regisss/math_qa huggingface dataset:
Problem: how much time does a train 160 metres long running at 72 km / hr take to pass a pole ?
Options: a ) 8 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s
Rationale: "explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 160 / t t = 8 s answer : a"
Answer: a
Problem: a certain company had a total annual expenditure of 1.26 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 30,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 1.26 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 3 = 1260 therefore try to bring the numerator in terms of 1260 average salary = ( 1260 * 10 ^ 4 ) / 420 = 3 * 10 ^ 4 = 30,000 option d"
Answer: d
Problem: when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 61.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 65 , d ) 70 , e ) 81
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 61.2 , we can say that k = 61.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : c"
Answer: c
Problem: what is the remainder when 3 ^ 25 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 25 has the form 4 k + 1 , so the units digit of 3 ^ 25 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 36 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 40 / 6 , b ) 40 / 3 , c ) 40 / 9 , d ) 40 / 2 , e ) 40 / 1
Rationale: "relative speed = ( 36 + 72 ) * 5 / 18 = 30 mps . the time required = d / s = ( 100 + 100 + 200 ) / 30 = 400 / 30 = 40 / 3 sec . answer : b"
Answer: b
Problem: find the smallest 4 - digit number which is a multiple of 112 .
Options: a ) 896 , b ) 1008 , c ) 1120 , d ) 1024 , e ) none of these
Rationale: the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b
Answer: b
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 24 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 3 march 1 = c - 6 april 1 = c - 9 may 1 = c - 12 june 1 = c - 15 july 1 = c - 18 aug 1 = c - 21 sept 1 = c - 24 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 24 ) = 24 hence answer will be ( c )"
Answer: c
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 15 , c ) 6 , d ) 8 , e ) 76
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a ) 11"
Answer: a
Problem: the sale price of a trolley bag including the sale tax is rs . 560 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 1000 , b ) rs 900 , c ) rs 400 , d ) rs 600 , e ) none of these
Rationale: "explanation : 112 % of s . p . = 560 s . p . = rs . ( 560 x 100 / 112 ) = rs . 500 . c . p . = rs ( 100 / 125 x 500 ) = rs 400 answer : c"
Answer: c
Problem: stacy and heather are 40 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ?
Options: a ) 4 miles , b ) 8 miles , c ) 17 miles , d ) 6 miles , e ) 12 miles
Rationale: "original distance between s and h = 40 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 40 miles - - - > 6 * ( t + 2 / 5 ) + 5 * t = 40 - - - > t = 188 / 55 hours . thus h has traveled for 188 / 55 hours giving you a total distance for h = 5 * 188 / 55 = 17 miles . c is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles ."
Answer: c
Problem: if a 1 mm thick paper is folded so that the area is halved at every fold , then what would be the thickness of the pile after 50 folds ?
Options: a ) 100 km
b ) 1000 km
c ) 1 million km
d ) 1 billion km
e ) none
Rationale: after 1 hold , thickness will be 2 mm after 2 hold , thich ness will be 4 mm after 50 th hold thick ness will be 2 ^ 50 mm . . converting to km . . . . gives 1 billion km answer : d
Answer: d
Problem: a motorcyclist goes from bombay to pune , a distance of 128 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 3 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 1 , e ) 1 : 8
Rationale: "t = 128 / 32 = 4 h t = 4 - 3 = 1 time ratio = 4 : 1 = 4 : 1 speed ratio = 1 : 4 answer : c"
Answer: c
Problem: a man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 1 kmph , b ) 5 kmph , c ) 6 kmph , d ) 4 kmph , e ) 7 kmph
Rationale: "explanation : speed of man = 5.5 kmph speed of stream = 1.5 kmph speed in downstream = 7 kmph speed in upstream = 4 kmph average speed = ( 2 x 7 x 4 ) / 11 = 5 kmph . answer : b"
Answer: b
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 5 , the quotient is 3 y and the remainder is 4 . what is the value of 4 y – x ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 15 y + 4 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 y = x 4 y - x = 0 the answer is c ."
