regisss/math_qa huggingface dataset:
Problem: a company pays 12.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 12.5 * 50 ) / 100 = rs . 6.25 rs . 25 is income on an investment of rs . 100 rs . 6.25 is income on an investment of rs . ( 6.25 * 100 ) / 25 = rs . 25 answer : a"
Answer: a
Problem: a box contains 10 tablets of medicine a and 13 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 13 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13 + 2 = 15 tablets . answer : b ."
Answer: b
Problem: what is the smallest number which , when increased by 7 , is divisible by 7 , 8 , and 24 ?
Options: a ) 154 , b ) 161 , c ) 168 , d ) 175 , e ) 182
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 7 = 161 . the answer is b ."
Answer: b
Problem: find the simple interest on rs . 73,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8125 , d ) 9125 , e ) none of them
Rationale: "p = rs . 73000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 73,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9125 answer is d ."
Answer: d
Problem: find large number from below question the difference of 2 no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1245 , b ) 1430 , c ) 1540 , d ) 1600 , 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: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes at 13 km / hr downstream and 4 km / hr upstream .
Options: a ) 4.5 kmph , b ) 9.5 kmph , c ) 7.5 kmph , d ) 8.5 kmph , e ) 5.5 kmph
Rationale: "speed in still water = ( 13 + 4 ) 1 / 2 kmph = 8.5 kmph . answer : d"
Answer: d
Problem: two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 7 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 64 / 21
Rationale: rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 7 combined = 13 / 42 work done in 2 days = 13 / 21 work left = 8 / 21 rate * time = work left 1 / 8 * time = 8 / 21 time = 64 / 21 e
Answer: e
Problem: car dealership x , the total profit from sales increased by 10 percent over the previous years , while the number of cars sold decreased by 10 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 23 % , e ) 25 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.1 x / 0.9 y = 11 / 9 ( x / y ) increase in profit per car = ( ( 2 / 9 ) ( x / y ) ) / ( x / y ) * 100 = 22.22 % answer = c"
Answer: c
Problem: of 70 players on a football team , 28 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 56 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 28 rest = 70 - 28 = 42 left handed = 42 / 3 = 14 right handed = 28 if all thrower are right handed then total right handed is 28 + 28 = 56 so a . 56 is the right answer"
Answer: a
Problem: on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 900 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 12.75 , c ) $ 51.75 , d ) $ 100.75 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 900 ( 1.05 ) ^ 2 = 900 ( 1.1025 ) = 992.25 thus , tim earned 105 dollars , while lana earned 92.25 dollars the difference is $ 12.75 and the answer is b ."
Answer: b
Problem: a cube of sides 9 is first painted red and then cut into smaller cubes of side 3 . how many of the smaller cube have painted on exactly 2 sides ?
Options: a ) 30
b ) 24
c ) 12
d ) 8
e ) 9
Rationale: n = side of big cube / side of small cube and no . of smaller cubes with two surfaces painted is ( n - 2 ) * 12 ( 3 - 2 ) * 12 = 12 ans answer : c
Answer: c
Problem: sam invested rs . 5000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 500.2 , b ) 320.0 , c ) 220.5 , d ) 100.1 , e ) 230.2
Rationale: "p = rs . 5000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 5000 * ( 1 + 5 / 100 ) 2 ] = ( 5000 * 21 / 20 * 21 / 20 ) = rs . 220.50 answer : c"
Answer: c
Problem: a person incurs 20 % loss by selling a watch for $ 1000 . at what price should the watch be sold to earn 20 % profit ?
Options: a ) $ 1000 , b ) $ 950 , c ) $ 1500 , d ) $ 1150 , e ) $ 1250
Rationale: "let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 20 ) / 1000 = ( 100 + 20 ) / x x = 120 * 1000 / 80 = 1500 answer is c"
Answer: c
Problem: a , b and c can complete a piece of work in 24 , 6 and 12 days respectively . working together , they will complete the same work in :
Options: a ) 33 / 7 , b ) 43 / 7 , c ) 24 / 7 , d ) 19 / 7 , e ) none
Rationale: if a can do a piece of work in n days , then a ' s 1 day ' s work = 1 / n ( a + b + c ) ' s 1 day ' s work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 so , all the three together will complete the job in = 24 / 7 days answer : c
Answer: c
Problem: a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is :
Options: a ) 35 , b ) 36 , c ) 37 , d ) 40 , e ) 45
Rationale: "according to given condition vt = ( v + 3 ) ( t - 2 / 3 ) vt = ( v - 2 ) ( t + 2 / 3 ) here v is velocity in kmph , t is time in hours and 2 / 3 is value of 40 min in hour on solving we will get t = 10 / 3 and and v = 12 so distance = ( 10 / 3 ) * 12 = 40 kms answer : d"
Answer: d
Problem: two pipes a and b can fill a cistern in 20 and 30 minutes respectively , and a third pipe c can empty it in 60 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 15 min , b ) 15 1 / 7 min , c ) 17 1 / 7 min , d ) 7 1 / 7 min , e ) 7 2 / 7 min
Rationale: "1 / 20 + 1 / 30 - 1 / 60 = 4 / 60 60 / 4 = 15 answer : a"
Answer: a
Problem: a shoe merchant has declared a 10 % rebate in prices . how much rebate would one get if he purchases 5 pairs of shoes at rs . 28 each ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: explanation : 5 shirts * rs . 28 = rs . 140 rebate = 10 % * 140 = 14 correct option : d
Answer: d
Problem: if the average of 8 digits is 20 and the average of 5 of them is 12 , calculate the average of the remaining 3 numbers ?
