Cheukting/mathqa huggingface dataset:
Question (other): a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 7 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 28 : 35 , d ) 2 : 5 , e ) 4 : 6
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 7 - - > x ( a - b ) = 7 . since 7 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 7 . the above implies that either x = 1 and a - b = 7 or x = 7 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 7 . for the original question only option which fits is e , 4 : 5 . cats = 7 * 4 = 28 and dogs = 7 * 5 = 35 . answer : c ."
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 18 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 170 meter , c ) 156 meter , d ) 300 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 18 = 300 meter answer : d"
Answer: d
Question (other): the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 13 and 14 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 322 , d ) 231 , e ) 121
Rationale: "clearly , the numbers are ( 23 * 13 ) and ( 23 * 14 ) . larger number = ( 23 * 14 ) = 322 . answer : c"
Answer: c
Question (gain): 60 is subtracted from 50 % of a number , the result is 10 . find the number ?
Options: a ) 150 , b ) 120 , c ) 266 , d ) 288 , e ) 271
Rationale: "( 50 / 100 ) * x – 50 = 10 5 x = 600 x = 120 answer : b"
Answer: b
Question (general): 80 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 35 , b ) 32 , c ) 36 , d ) 40 , e ) 52
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 80 = 35 answer : a"
Answer: a
Question (general): the value of ( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2
Options: a ) 100 , b ) 1000 , c ) . 001 , d ) . 0001 , e ) . 01
Rationale: ( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2 = a 2 + b 2 + c 2 / ( a / 10 ) 2 + ( b / 10 ) 2 + ( c / 10 ) 2 where a = . 02 , b = . 52 , c = . 035 = 100 ( a 2 + b 2 + c 2 ) / a 2 + b 2 + c 2 = 100 answer : a
Answer: a
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (geometry): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (geometry): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (geometry): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (probability): 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
Question (general): 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