Answer: c
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 18.40 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18.4 0.4 x = 2.4 = > x = 6 discounted tickets = 10 - x = 4 ans : b
Answer: b
Problem: the area of a square field is 625 km 2 . how long will it take for a horse to run around at the speed of 25 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 8 h , d ) 4 h , e ) none of these
Rationale: explanation area of field = 625 km 2 . then , each side of field = √ 625 = 25 km distance covered by the horse = perimeter of square field = 25 × 4 = 100 km ∴ time taken by horse = distances / peed = 100 / 25 = 4 h answer d
Answer: d
Problem: how is 3 % expressed as a decimal fraction ?
Options: a ) 0.3 , b ) 0.03 , c ) 0.003 , d ) 0.0003 , e ) 3
Rationale: "3 / 100 = 0.03 answer : b"
Answer: b
Problem: the cross section of a canal is trapezium in shape . the canal is 12 m wide at the top and 8 m wide at the bottom . if the area of the cross section is 840 sq . m , the depth of the canal is :
Options: a ) 42 m , b ) 84 m , c ) 63 m , d ) 8.75 m , e ) 9.75 m
Rationale: ½ ( 12 + 8 ) d = 840 or d = 84 m answer : b
Answer: b
Problem: if x / 4 years ago roger was 21 years old and x / 4 years from now he will be 4 x years old , how old will he be 5 x years from now ?
Options: a ) 32 , b ) 35 , c ) 30 , d ) 40 , e ) 70
Rationale: assume the current age = a a - x / 4 = 28 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 28 or 14 x / 4 = 28 therefore x = 8 and a = 30 5 x years from now , age will be 30 + 5 * 8 = 70 option e
Answer: e
Problem: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 21 per kg , then his gain percent is
Options: a ) 12 % , b ) 13 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 21 ) = rs . 168 . profit = 168 - 150 = 18 so , profit % = ( 18 / 150 ) * 100 = 12 % option a"
Answer: a
Problem: what should be added to 4872 so that it may become a perfect square ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "70 x 70 = 4900 4900 - 4872 = 28 if added to 28 get perfect square answer = e"
Answer: e
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 54 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 15 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 54 = > 45 - [ 28 - { 37 - 15 + * } ] = 54 45 - [ 28 - 37 + 15 - * ] = 54 = > 45 [ 43 - 37 - * ] = 54 45 - [ 6 - * ] = 54 = > 45 - 6 + * = 54 39 + * = 54 = > * = 54 - 39 = 19 answer : c"
Answer: c
Problem: if 2 tic equals 3 tacs and 2 tacs equal 7 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 21 / 4 , d ) 3 / 10 , e ) 1 / 15
Rationale: 2 tic = 3 * tac and 2 * tac = 7 * toc ; 4 * tic = 6 * tac and 6 * tac = 21 * toc - - > 4 * tic = 21 * toc - - > tic / toc = 21 / 4 . answer : c .
Answer: c
Problem: how many prime numbers are between 29 / 3 and 87 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "29 / 3 = 58 / 6 = 10 - 87 / 6 = 15 - prime numbers between 10 and 15 are 11 and 13 - sign signifies that the number is marginally less . answer b"
Answer: b
Problem: find the greatest number which leaves the same remainder when it divides 25 , 57 and 105 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: 105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 the h . c . f of 32 , 48 and 80 is 16 . answer : d
Answer: d
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
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 50 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %
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 50 % more ie . , 150 recliners hence her sales yields 150 * 80 = $ 12000 increase in sales = 12000 - 10000 = $ 2000 so % increase = 2000 * 100 / 10000 = 20 % c is the answer"
Answer: c
Problem: 108 ã — 108 + 92 ã — 92 = ?
