Cheukting/mathqa huggingface dataset:
Question (geometry): what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 2 , 3 and 5 ?
Options: a ) 2.5 , b ) 3 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5 ans . a"
Answer: a
Question (general): the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is
Options: a ) rs . 3800 , b ) rs . 3900 , c ) rs . 4000 , d ) rs . 4200 , e ) rs . 4400
Rationale: "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . b"
Answer: b
Question (general): if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 7 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 7 / 64 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 7 = 7 c 2 total possible outcomes - 2 ^ 7 ( each child can be either a girl or a boy ) probability = 2 c 1 * 7 c 2 / 2 ^ 7 = 2 * 7 / 2 * 2 * 2 * 2 * 2 * 2 * 2 = 7 / 64 ans = d"
Answer: d
Question (general): instead of multiplying a number by 2 , the number is divided by 10 . what is the percentage of error obtained ?
Options: a ) 94 % , b ) 92 % , c ) 95 % , d ) 93 % , e ) 97 %
Rationale: let the number be x the right number is 2 x the wrong number is x / 10 error is ( 2 x - x / 10 ) = 19 x / 10 percentage of error is ( ( 19 x / 10 ) / 2 x ) * 100 = 95 % answer : c
Answer: c
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 54 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 54 * ( n + 1 ) - - > n = 9 . or as 40 extra units increased the average for n + 1 days by 4 units per day then 40 / ( n + 1 ) = 4 - - > n = 9 . answer d ."
Answer: d
Question (gain): the cash difference between the selling prices of an article at a profit of 2 % and 4 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) 51 : 52
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 102 % of x ) / ( 104 % of x ) = 102 / 104 = 51 / 52 = 51 : 52 . answer : e"
Answer: e
Question (physics): jose completes a piece of work in 10 days , raju completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is
Options: a ) 5 days , b ) 6 days , c ) 8 days , d ) 10 days , e ) 12 days
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days . c )
Answer: c
Question (physics): wilson can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ?
Options: a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes .
Rationale: rate = output / time wilson rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min
Answer: c
Question (physics): 5 men and 12 boys finish a piece of work in 4 days , 7 men and 6 boys do it in 5 days . the ratio between the efficiencies of a man and boy is ?
Options: a ) 6 : 8 , b ) 6 : 4 , c ) 6 : 2 , d ) 6 : 5 , e ) 6 : 2
Rationale: 5 m + 12 b - - - - - 4 days 7 m + 6 b - - - - - - - 5 days 20 m + 48 b = 35 m + 30 b 18 b = 15 m = > 5 m = 6 b m : b = 6 : 5 answer : d
Answer: d
Question (geometry): the volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :
Options: a ) 89.8 cm ³
b ) 92.5 cm ³
c ) 132.8 cm ³
d ) 144.5 cm ³
e ) none
Rationale: sol . volume of the block = ( 10 * 5 * 2 ) cm ³ . volume of the cone carved out = [ 1 / 3 * 22 / 7 * 3 * 3 * 7 ] cm ³ = 66 cm ³ ∴ wood wasted = ( 100 - 66 ) % = 34 % . answer a
Answer: a
Question (physics): two trains of length 100 meters and 200 meters are 140 meters apart . they are moving towards each other on parallel tracks , at speeds of 54 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the speeds are 54000 / 3600 = 15 m / s and 72000 / 3600 = 20 m / s the relative speed is 35 m / s . time = 140 / 35 = 4 seconds the answer is b ."
Answer: b
Question (physics): two trains start simultaneously from opposite ends of a 140 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 140 - km trip in 4 hours . train y , travelling at a constant rate , completes the 140 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 60 , b ) 64 , c ) 68 , d ) 72 , e ) 76
Rationale: "if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 140 km to the meeting point , then train x travels ( 3 / 7 ) * 140 = 60 km . the answer is a ."
Answer: a
Question (general): the year next to 1991 having the same calendar as that of 1990 is –
Options: a ) 1998 , b ) 2001 , c ) 2002 , d ) 2003 , e ) none of these
Rationale: we go on counting the odd days from 1991 onward still the sum is divisible by 7 . the number of such days are 14 upto the year 2001 . so , the calender for 1991 will be repeated in the year 2002 . answer c
Answer: c
Question (general): find ( 7 x + 6 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 6 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 6 y ) / ( 3 y - 2 y ) = > 27 y / y = 27 answer : d"
Answer: d
Question (general): a car was driving at 72 km / h for 20 minutes , and then at 81 km / h for another 40 minutes . what was its average speed ?
