 answer = b"
Answer: b
Problem: two friends plan to walk along a 36 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 25 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: if q complete x kilometers , then p completes 1.25 x kilometers . x + 1.25 x = 36 2.25 x = 36 x = 16 then p will have have walked 1.25 * 16 = 20 km . the answer is b .
Answer: b
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 3,675 , what is the least possible value of k ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 21 , e ) 25
Rationale: "we basically need 5,5 , 3,7 and 7 in the number . 14 ! , has 3 , 5 , 7 , 10 , 14 now 10 = 2 x 5 14 = 2 x 7 cross check : k ! = 3675 * m ( m is a positive integer ) k ! = 3 * 5 * 5 * 7 * 7 14 ! has all the numbers above . . therefore b . . ! answer : b"
Answer: b
Problem: l . c . m of two numbers is 192 and there h . c . f is 16 . if one of them is 48 . find the other
Options: a ) 32 , b ) 64 , c ) 48 , d ) 68 , e ) 78
Rationale: explanation : product of two numbers = product of their l . c . m and h . c . f 48 x a = 192 x 16 a = ( 192 x 16 ) / 48 = 64 answer : option b
Answer: b
Problem: at 3.40 , the hour hand and the minute hand of a clock form an angle of
Options: a ) 378 , b ) 277 , c ) 297 , d ) 267 , e ) 130
Rationale: sol : use formula θ = ∣ ∣ ∣ 30 h − 112 m ∣ ∣ ∣ θ = | 30 h − 112 m | angle = 30 × 3 – 11 / 2 × 40 = 90 – 220 = 130 ° answer : e
Answer: e
Problem: x and y started a business with capitals rs . 20000 and rs . 25000 . after few months z joined them with a capital of rs . 30000 . if the share of z in the annual profit of rs . 50000 is rs . 14000 , then after how many months from the beginning did z join ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 5
Rationale: investments of x , y and z respectively are rs . 20000 , rs . 25000 and rs . 30000 let investment period of z be x months . ratio of annual investments of x , y and z is ( 20000 * 12 ) : ( 25000 * 12 ) : ( 30000 * x ) = 240 : 300 : 30 x = 8 : 10 : x the share of z in the annual profit of rs . 50000 is rs . 14000 . = > [ x / ( 18 + x ) ] 50000 = 14000 = > [ x / ( 18 + x ) ] 25 = 7 = > 25 x = 7 x + ( 18 * 7 ) = > x = 7 months . z joined the business after ( 12 - 7 ) months . i . e . , 5 months . answer : e
Answer: e
Problem: if 18 men take 15 days to to complete a job , in how many days can 24 men finish that work ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: ans . 10 days
Answer: a
Problem: a boat goes 100 km downstream in 10 hours , and 75 m upstream in 15 hours . the speed of the stream is ?
Options: a ) 22 1 / 9 kmph , b ) 22 8 / 2 kmph , c ) 22 1 / 8 kmph , d ) 22 1 / 2 kmph , e ) 22 1 / 4 kmph
Rationale: 100 - - - 10 ds = 10 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 10 - 5 ) / 2 = 2 21 / 2 kmph answer : d
Answer: d
Problem: if k is an integer and 121 < k ^ 2 < 225 , then k can have at most how many values ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: given k is an integer 121 < k ^ 2 < 225 11 < | k | < 15 k = - 12 , - 13 , - 1412 , 1314 answer : d
Answer: d
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 5 , 500,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 1 , 800,000 = 2 , 800,000 answer : b"
Answer: b
Problem: a sum of rs . 2040 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 360 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 2040 = > 17 x / 12 = 2040 = > 2040 x 12 / 17 = rs . 1440 hence , b ’ s share = rs . ( 1440 / 4 ) = rs . 360 . answer d"
Answer: d
Problem: an error 17 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 36.89 % , c ) 15.64 % , d ) 26.64 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 17 + 17 + ( 17 ã — 17 ) / 100 ) % = 36.89 % answer : b"
Answer: b
Problem: a boat can travel with a speed of 40 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 45 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 40 + 5 ) km / hr = 45 km / hr . time taken to travel 45 km downstream = 45 / 45 hrs = 1 hrs . answer : a"
Answer: a
Problem: 3 candidates in an election and received 1036 , 4636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 57 % , d ) 60 % , e ) 67.2 %
Rationale: total number of votes polled = ( 1036 + 4636 + 11628 ) = 17300 so , required percentage = 11628 / 17300 * 100 = 67.2 % e
Answer: e
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 2 % per first year and 3 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 5253
Rationale: "5000 * 102 / 100 * 103 / 100 = > 5253 answer : e"
Answer: e
Problem: in plutarch enterprises , 60 % of the employees are marketers , 30 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 260,000 , d ) $ 290,000 , e ) $ 320,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 6 marketers , 3 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 6 * $ 50,000 ) and the engineers ( 3 * $ 80,000 ) > > > $ 800,000 - $ 300,000 - $ 240,000 = $ 260,000 . the correct answer is c ."