Options: a ) 20120 , b ) 11500 , c ) 20128 , d ) 20660 , e ) 20228
Rationale: explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1082 + 922 = ( 100 + 8 ) 2 + ( 100 â ˆ ’ 8 ) 2 = 2 ( 1002 + 82 ) = 2 ( 10000 + 64 ) = 20128 . answer : option c
Answer: c
Problem: 7.515 / 10.02 =
Options: a ) 0.35 , b ) 0.3505 , c ) 0.3509 , d ) 0.351 , e ) 0.75
Rationale: "7.515 / 10.02 7.515 / 1002 = 7.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.75 . answer : e"
Answer: e
Problem: 1 - 1 - 1 - 1 - 1 - 1 do any operations between the numbers to make the sum as 37 ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: 1 + 1 + 1 = 3 3 factorial = 6 6 to the power 1 + 1 = 6 ^ 2 = 36 36 + 1 = 37 answer : d
Answer: d
Problem: 150 college students were asked in a survey if they preferred windows or mac brand computers . 40 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 40 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 70 , d ) 60 , e ) 75
Rationale: "150 = 40 ( mac ) + x ( window ) + 40 ( both ) = > x = 70 answer : c"
Answer: c
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 18 seconds . the length of each train is :
Options: a ) 25 m , b ) 50 m , c ) 72 m , d ) 80 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 18 secs the total distance traveled is 18 x 25 / 9 = 50 m . therefore the length of each train is = 50 / 2 = 25 m . answer a"
Answer: a
Problem: what is the area of a square field whose sides have a length of 11 meters ?
Options: a ) 225 sq m , b ) 205 sq m , c ) 121 sq m , d ) 167 sq m , e ) 156 sq m
Rationale: "11 * 11 = 121 sq m the answer is c ."
Answer: c
Problem: what is the unit digit of ( 6 ! * 3 ! / 3 ! * 4 ! ) ?
Options: a ) 5 , b ) 6 , c ) 0 , d ) 3 , e ) 4
Rationale: "( 6 ! * 3 ! / 3 ! * 4 ! ) = ( 6 ! / 4 ! ) = 5 * 6 = 30 units digit of the above product will be equal to 0 answer c"
Answer: c
Problem: in the coordinate plane , points ( x , 2 ) and ( 4 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x - y =
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 2 ) = ( 8 , 2 ) and ( 4 , y ) = ( 4,1 ) - - > x - y = 8 - 1 = 7 . answer : b"
Answer: b
Problem: 275 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "26 trees have 25 gaps between them , required distance ( 275 / 25 ) = 11 a"
Answer: a
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 60 % of the scouts arrived with signed permission slips . if 45 % of the scouts were boy scouts and 50 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .
Options: a ) 64 , b ) 68 , c ) 72 , d ) 76 , e ) 80
Rationale: "45 % were boy scouts so 55 % ( 100 - 45 = 55 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 50 % of 45 % of the total going ) + ( ? % of 55 % of the total going ) = 60 % of the total going we can let the ` ` total going ' ' = 1,000 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 50 * . 45 * 1,000 + x * . 55 * 1,000 = . 60 * 1,000 225 + x * 550 = 600 550 x = 375 x = 375 / 550 x = . 6818181818 which converts to a percent of 68.18181818 % which rounds to 68 % b"
Answer: b
Problem: the length of the bridge , which a train 155 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 220 m , d ) 187 m , e ) 176 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 155 + x ) / 30 = 25 / 2 = > 2 ( 155 + x ) = 750 = > x = 220 m . answer : c"
Answer: c
Problem: the shopkeeper sale , all of the prices of the items sold were different . if the price of a radio sold at the shopkeeper sale was both the 9 th highest price and the 14 th lowest price among the prices of the items sold , how many items were sold at the shopkeeper sale ?
Options: a ) 23 , b ) 22 , c ) 32 , d ) 26 , e ) 17
Rationale: 8 + 13 + 1 = 22 answer : b
Answer: b
Problem: find the value of 2 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) none
Rationale: "answer 2 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 2 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 2 x 4 x 4 x 50 = 1600 correct option : d"
Answer: d
Problem: 20 is subtracted from 80 % of a number , the result is 60 . find the number ?
Options: a ) 150 , b ) 997 , c ) 100 , d ) 288 , e ) 271
Rationale: "( 80 / 100 ) * x – 20 = 60 8 x = 800 x = 100 answer : c"
Answer: c
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 40 paise per sq . metre
Options: a ) s 340 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 40 = 34000 p in rs = 34000 / 100 = rs 340 answer : a
Answer: a
Problem: there are 280 doctors and nurses at a hospital . if the ratio of doctors to nurses is 5 to 9 , how many nurses are at the hospital ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: the number of nurses at the hospital is ( 9 / 14 ) * 280 = 180 . the answer is d .