Options: a ) 76 . , b ) 77 . , c ) 78 . , d ) 79 . , e ) 80 .
Rationale: driving at 72 km / h for 20 minutes , distance covered = 72 * 1 / 3 = 24 km driving at 90 km / h for 40 minutes , distance covered = 81 * 2 / 3 = 54 km average speed = total distance / total time = 78 / 1 = 78 km / h answer : a
Answer: a
Question (physics): a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 33 , b ) 77 , c ) 66 , d ) 11 , e ) 99
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 4 days = 4 * ( 1 / 24 + 1 / 30 ) = 3 / 10 remaining work = 7 / 10 the number of days required for this initial work = 7 days . the total number of days required = 4 + 7 = 11 days . answer : d"
Answer: d
Question (physics): nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 36 meter head start . if cristina runs at a pace of 4 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 36 seconds , e ) 45 seconds
Rationale: used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 36 for cristina = c = 5 * t @ t = 36 , n = 144 c = 144 right answer ans : d
Answer: d
Question (general): what is the largest integral value of ' k ' for which the quadratic equation x 2 - 6 x + k = 0 will have two real and distinct roots ?
Options: a ) 9 , b ) 7 , c ) 3 , d ) 8 , e ) 12
Rationale: explanatory answer any quadratic equation will have real and distinct roots if the discriminant d > 0 the discriminant ' d ' of a quadratic equation ax 2 + bx + c = 0 is given by b 2 - 4 ac in this question , the value of d = 62 - 4 * 1 * k if d > 0 , then 36 > 4 k or k < 9 . therefore , the highest integral value that k can take is 8 . correct choice is ( d )
Answer: d
Question (general): a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 20 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 320 , b ) $ 420 , c ) $ 720 , d ) $ 220 , e ) $ 200
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 20 a = 20 + b ( 1 ) = = = > c = 60 + 3 b - b = 2 b + 60 = = > 2 b - c = - 60 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 20 = 2.5 b - 20 = = > 2.5 b - c = 20 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 80 b = $ 160 a = $ 180 c = 540 - 160 = $ 380 total amount = 180 + 160 + 380 = $ 720 answer : c"
Answer: c
Question (general): if x , y , and z are positive integers and 3 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 45 , b ) 79 , c ) 50 , d ) 55 , e ) 60
Rationale: "given 3 x = 5 y = 8 z x + y + z in terms of x = x + ( 3 x / 5 ) + ( 3 x / 8 ) = 79 x / 40 now checking with each of the answers and see which value gives a minimum integer value . a x = 40 / 79 * 45 , not an integer c , d , e can be ruled out similarly . b is minimum value as x = 79 * 40 / 79 = 79 answer is b"
Answer: b
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 4 = f ( 3 x – 6 )
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = a = 3 f ( x ) = 3 x – 5 2 * [ f ( x ) ] – 4 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) - 4 = 3 ( 3 x - 6 ) - 5 6 x - 14 = 9 x - 23 x = 3"
Answer: a
Question (physics): a can do a job in 8 days and b can do it in 20 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 11 3 / 7 days , c ) 23 ½ days , d ) 12 ½ days , e ) none of these
Rationale: "explanation : 1 / 8 + 1 / 20 = 7 / 40 40 / 7 = 40 / 7 * 2 = 11 3 / 7 days answer : b"
Answer: b
Question (geometry): in an electric circuit , two resistors with resistances 8 ohms and 9 ohms are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is r value ?
Options: a ) 17
b ) 45 / 78
c ) 72 / 17
d ) 17 / 72
e ) 72
Rationale: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 8 + 1 / 9 , from which it follows that r = 72 / 17 . answer : c .
Answer: c
Question (general): the average of runs of a cricket player of 10 innings was 35 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 79 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 35 so , total = average x no . of innings = 35 x 10 = 350 . now increase in avg = 4 runs . so , new avg = 35 + 4 = 39 runs total runs = new avg x new no . of innings = 39 x 11 = 429 runs made in the 11 th inning = 429 - 350 = 79 answer : b"
Answer: b
Question (geometry): the side of a square is increased by 10 % then how much % does its area increases ?
Options: a ) 21 , b ) 56.25 , c ) 50.75 , d ) 42.75 , e ) 52.75
Rationale: "a = 100 a 2 = 10000 a = 110 a 2 = 12100 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 2100 100 - - - - - - - ? = > 21 % answer : a"
Answer: a
Question (general): on dividing 161 by a number , the quotient is 10 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 161 - 1 ) / 10 = 160 / 10 = 16 c )"
Answer: c
Question (physics): 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 6 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 6 girls = 8 ã — 6 / 4 + 12 = 12 + 6 = 18 girls 8 days to complete the work answer : option d"
Answer: d
Question (geometry): a square of side 8 cm has been made to a rectangle by combining it with a rectangle of dimensions of length 8 cm and breadth 4 cm . what is the perimeter of the newly formed rectangle ?