Answer: c
Problem: find the missing figures : 0.25 % of ? = 0.04
Options: a ) 16 , b ) 20 , c ) 17 , d ) 12 , e ) 18
Rationale: "let 0.25 % of x = 0.04 . then , 0.25 * x / 100 = 0.04 x = [ ( 0.04 * 100 ) / 0.25 ] = 16 . answer is a ."
Answer: a
Problem: how many 6 digit number contain number 4 ?
Options: a ) 317608 , b ) 327608 , c ) 337608 , d ) 427608 , e ) 357608
Rationale: "total 6 digit no . = 9 * 10 * 10 * 10 * 10 * 10 = 900000 not containing 4 = 8 * 9 * 9 * 9 * 9 * 9 = 472392 total 6 digit number contain 4 = 900000 - 472392 = 427608 answer : d"
Answer: d
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 262 runs ?
Options: a ) 6 , b ) 6.25 , c ) 5.75 , d ) 7.5 , e ) 8
Rationale: "required run rate = 262 - ( 3.2 x 10 ) = 230 = 5.75 40 40 c"
Answer: c
Problem: the mean of 40 observations was 36 . it was found later that an observation 34 was wrongly taken as 20 . the corrected new mean is
Options: a ) 76.55 , b ) 36.35 , c ) 46.15 , d ) 16.05 , e ) 20
Rationale: "explanation : correct sum = ( 36 * 40 + 34 - 20 ) = 1454 correct mean = = 1454 / 40 = 36.35 answer : b"
Answer: b
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 40 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1312.5 , c ) 1400 , d ) 1600 , e ) 1625
Rationale: "300 gallons of water increases capacity by 40 % that means 40 % is 300 gallons , so 100 % would be = 300 * 100 / 40 = 750 gallons now 750 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1050 * 100 / 80 = 1312.5 b is the answer"
Answer: b
Problem: the speed of a car is 10 m / s . what is the its speed in kmph .
Options: a ) 25 kmph , b ) 30 kmph , c ) 50 kmph , d ) 36 kmph , e ) 37 kmph
Rationale: explanation : m / sec to km / hr conversion : x m / sec = [ x x ( 18 / 5 ) ] km / hr 10 x ( 18 / 5 ) 36 kmph answer : option d
Answer: d
Problem: total dinning bill of 5 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 32.84 , b ) 22.84 , c ) 30.58 , d ) 24.84 , e ) 30.84
Rationale: "dinner bill of 5 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 5 = $ 30.58 answer : c"
Answer: c
Problem: at a monthly meeting , 3 / 5 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 6 / 25 , b ) 11 / 50 , c ) 14 / 75 , d ) 23 / 100 , e ) 31 / 150
Rationale: "males who did not arrive on time are 1 / 5 * 3 / 5 = 3 / 25 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 5 = 1 / 15 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 25 + 1 / 15 = 14 / 75 the answer is c ."