Answer: d
Problem: a man sells a car to his friend at 10 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 25000 , b ) rs . 37500 , c ) rs . 50000 , d ) rs . 60000 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 × 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 10 % . now s . p = rs . 45000 and loss = 10 % c . p . rs . [ 10090 × 45000 ] = rs . 50000 . correct option : c"
Answer: c
Problem: addison high school ’ s senior class has 160 boys and 200 girls . if 75 % of the boys and 84 % of the girls plan to attend college , what percentage of the total class plan to attend college ?
Options: a ) 75 , b ) 79.5 , c ) 80 , d ) 83.5 , e ) 84
Rationale: "number of boys attending the party : 0.75 * 160 = 120 number of girls attending the party : 0.84 * 200 = 168 total attending = 120 + 168 = 288 total people = 160 + 200 = 360 % of people attending = 288 / 360 = 80 % . c is the correct answer"
Answer: c
Problem: jim ’ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 35 = 2.25 + 9 * . 35 = 5.4 $ answer e"
Answer: e
Problem: 5.005 / 4.004 =
Options: a ) 1.05 , b ) 1.50015 , c ) 1.501 , d ) 1.5015 , e ) 1.25
Rationale: "5.005 / 4.004 = 5005 / 4004 = 5 ( 1001 ) / 4 ( 1001 ) = 5 / 4 = 1.25 the answer is e ."
Answer: e
Problem: if a ( a + 7 ) = 60 and b ( b + 7 ) = 60 , where a ≠ b , then a + b =
Options: a ) − 7 , b ) − 2 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 5 then b = - 12 or if a = - 12 then b = 5 but in each case a + b = - 12 + 5 = - 7 answer : option a"
Answer: a
Problem: find the probability that the number drawn is a multiple of 6 and 8 .
Options: a ) 3 / 50 , b ) 2 / 25 , c ) 1 / 50 , d ) 1 / 25 , e ) 4 / 25
Rationale: "from 1 to 100 there are 4 numbers which are multiples of 6 and 8 . ( i . e , multiples of 24 ) therefore , required probability = 4 / 100 = 1 / 25 answer : d"
Answer: d
Problem: the average age of 36 students in a group is 18 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 55 years , c ) 51 years , d ) 54 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 37 * 19 - 36 * 18 ) years = 55 years . answer : b"
Answer: b
Problem: fred and sam are standing 55 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 6 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: "relative distance = 55 miles relative speed = 6 + 5 = 11 miles per hour time taken = 55 / 11 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c"
Answer: c
Problem: an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 65 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 27.08 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 65 percent of the votes cast number of votes for winning candidate = ( 65 / 100 ) * 525 = 341.25 percent of total membership that voted for winning candidate = ( 341.25 / 1260 ) * 100 = 27.08 % answer d"
Answer: d
Problem: what is the remainder of ( 3682 * 3684 * 3686 ) divided by 19 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "3686 % 19 = 0 so ans = 0 answer : a"
Answer: a
Problem: a can do a work in 24 days and b can do it in 12 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 days , d ) 5 days , e ) 8 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 12 they work together = 1 / 24 + 1 / 12 = 3 / 24 = 24 / 3 = 8 days answer : option e"
Answer: e
Problem: a prize of $ 1200 is to be distributed among 40 winners , each of whom must be awarded at least $ 40 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 100 , b ) $ 120 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: "total value of the prize = $ 1200 number of people = 40 2 / 5 of 1200 ( = $ 480 ) should be distributed among 3 / 5 of 40 ( = 24 people ) with each getting $ 40 each . remaining money = 1200 - 480 = $ 720 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 40 . thus , minimising the remaining 15 people ( = 40 - 24 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 15 * 40 = 600 . thus the maximum award can be = 720 - 600 = $ 120 , hence b is the correct answer ."