Options: a ) 13.3 , b ) 38.3 , c ) 35.3 , d ) 31.3 , e ) 33.3
Rationale: "explanation : total of the 8 digits - 8 * 20 = 160 total of the 5 digits - 5 * 12 = 60 total of the remaining 3 digits - 160 - 60 = 100 average of the remaining 3 numbers = 100 / 3 = 33.3 answer : e"
Answer: e
Problem: in a restaurant , the profit is 120 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 49 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 120 , s . p . = rs . 220 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 220 . profit = rs . ( 220 - 112 ) = rs . 108 . required percentage = ( 108 / 220 * 100 ) % = 49 % appox answer : b"
Answer: b
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 272
Rationale: "10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 – 1050 = 450 answer : d"
Answer: d
Problem: a shop owner sells 30 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 30 m cloth ) – ( c . p . of 30 m cloth ) selling price of 20 m cloth = selling price of 30 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 20 m cloth = rs . 2000 and s . p . of 20 m cloth = rs . rs . 3000 profit % = 10 × 100 = 50 % 20 profit of 50 % was made by the merchant . c"
Answer: c
Problem: a certain dark blue paint contains 40 percent blue pigment and 60 percent red pigment by weight . a certain green paint contains 40 percent blue pigment and 60 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 3 , e ) 5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 6 = 3 grams of red pigment
Answer: d
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds x in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out x : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Problem: if ( a – b ) is 13 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 13 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 13 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 13 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 13 = ( c – a ) – 3 = > 2 ( a – c ) = 10 = > ( a – c ) = 5 answer : e"
Answer: e
Problem: how many integers between 1 and 1,400 are divisible by 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e"
Answer: e
Problem: rahul can done a work in 5 days and meena can done a work in 10 days . in how many days that both are work together ?
Options: a ) 3 / 10 , b ) 10 / 3 , c ) 1 / 3 , d ) 5 , e ) 6 / 3
Rationale: a ' s one day work = 1 / 5 b ' s one day work = 1 / 10 a + b = 1 / 5 + 1 / 10 = 10 + 5 / 50 = 10 / 3 days ans : option b
Answer: b
Problem: a bicycle wheel has a diameter of 0.75 m . how many complete revolutions does it make in 1 km ?
Options: a ) 424 , b ) 448 , c ) 1408 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.75 m ) = 424.6 . hence 424 complete revolutions . answer a"
Answer: a
Problem: country x taxes each of its citizens an amount equal to 15 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b .
Answer: b
Problem: if a ^ 2 + b ^ 2 = 10 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 10 - 20 = - 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 10 + 20 = 30 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 30 - 10 = 20 b"
Answer: b
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 8 = 22 the answer is c ."
Answer: c
Problem: on a windy day , out of every 3 sand dunes formed , only 1 remains . out of 5 blown - out sand - dunes , 1 has treasure and only 2 out of 3 sand dunes formed have lucky coupons . find the probability that the blown - out sand dune will contain both the things .
Options: a ) 2 / 25 , b ) 4 / 75 , c ) 7 / 75 , d ) 3 / 5 , e ) 4 / 45
Rationale: probability of sand dune blown out = 2 / 3 probability that it has treasure = 1 / 5 probability that it has lucky coupon = 2 / 3 total probability = 2 / 3 * 1 / 5 * 2 / 3 = 4 / 45 answer : e
Answer: e
Problem: in the faculty of reverse - engineering , 250 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 674 . , e ) 666 .
Rationale: "answer is d : 674 solution : total number of students studying both are 423 + 250 - 134 = 539 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 539 , so 100 % is approx . 674 ."