Answer: c
Problem: the sum of 7 consecutive integers is 980 . how many of them are prime ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the middle number is 140 and the seven numbers are 137 , 138 , 139 , · · · , 143 . now 138 , 140 , and 142 are even , 141 is divisible by 3 , and 143 - by 11 . the remaining numbers 137 and 139 are prime ( it is easy to check that they are not divisible by 23 , 57 and 11 ) . correct answer c
Answer: c
Problem: if n = 8 ^ 8 – 7 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 7 , e ) 4
Rationale: "8 ^ 8 - 8 = 8 ( 8 ^ 7 - 1 ) = = > 8 ( 2 ^ 21 - 1 ) last digit of 2 ^ 21 is 2 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit . now on multiply this with 7 , we get unit digit as 7 answer : d"
Answer: d
Problem: how many prime numbers between 1 and 100 are factors of 210 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: factor of 210 = 2 * 3 * 5 * 7 - - - 4 prime numbers b
Answer: b
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 12 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 96 % , d ) 124.2 % , e ) 138 %
Rationale: "0,096 r = x / 100 * 0.1 r answer c"
Answer: c
Problem: when positive integer x is divided by 7 , the quotient is y and the remainder is 3 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 2 . what is the value of 11 y – x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "( 1 ) x = 7 y + 3 ( 2 ) 2 x = 18 y + 2 ( 2 ) - ( 1 ) : x = 11 y - 1 11 y - x = 1 the answer is d ."
Answer: d
Problem: n is a positive integer . when n + 1 is divided by 9 , the remainder is 1 . what is the remainder when n is divided by 9 ?
Options: a ) 0 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "n + 1 = 9 a + 1 i . e . n + 1 = 10 , 19 , 28 , 37 , . . . etc . i . e . n = 9 , 18 , 27 , 36 , . . . etc . when n is divided by 9 remainder is always 0 answer : a"
Answer: a
Problem: how many positive integers less than 23 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 17 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "8 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 } 2 odd multiples of 5 : { 5 , 15 } 9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 8 + 1 + 9 - 1 = 17 . answer : a ."
Answer: a
Problem: we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed ?
Options: a ) 8
b ) 9
c ) 10
d ) 11
e ) 12
Rationale: total no . of cubes = n ^ 3 here n ^ 3 = 125 which makes n = 5 , also minimum no . of cuts required = 3 ( n - 1 ) hence , 3 ( 5 - 1 ) = 12 cuts . answer : e
Answer: e
Problem: if a : b : : 3 : 7 , then what is ( 5 a + 6 b ) : ( a - 2 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 11 : 10 , e ) - 1 : 10
Rationale: a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 6 ] / [ ( 3 / 7 ) - 2 ] = - 57 / 11 answer : b
Answer: b
Problem: a block of wood has dimensions 10 cm x 10 cm x 50 cm . the block is painted red and then cut evenly at the 25 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5.5 % , b ) 8.3 % , c ) 11.6 % , d ) 14.2 % , e ) 17.5 %
Rationale: "the area of each half is 100 + 4 ( 250 ) + 100 = 1200 the area that is not painted is 100 . the fraction that is not painted is 100 / 1200 = 1 / 12 = 8.3 % the answer is b ."
Answer: b
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 30 percent .
Options: a ) 145 , b ) 90 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 30 percent 90 min . answer : b
Answer: b
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 5 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 304
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with five 5 - s , 5 x 5 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : e ."
Answer: e
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 6 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 6 / 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 ) = 6 / 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 : = 6 / 7 x 1 / 5 = 6 / 35 answer : c"
Answer: c
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 6 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) - 16.16 % , b ) - 15.15 % , c ) - 14.14 % , d ) - 13.13 % , e ) - 12.12 %
Rationale: "( 100 % + 6 % ) * ( 100 % - 19 % ) = 1.06 * . 81 = 0.8586 . 1 - 0.8586 = 14.14 % lost = - 14.14 % the answer is c the organization has lost 14.14 % of its total volunteers from fall to spring ."
Answer: c
Problem: one hour after yolanda started walking from x to y , a distance of 31 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 1 miles per hour and bob â s was 2 miles per hour , how many miles had bob walked when they met ?
Options: a ) 19 , b ) 20 , c ) 22 , d ) 21 , e ) 19.5
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked ( t + 1 ) miles . these distances must sum to 31 miles , so 2 t + ( t + 1 ) = 31 , which may be solved for t as follows 2 t + ( t + 1 ) = 31 2 t + t + 1 = 31 3 t = 30 t = 10 ( hours ) therefore , bob had walked 2 t = 2 ( 10 ) = 20 miles when they met . the best answer is b ."