Answer: b
Problem: the profits of qrs company rose 20 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 44 % , d ) 62 % , e ) 80 %
Rationale: "assume 100 in march , then 120 in april as 20 % increase , then 96 in may as 20 % decrease from april , and then 144 in june which is 150 % of 96 . so overall increase is from 100 to 144 is 44 % answer c"
Answer: c
Problem: if the speed of a man is 63 km per hour , then what is the distance traveled by him in 25 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 375 m , d ) 437.5 m , e ) 440 m
Rationale: "the distance traveled in 25 sec = 63 * ( 5 / 18 ) * 25 = 437.5 m answer : d"
Answer: d
Problem: john purchased some shirts and trousers for $ 700 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11
Rationale: "given that the total purchase of two items cost 700 . so the average purchase of one item will cost 700 / 2 = 350 . its given as total shirt cost 400 $ less . hence total shirt cost = 350 - 50 and total trouser cost = 350 + 50 5 shirts = 150 $ = = > one shirt = 30 $ one trouser = 30 + 20 = 50 $ total trousers = 550 / 50 = 11 . e"
Answer: e
Problem: if a sum of money doubles itself in 10 years at simple interest , the ratepercent per annum is
Options: a ) 10 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 10 ) = 10 option a"
Answer: a
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 7 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "on the way down , the rate is 1.5 * 7 = 10.5 miles per day . the distance of the route down the mountain is 2 * 10.5 = 21 miles . the answer is d ."
Answer: d
Problem: of the goose eggs laid at a certain pond , 1 / 4 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1200 , b ) 1300 , c ) 1400 , d ) 1500 , e ) 1600
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 4 ) x = 120 ( 8 / 100 ) x = 120 x = 1500 the answer is d ."
Answer: d
Problem: 2.08 can be expressed in terms of percentage as
Options: a ) 2.08 % , b ) 20.8 % , c ) 208 % , d ) 0.208 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.08 * 100 = 208 answer : option c"
Answer: c
Problem: the population of a town is 8000 . it decreases annually at the rate of 30 % p . a . what will be its population after 2 years ?
Options: a ) 3920 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 5500
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 70 / 100 ã — 70 / 100 = 3920 answer : a"
Answer: a
Problem: a hall is 15 meters long and 10 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 900 the answer is d ."
Answer: d
Problem: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points e that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points e for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1990 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2009 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: she must gain at least 70 points , now she has 31 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1990 + 19 = 2009 . answer : b .
Answer: b
Problem: the average age of 17 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 39 , b ) 41 , c ) 45 , d ) 42 , e ) 50
Rationale: "age of the 15 th student = 17 * 15 - ( 14 * 5 + 16 * 9 ) = 255 - 214 = 41 years answer is b"
Answer: b
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 1500 km ?
Options: a ) 30 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 1500 km in = 1500 / 50 * 1 = 30 hours answer is a"
Answer: a
Problem: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 54 inches and the width of the wall is 68 inches , what is the length of the wall , in inches ?
Options: a ) 25.7
b ) 72.7
c ) 70.7
d ) 85.7
e ) 56.7
Rationale: since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 54 ^ 2 = 2916 . area of rectangle is double of that 2 * 2916 = 5832 . now a = lw and we need find w so a / l = w ; 5832 / 68 = 85.7 answer ! answer is d
Answer: d
Problem: fresh grapes contain 80 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 40 kgs of raisins ?
Options: a ) 150 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 40 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 80 = 20 % of whole weight ) , so 40 * 0.75 = x * 0.2 - - > x = 150 . answer : a ."
Answer: a
Problem: a is twice as good a work man as b and together they finish the work in 4 days . in how many days a alone can finish the work ?