Options: a ) 10
b ) 20
c ) 40
d ) 60
e ) 80
Rationale: dimensions of newly formed rectangle , length = 8 + 4 = 12 cm breadth = 8 cm perimeter of the new rectangle = 2 x ( 12 = 8 ) = 40 cm answer : c
Answer: c
Question (general): the average of 11 numbers is 10.7 . if the average of first 6 is 10.5 and that of the last 6.00001 is 11.4 the sixth number is ?
Options: a ) 9 , b ) 9.2 , c ) 10 , d ) 13.7 , e ) 12
Rationale: explanation : 1 to 11 = 11 * 10.7 = 117.7 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.4 = 68.4 63 + 68.4 = 131.4 – 117.7 = 13.7 6 th number = 13.7 d )
Answer: d
Question (general): the denominator of a fraction is 8 greater than the numerator . if the numerator and the denominator are increased by 5 , the resulting fraction is equal to 6 â  „ 7 . what is the value of the original fraction ?
Options: a ) 25 / 33 , b ) 31 / 39 , c ) 37 / 45 , d ) 43 / 51 , e ) 53 / 61
Rationale: "let the numerator be x . then the denominator is x + 8 . x + 5 / x + 13 = 6 / 7 . 7 x + 35 = 6 x + 78 . x = 43 . the original fraction is 43 / 51 . the answer is d ."
Answer: d
Question (other): evaluate 50 ! / 47 !
Options: a ) 102500 , b ) 112584 , c ) 117600 , d ) 118450 , e ) 128450
Rationale: "evaluate 50 ! / 47 ! = 50 * 49 * 48 * ( 47 ! ) / 47 ! = 50 * 49 * 48 = 117600 answer : c"
Answer: c
Question (physics): a 425 meter long train crosses a platform in 55 seconds while it crosses a signal pole in 40 seconds . what is the length of the platform ?
Options: a ) 155.68 , b ) 160 , c ) 159.38 , d ) 180 , e ) 175
Rationale: "speed = [ 425 / 40 m / sec = 42.5 / 4 m / sec . let the length of the platform be x meters . then , x + 425 / 55 = 42.5 / 4 4 ( x + 425 ) = 2337.5 è x = 159.38 m . answer : c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 8 seconds . find the length of the train .
Options: a ) 133.33 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 8 = 133.33 meter . answer : a"
Answer: a
Question (physics): annika hikes at a constant rate of 12 minutes per kilometer . she has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 40 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 40 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 3 , d ) 3.04 , e ) 4
Rationale: "set up two r x t = d cases . 1 . 1 / 12 km / min x t = 2.75 from which t = 33 mins . we know total journey time now is 40 + 33 = 73 . the rate is the same ie 1 / 12 km / min . set up second r x t = d case . 1 / 12 km / min x 73 = 6.08 km now the total journey would be halved as distance would be same in each direction . 6.08 / 2 = 3.04 d ."
Answer: d
Question (general): tom and jerry enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if tom received $ 800 more than jerry did , what was the profit made by their business in that year ?
Options: a ) 3000 , b ) 4000 , c ) 5000 , d ) 6900 , e ) 6677
Rationale: say the profit was $ x . tom share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 jerry share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is a
Answer: a
Question (general): simplify : 0.72 * 0.43 + 0.12 * 0.34
Options: a ) 0.3504 , b ) 0.4209 , c ) 0.4889 , d ) 0.6412 , e ) 0.4612
Rationale: given exp . = 0.72 * 0.43 + ( 0.12 * 0.34 ) = 0.3096 + 0.0408 = 0.3504 answer is a
Answer: a
Question (physics): a jeep takes 8 hours to cover a distance of 280 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 28 kmph , b ) 52 kmph , c ) 20 kmph , d ) 23 kmph , e ) 65 kmph
Rationale: "time = 8 distance = 280 3 / 2 of 8 hours = 8 * 3 / 2 = 12 hours required speed = 280 / 12 = 23 kmph d )"
Answer: d
Question (gain): the simple interest on rs . 34 for 8 months at the rate of 6 paise per rupeeper month is
Options: a ) 16.32 , b ) 16.9 , c ) 12.25 , d ) 13.21 , e ) none
Rationale: "sol . s . i . = rs . [ 34 * 6 / 100 * 8 ] = rs . 16.32 answer a"
Answer: a
Question (physics): a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 3 km ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.0 , d ) 2.25 , e ) 2.5
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 3 / 2 = 1.5 hours . the answer is a ."