Answer: b
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5565 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 288 , d ) 210 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5565 [ 4 l - 40 ] = 5565 / 26.50 = 210 4 l = 250 l = 250 / 4 = 62.5 meters . answer : d"
Answer: d
Problem: if the perimeter of δ acd is 9 + 3 √ 3 , what is the perimeter of equilateral triangle δ abc ?
Options: a ) 9
b ) 18 − 3 √ 3
c ) 18
d ) 18 + 3 √ 3
e ) 27
Rationale: the altitude of an equilateral triangle is side * √ 3 / 2 . as perimeter of triangle acd is 9 + 3 √ 3 , ac + cd + ad = ( side + side / 2 + side * √ 3 / 2 ) = 9 + 3 √ 3 or side = 6 . perimeter of equilateral triangle , abc is 3 ( side ) or 18 . answer : ( optionc )
Answer: c
Problem: if 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 28 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 8 * 7 / 2 = 28 answer : b"
Answer: b
Problem: a man ' s basic pay for a 40 hour week is rs . 20 . overtime is paid for at 25 % above the basic rate . in a certain week he worked overtime and his total wage was rs . 25 . he therefore worked for a total of :
Options: a ) 45 hours , b ) 47 hours , c ) 48 hours , d ) 50 hours , e ) none
Rationale: explanation : basic rate per hour = rs . ( 20 / 40 ) = rs . 1 / 2 overtime per hour = 125 % of rs . 1 / 2 = 125 / 100 × 1 / 2 = rs . 5 / 8 suppose he worked x hours overtime . then , 20 + 5 / 8 x = 25 or 5 / 8 x = 5 x = 5 × 8 / 5 = 8 hours so he worked in all for ( 40 + 8 ) hours = 48 hours . correct option : c
Answer: c
Problem: a can complete a work in 15 days and b can do the same work in 7 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 5 1 / 2 days , c ) 6 1 / 2 days , d ) 7 1 / 2 days , e ) 10 days
Rationale: "the required answer = ( 15 - 3 ) * 7 / 15 = 84 / 15 = 5 1 / 2 days answer is b"
Answer: b
Problem: how many positive integers less than 60 have a reminder 01 when divided by 3 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 20
Rationale: "1 also gives the remainder of 1 when divided by 3 . so , there are total of 20 numbers . answer : e ."
Answer: e
Problem: it takes six minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video ?
Options: a ) 13.8 , b ) 14.1 , c ) 14.4 , d ) 14.6 , e ) 14.8
Rationale: "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 6 ) = 1 / 360 of the video per second . the combined rate is 1 / 15 + 1 / 360 = 25 / 360 of the video per second . the time required to load the video is 360 / 25 = 14.4 seconds . the answer is c ."
Answer: c
Problem: a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1200 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price .
Options: a ) 122 , b ) 132 , c ) 142 , d ) 152 , e ) 162
Rationale: "cost price = 1200 profit = 10 % = 10 % of 1200 = 120 selling price = cp + profit sp = 1320 a discount of 10 % to employees means 10 % off on 1320 so 10 % of 1320 = 132 ans b"
Answer: b
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 12 , then v =
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: ( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 12 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 27 the answer is e .
Answer: e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions .
Options: a ) 287 m , b ) 704 m , c ) 168 m , d ) 278 m , e ) 107 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : b"
Answer: b
Problem: 20 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.2 * 0.6 = 0.12 of the class are female science majors . then 0.28 of the class are male science majors . 0.4 x = 0.28 x = 0.7 = 70 % the answer is d .
Answer: d
Problem: a grocer has a sale of rs . 8435 , rs . 8927 , rs . 8855 , rs . 9230 and rs . 8562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 8500 ?
Options: a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 6991
Rationale: "explanation : total sale for 5 months = rs . ( 8435 + 8927 + 8855 + 9230 + 8562 ) = rs . 44009 . required sale = rs . [ ( 8500 x 6 ) â € “ 44009 ] = rs . ( 51000 â € “ 44009 ) = rs . 6991 . answer e"
Answer: e