Options: a ) 3 , b ) 2 , c ) 7 , d ) 9 , e ) 6
Rationale: "wc = 2 : 1 2 x + x = 1 / 4 = > x = 1 / 12 2 x = 1 / 6 a can do the work in 6 days . answer : e"
Answer: e
Problem: if p is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "no need to actually find the product of 1 to 30 . just look at the numbers that have factors of 3 . 3 = 3 6 = 3 * 2 9 = 3 * 3 12 = 3 * 2 * 2 15 = 3 * 5 18 = 3 * 3 * 2 21 = 3 * 7 24 = 3 * 2 * 2 * 2 27 = 3 * 3 * 3 30 = 3 * 2 * 5 there are 14 3 ' s , so the largest factor of p for 3 k is 3 * 14 answer : c"
Answer: c
Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24
Rationale: "probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( d ) answer : d"
Answer: d
Problem: a woman swims downstream 45 km and upstream 15 km taking 3 hours each time , what is the speed of the woman in still water ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 45 - - - 3 ds = 15 ? - - - - 1 15 - - - - 3 us = 5 ? - - - - 1 m = ? m = ( 15 + 5 ) / 2 = 10 answer : a
Answer: a
Problem: in order to obtain an income of rs . 1000 from 50 % stock at rs . 500 , one must make an investment of
Options: a ) rs . 17000 , b ) rs . 16050 , c ) rs . 15400 , d ) rs . 10000 , e ) rs . 10500
Rationale: "explanation : market value = rs . 500 . required income = rs . 1000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 50 ( ie , 50 % of the face value 100 ) , investment = rs . 500 to obtain rs . 1000 , investment = 500 / 50 ã — 1000 = 10000 answer : option d"
Answer: d
Problem: jack and jill are marathon runners . jack can finish a marathon ( 40 km ) in 4.5 hours and jill can run a marathon in 4.0 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 8 / 9 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 40 / ( 9 / 2 ) = 80 / 9 average speed of jill = 40 / ( 4.0 ) = 10 ratio of average speed of jack to jill = ( 80 / 9 ) / 10 = 8 / 9 answer c"
Answer: c
Problem: a snooker tournament charges $ 45.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 300 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 212 , b ) 240 , c ) 220 , d ) 230 , e ) 225
Rationale: "let no of sits in vip enclosure is x then x * 45 + 15 ( 300 - x ) = 7500 or 30 x = 7500 - 4500 , x = 3000 / 30 = 100 vip = 100 general 220 c"
Answer: c
Problem: the length of a rectangular floor is more than its breadth by 100 % . if rs . 600 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
Options: a ) 15.0 m . , b ) 14.4 m . , c ) 12.0 m . , d ) 16.2 m . , e ) 16.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 100 % of b = l + 1 b = 2 b area of the floor = 600 / 3 = 200 sq m l b = 200 i . e . , l * l / 2 = 108 l 2 = 216 = > l = 14.4 m . answer : b"
Answer: b
Problem: 5 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 2776 , c ) 4400 , d ) 4675 , e ) 881
Rationale: "x * ( 95 / 100 ) * ( 80 / 100 ) = 3553 x = 4675 answer : d"
Answer: d
Problem: what is the sum of the odd integers from 35 to 55 , inclusive ?
Options: a ) 495 , b ) 550 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 45 . sum = mean ( # of elements ) there are 11 odd numbers between 35 - 55 inclusive . 11 * 45 = 495 a"
Answer: a
Problem: every monday , marina eats one croissant and every tuesday she eats two croissants . on each subsequent day of the week , she eats a number of croissants equal to the sum of the croissants eaten on the two previous days , with the exception that if she eats more than 4 croissants on any particular day , the next day she will eat only one croissant . at the end of the week ( which runs from monday through sunday ) , the cycle resets , and marina goes back to eating one croissant on monday , two on tuesday , and so forth . if a particular month begins on a saturday , how many croissants will marina eat on the 30 th of that month ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: she eat as follow mon - 1 tue - 2 wed - 3 thr - 5 fri - 1 ( since she had more than 4 previous day ) sat - 6 sunday - 1 ( since she had more than 4 previous day ) so 30 th day of month she will have 1 . answer is a
Answer: a
Problem: a boy swims downstream 48 km and upstream 12 km taking 6 hours each time ; what is the speed of the current ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "48 - - - 6 ds = 8 ? - - - - 1 12 - - - - 6 us = 2 ? - - - - 1 s = ? s = ( 8 - 2 ) / 2 = 3 answer : c"
Answer: c
Problem: if the sides of a cube are in the ratio 5 : 3 . what is the ratio of their diagonals ?