Answer: a
Question (general): what sum of money put at c . i amounts in 2 years to rs . 8880 and in 3 years to rs . 9261 ?
Options: a ) 8164 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8880 - - - - 381 100 - - - - ? = > 4.29 % x * 104.29 / 100 * 104.29 / 100 = 8880 x * 1.0876 = 8880 x = 8880 / 1.0876 = > 8164.38 answer : a"
Answer: a
Question (physics): how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 30 km / hr ?
Options: a ) 25 , b ) 30 , c ) 45 , d ) 64 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 30 - 6 ) km / hr = 24 km / hr = ( 24 x 5 / 18 ) m / sec = 6.66 m / sec time taken to pass the man = ( 400 / 6.66 ) sec = 60 sec . answer : e"
Answer: e
Question (physics): what is the maximum number of pieces of birthday cake of size 4 ” by 4 ” that can be cut from a cake 16 ” by 16 ” ?
Options: a ) 5 , b ) 4 , c ) 16 , d ) 20 , e ) 25
Rationale: "the prompt is essentially asking for the maximum number of 4 x 4 squares that can be cut from a larger 16 by 16 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 4 ' pieces ' each , we have ( 4 ) ( 4 ) = 16 total smaller squares ( at maximum ) . c"
Answer: c
Question (gain): a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 10 marks , find the maximum marks set for the test .
Options: a ) 240 , b ) 300 , c ) 360 , d ) 420 , e ) 480
Rationale: "30 % = 90 marks 1 % = 3 marks 100 % = 300 marks the answer is b ."
Answer: b
Question (physics): a work crew of 6 men takes 9 days to complete one - half of a job . if 12 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 3 1 / 3 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 6 men will do in . . 6 / x = 1 / 9 * 1 / 2 as half job is done x = 108 now 12 more are added then 18 / 108 = 1 / 2 * 1 / d for remaining half job d = 3 number of days b"
Answer: b
Question (general): in a class , 6 students can speak gujarati , 15 can speak hindi and 6 can speak marathi . if two students can speak two languages and one student can speak all the 3 languages , then how many students are there in the class
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: n ( aubuc ) = 6 + 15 + 6 - 2 - 2 - 2 + 1 = 22 answer : b
Answer: b
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 41 km ) in 4.5 hours and jill can run a marathon in 4.1 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 41 / 45 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 41 / ( 9 / 2 ) = 82 / 9 average speed of jill = 41 / ( 4.1 ) = 10 ratio of average speed of jack to jill = ( 82 / 9 ) / 10 = 82 / 90 = 41 / 45 answer a"
Answer: a
Question (gain): if the selling price of 100 articles is equal to the cost price of 40 articles , then the loss or gain percent is :
Options: a ) 25 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) 50 %
Rationale: let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 40 . loss % = 60 / 100 * 100 = 60 % answer : c
Answer: c
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 6 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5184 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 12 ) m = 36 m , b = ( 36 - 12 ) m = 24 m , h = 8 m . volume of the box = ( 36 x 24 x 12 ) m 3 = 5184 m 3 . answer : option b"
Answer: b
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 700 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 511 , b ) 546 , c ) 552 , d ) 562 , e ) 570
Rationale: "number of newborns that can die in first month = 1 / 10 * 700 = 70 survived = 630 number of newborns that can die in second month = 1 / 10 * 630 = 63 survived = 567 number of newborns that can die in third month = 1 / 10 * 567 = 56 survived = 511 answer : a"
Answer: a
Question (other): the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach ( b ) to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 40 , b ) 60 , c ) 50 , d ) 30 , e ) 70
Rationale: "b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be b b"
Answer: b
Question (general): in x game of billiards , x can give y 20 points in 60 and he can give z 50 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 75
Rationale: "x scores 60 while y score 40 and z scores 10 . the number of points that z scores when y scores 100 = ( 100 * 50 ) / 40 = 25 . in x game of 100 points , y gives ( 100 - 25 ) = 75 points to c . e"
Answer: e
Question (physics): jack and jill work at a hospital with 5 other workers . for an internal review , 2 of the 7 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 21 , d ) 3 / 8 , e ) 2 / 3
Rationale: "1 / 7 c 2 = 1 / 21 . answer : c ."
Answer: c