Answer: d
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 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
Problem: 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
Problem: 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
Problem: 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
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 10 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 5 cm , c ) 6 cm , d ) 8 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 5 x 10 â ‡ ’ r 2 = ( 5 x 10 / 2 ) â ‡ ’ 25 â ‡ ’ r = 5 cm . answer b"
Answer: b
Problem: find a number such that it exceeds 18 by 3 times the number by which it is less than 86 ?
Options: a ) 67 , b ) 68 , c ) 69 , d ) 70 , e ) 71
Rationale: x - 18 = 3 [ 86 - x ] x = 69 answer : c
Answer: c
Problem: of the 3600 employees of company x , 12 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 40 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 %
Answer: a
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 40 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 31 % , e ) 60 %
Rationale: "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 40 % of 200 seeds germinated , so 0.4 x 200 = 80 seeds germinated . since 75 + 80 = 155 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 155 / 500 ) x 100 % , or 31 % . answer : d ."
Answer: d
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 60 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 360 cm
Rationale: "we have 60 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 30 and continues . so we have 60 , 30,15 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 60 / 1 - ( 1 / 2 ) = 120 equilateral triangle perimeter is 3 a = 3 * 120 = 360 . so option e ."
Answer: e
Problem: in an election , candidate douglas won 66 percent of the total vote in counties x and y . he won 74 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 75 % , e ) 80 %
Rationale: given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 66 % voted means 74 * 200 = 148 votes combined for xy has 300 voters and voted 66 % so total votes = 198 balance votes = 198 - 148 = 50 as y has 100 voters so 50 votes means 50 % of votes required ans c
Answer: c
Problem: amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is
Options: a ) rs . 4250 , b ) rs . 4228 , c ) rs . 4128 , d ) rs . 4988 , e ) rs . 4192
Rationale: amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } / { 6 } = 4250 answer : a
Answer: a
Problem: one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 16 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 14 , e ) 8
Rationale: "n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 16 r = 8 e"
Answer: e
Problem: a person walks from one end to the other of a 80 - meter long moving walkway at a constant rate in 40 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 40 ( v + x ) = 80 then 120 ( v + x ) = 240 120 ( v - x ) = 80 when we add the two equations : 240 v = 320 v = 4 / 3 time = 80 / ( 4 / 3 ) = 60 seconds the answer is b ."
Answer: b
Problem: neha ' s mother was 4 times her age 12 years ago . she will be twice as old as neha 12 years from now . what is the present age of neha ' s mother ?
Options: a ) 60 years , b ) 33 , c ) 77 , d ) 66 , e ) 101
Rationale: explanation : let neha ' s present age be ' x ' years . her age 12 years ago = ( x – 12 ) years therefore , her mother ' s age 12 years ago = 4 ( x – 12 ) her mother ' s present age = 4 x – 48 + 12 = 4 x – 36 neha ' s age after 12 years = x + 12 her mother ' s age after 12 years = 4 x – 36 + 12 = 4 x – 24 4 x – 24 = 2 ( x + 12 ) 4 x – 2 x = 24 + 24 x = 24 therefore , neha ' s present age = 24 her mother ' s present age = 4 x – 36 = 4 ( 24 ) – 36 = 60 years answer : a
Answer: a
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 3 , 4 , and 5 ?
Options: a ) 3.5 , b ) 3 , c ) 5 , d ) 4 , e ) 2.5
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 circum raduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5 ans . e"
Answer: e
Problem: what is the sum of the numbers between 1 and 5 , inclusive ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "sol . add numbers between 1 and 5 . answer = c , 15 ."
Answer: c
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 96 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 73.42 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 96 = 2570 correct average = 2570 / 35 = 73.42 answer : c"
Answer: c
Problem: if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ?
Options: a ) 320 cm 2 , b ) 360 cm 2 , c ) 340 cm 2 , d ) 310 cm 2 , e ) 300 cm 2
Rationale: "the triangle with sides 36 cm , 34 cm and 20 cm is right angled , where the hypotenuse is 36 cm . area of the triangle = 1 / 2 * 34 * 20 = 340 cm 2 answer : c"
Answer: c
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 3 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "on the way down , the rate is 1.5 * 3 = 4.5 miles per day . the distance of the route down the mountain is 2 * 4.5 = 9 miles . the answer is c ."
Answer: c
Problem: how many ounces of a 60 % salt solution must be added to 70 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 70
Rationale: let x = ounces of 60 % salt solution to be added . 2 * 70 + . 6 x = . 4 ( 70 + x ) x = 70 answer e
Answer: e
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 15 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 13 a – d = 3 a + d = 15 2 d = 12 d = 6 answer c"
Answer: c
Problem: how many plants will be there in a circular bed whose outer edge measure 33 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 21 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 33 cm area of circular bed = ( 33 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 33 ) 2 â  „ 4 ï € ã · 4 = 21.65 = 21 ( approx ) answer c"
Answer: c