Options: a ) 5 : 9
b ) 9 : 3
c ) 5 : 4
d ) 3 : 5
e ) 5 : 3
Rationale: explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 3 d 1 : d 2 = 5 : 3 where √ 3 cancelled both side answer : e
Answer: e
Problem: the average weight of 26 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 49.05 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25
Rationale: "explanation : average weight of 26 boys = 50.25 total weight of 26 boys = 50.25 × 26 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 26 ) + ( 45.15 × 8 ) total boys = 26 + 8 = 34 average weight of all the boys = ( 50.25 × 26 ) + ( 45.15 × 8 ) / 34 = 49.05 answer : option a"
Answer: a
Problem: a one - foot stick is marked in 1 / 4 and 1 / 5 portion . how many total markings will there be , including the end points ?
Options: a ) 18 , b ) 16 , c ) 13 , d ) 9 , e ) 11
Rationale: lcm of 20 = 20 1 / 4 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 . . . . . . 20 ( total = 5 ) 1 / 5 marking are ( table of 4 ) 0 . . . . . . . 4 . . . . . . 8 . . . . . . 12 . . . . . . . . 16 . . . . . . 20 ( total = 6 ) overlapping markings are 0 . . . . . . . . 20 ( total = 2 ) total markings = 5 + 6 - 2 = 9 answer = d
Answer: d
Problem: find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years ?
Options: a ) 272.22 , b ) 128.29 , c ) 306.04 , d ) 198.39 , e ) 212.22
Rationale: "explanation : a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Problem: the average score of a cricketer in 2 matches is 30 and in other 3 matches is 40 . then find the average score in all the 5 matches ?
Options: a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 36
Rationale: average in 5 matches = ( 2 * 30 + 3 * 40 ) / 2 + 3 = 60 + 120 / 5 = 180 / 5 = 36 answer is e
Answer: e
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 9 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 50 / 4 , b ) 70 / 6 , c ) 80 / 7 , d ) 90 / 8 , e ) 100 / 9
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 1 / 9 = ( r - 10 ) / r r = 9 r - 90 r = 90 / 8 the answer is d ."
Answer: d
Problem: in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 64.50 per kg ?
Options: a ) 3 : 1 , b ) 2 : 1 , c ) 5 : 2 , d ) 3 : 2 , e ) 3 : 4
Rationale: mean price = ( 72 - 64.5 = 7.5 ) ( 64.5 - 62 = 2.5 ) req ratio = 7.5 : 2.5 = 3 : 1 answer a
Answer: a
Problem: a solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm . the height of the cone is :
Options: a ) 8 cm
b ) 6 cm
c ) 4 cm
d ) 3 cm
e ) none
Rationale: sol . let the height of the cone be h cm . then , 1 / 3 ∏ * 6 * 6 * h = 4 / 3 ∏ * 3 * 3 * 3 ⇒ h = [ 36 * 3 / 36 ] = 3 cm . answer d
Answer: d
Problem: the present worth of rs . 2310 due years hence , the rate of interest being 15 % per annum , is :
Options: a ) rs . 1440 , b ) rs . 1750 , c ) rs . 1680 , d ) rs . 1840 , e ) none of these
Rationale: "explanation : p . w . = rs . [ 100 × 2310 / 100 + ( 15 × 52 ) ] = rs . 1680 . answer : c"
Answer: c
Problem: if x is the median of the set { 8 / 2 , 11 / 3 , 27 / 9 , 21 / 5 , x } , x could be
Options: a ) 4 , b ) 17 / 5 , c ) 16 / 5 , d ) 30 / 7 , e ) 31 / 7
Rationale: the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( a )
Answer: a
Problem: how many seconds will a train 100 meters long take to cross a bridge 140 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 24 , c ) 25 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 140 = 240 s = 36 * 5 / 18 = 10 mps t = 240 / 10 = 24 sec answer : option b"
Answer: b
Problem: while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "both computers together process files at a rate of 240 / 12 + 240 / 6 = 20 + 40 = 60 files per hour . the time required to process 240 files is 240 / 60 = 4 hours the answer is c ."
Answer: c
Problem: a and b together can complete work in 6 days . a alone starts working and leaves it after working for 4 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 12 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 4 days so a can complete the whole work in 8 days a ’ s one day work = 1 / 8 b ’ s one day work = 1 / 6 - 1 / 8 = 2 / 48 = 1 / 24 b alone can complete the work in 24 days so half of the work in 12 days answer : option b"
Answer: b
Problem: in town x , 64 percent of the population are employed , and 46 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 28 % , d ) 40 % , e ) 52 %
Rationale: we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 46 are employed males , hence 18 % are employed females . ( employed females ) / ( total employed people ) = 18 / 64 = 28 % answer : c .
Answer: c
Problem: the lcm of two numbers is 2310 and hcf is 55 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 605 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 55 / 210 = 11 * 55 = 605 answer : d"
Answer: d
Problem: what is the sum of all possible solutions to | x - 2 | ^ 2 + | x - 2 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 8 , e ) 14
Rationale: "denote | x - 2 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 2 | , so it ' s an absolute value and thus can not be negative . y = | x - 2 | = 4 - - > x = 6 or x = - 2 . the sum = 8 answer : d ."
Answer: d
Problem: a and b invests rs . 2500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 11 : 5 , b ) 15 : 16 , c ) 15 : 2 , d ) 9 : 9 , e ) 11 : 1
Rationale: "( 2.5 * 6 + 5 * 6 ) : ( 4 * 12 ) 45 : 48 = > 15 : 16 answer : b"
Answer: b
Problem: find the average of first 4 multiples of 11 ?
Options: a ) 10 , b ) 12.6 , c ) 27.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 11 + 22 + 33 + 44 ) / 4 = 27.5 answer is c"
Answer: c
Problem: a car traveled from san diego to san francisco at an average speed of 54 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: let the time taken be = x one way distance = 54 x total distance traveled = 2 * 54 x = 108 x total time taken = x + 2 x = 3 x average speed = 108 x / 3 x = 36 answer : c
Answer: c
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 8 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 8 t 1 = 8 and so t 2 = 16 . the answer is c ."
Answer: c
Problem: a pump will fill a tank in 3 hours . because of a leak in the tank , it took 3 hours 30 min to fill the tank . in what time the leak can drain out all the water of the tank and will make tank empty ?
Options: a ) 20 hrs , b ) 21 hrs , c ) 22 hrs , d ) 23 hrs , e ) 24 hrs
Rationale: work done for 1 hr without leak = 1 / 3 work done with leak = 31 / 2 = = > 7 / 2 work and leak in 1 hr = 2 / 7 work leak in 1 hr = 1 / 3 - 2 / 7 = 1 / 21 so 21 hrs answer b
Answer: b
Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = p + 21 , what is the perimeter of the garden in feet ?
Options: a ) 24
b ) 28
c ) 32
d ) 36
e ) 40
Rationale: let x be the length of one side of the square garden . x ^ 2 = 4 x + 21 x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 , - 3 p = 4 ( 7 ) = 28 the answer is b .
Answer: b
Problem: a train 100 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 88 , d ) 41 , e ) 12
Rationale: "speed of the train relative to man = ( 100 / 10 ) m / sec = ( 10 ) m / sec . [ ( 10 ) * ( 18 / 5 ) ] km / hr = 36 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 36 = = > x = 41 km / hr . answer : d"
Answer: d
Problem: a positive number x is multiplied by 2 , and this product is then divided by 4 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 9 / 4 because x is positive , x = 9 / 4 . the answer is a ."
Answer: a
Problem: how many multiples of 3 are there between 10 and 100 , exclusive ?
Options: a ) 30 , b ) 29 , c ) 28 , d ) 31 , e ) 33
Rationale: "3 * 4 = 12 3 * 33 = 99 total multiples = ( 33 - 4 ) + 1 = 30 exclude 10 and 100 = 30 answer is a"
Answer: a
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 28 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 28 gallons then 0.12 a + 0.16 ( 200 - a ) = 28 - - > a = 100 . answer : c ."
Answer: c