regisss/math_qa huggingface dataset:
Problem: a and b can do a piece of work in 45 days and 40 days respectively . they began to do the work together but a leaves after some days and then b completed the remaining work in 23 days . the number of days after which a left the work was
Options: a ) 5 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 8 days
Rationale: "does the job in 40 days = 1 / 40 a & b together completes the job = ? after a leaves , b completes the remaining job in 23 days . i . e b ' s part of job in 23 days = 23 / 40 remaining part 17 / 40 is done by a & b together in x no . of days . i . e ( x / 45 ) + ( x / 40 ) = 17 / 40 = > x = 9 days answer : d"
Answer: d
Problem: virginia , adrienne , and dennis have taught history for a combined total of 75 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 34 , c ) 35 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 75 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 96 = > 3 d = 75 + 27 = 102 = > d = 34 answer b"
Answer: b
Problem: a big container is 40 % full with water . if 28 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 68 , b ) 72 , c ) 76 , d ) 80 , e ) 84
Rationale: "28 liters is 35 % of the capacity c . 28 = 0.35 c c = 28 / 0.35 = 80 liters . the answer is d ."
Answer: d
Problem: x starts a business with rs . 54000 . y joins in the business after 9 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 8 : 3 , d ) 3 : 5 , e ) 8 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 54000 * 12 : 27000 * 3 = 54 * 12 : 27 * 3 = 2 * 4 : 1 = 8 : 1 . answer : option e"
Answer: e
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 2 : 1 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 2 / 3 , b ) 4 / 5 , c ) 6 / 2 , d ) 5 / 2 , e ) 4 / 9
Rationale: "red : blue = 2 : 1 let red = 2 x and blue = 1 x 1 / 3 of red are left handed = > 1 / 3 * 2 x = 2 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 1 x = 2 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 2 x / 3 + 2 x / 3 ) / ( 2 x + 1 x ) = 4 / 9 answer : e"
Answer: e
Problem: if 4 men can colour 48 m long cloth in 2 days , then 6 men can colour 72 m long cloth in
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 72 / 6 × 6 = 2 day . b"
Answer: b
Problem: how many 4 digit even numbers do not use any digit more than once
Options: a ) 1720 , b ) 2160 , c ) 2240 , d ) 2460 , e ) 2520
Rationale: "a b c d ( thousand , hundreds , tens , units ) d can be 0 2 4 6 8 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities c can be anything except a and b so 8 possibilities b can be anything except ( a d c ) so 7 possibilities total ways are 8 * 7 * 8 * 5 = 2240 ans : c"
Answer: c
Problem: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 10 km / hr downstream and 4 km / hr upstream .
Options: a ) 7 kmph , b ) 8 kmph , c ) 9 kmph , d ) 7 kmph , e ) 6 kmph
Rationale: speed in still water = ( 10 + 4 ) 1 / 2 kmph = 7 kmph . answer : a
Answer: a
Problem: how many times digit 10 is used while writing numbers from 100 to 1000 ?
Options: a ) 100 , b ) 90 , c ) 85 , d ) 110 , e ) 120
Rationale: "in 100 to 300 there are 20 ten ' s in 300 to 500 there are 20 ten ' s in 500 to 700 there are 20 ten ' s in 700 t 0 900 there are 20 ten ' s in 900 to 1000 there are 10 ten ' s so total is 90 ten ' s correct option : b"
Answer: b
Problem: jacob is 10 years old . he is 5 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "j = 10 ; j = 5 b ; b = 10 / 5 = 2 ; twice as old so b = 2 ( now ) + ( 2 ) = 4 ; jacob is 10 + 4 = 14 answer : b"
Answer: b
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 option b"
Answer: b
Problem: a steel vessel has a base of length 60 cm and breadth 30 cm . water is poured in the vessel . a cubical steel box having edge of 30 cm is immersed completely in the vessel . how much will the water rise ?
Options: a ) 7.5 cm rise
b ) 10 cm rise
c ) 15 cm rise
d ) 30 cm rise
e ) none of these
Rationale: explanation : volume of cube = a 3 = a * a * a 60 cm * 30 cm * h = 30 cm * 30 cm * 30 cm h = 15 cm answer is c
Answer: c
Problem: a 3 - digit number 4 a 3 is added to another 3 - digit number 984 to give a 4 - digit number 13 b 7 , which is divisible by 11 . then , ( a + b ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 15 , e ) 16
Rationale: 4 a 3 | 9 8 4 } = = > a + 8 = b = = > b - a = 8 13 b 7 | also , 13 b 7 is divisible by 11 = > ( 7 + 3 ) – ( b + 1 ) = ( 9 – b ) ( 9 – b ) = 0 b = 9 ( b = 9 and a = 1 ) = > ( a + b ) = 10 . answer a
Answer: a
Problem: if 3 ^ x * 4 ^ y = 19,683 and x – y = 9 , then x = ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b .
Answer: b
Problem: in what time will a railway train 64 m long moving at the rate of 46 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6 , e ) 7
Rationale: "t = 64 / 46 * 18 / 5 = 5 sec answer : b"
Answer: b
Problem: matt gets a $ 1,600 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ?
Options: a ) 9 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1600 new average = ( xy + 1600 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1600 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1600 ) = ( xy + x + 150 y + 150 ) i . e . ( 1450 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 8 new sales = y + 1 = 9 answer : option a"
Answer: a
Problem: if the sides of a triangle are 30 cm , 28 cm and 14 cm , what is its area ?
Options: a ) 196 cm 2 , b ) 187 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2
Rationale: "the triangle with sides 30 cm , 28 cm and 14 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 14 = 196 cm 2 answer : a"
Answer: a
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1232 ?
Options: a ) 1000 , b ) 2217 , c ) 1100 , d ) 2777 , e ) 2991
Rationale: "1232 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1100 answer : c"
Answer: c
Problem: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 30 speak english well , while 40 of them do not speak english . if 86 % of students do not speak french , how many students were surveyed ?
Options: a ) 500 , b ) 450 , c ) 250 , d ) 350 , e ) 525
Rationale: "number of students who speak french are 30 + 40 = 70 of total students , the percentage of students who do not speak french was 86 % - - > percentage of who do is 14 % 70 - - - - - - - 14 % x - - - - - - - 100 % x = 70 * 100 / 14 = 500 = number of all students answer is a"
Answer: a
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 4 cm and breadth 2 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 4.51 , b ) 4.71 , c ) 4.32 , d ) 4.21 , e ) 4.68
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 4 + 2 ) = 12 cm parameter of the square = 12 cm i . e . 4 a = 12 a = 3 diameter of the semicircle = 3 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 3 ) = 1 / 2 ( 22 / 7 ) ( 3 ) = 66 / 14 = 4.71 cm to two decimal places answer : b"
Answer: b
Problem: 15 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 2100 , e ) 2940
Rationale: "no . of ways of picking 2 biology books ( from 15 books ) = 15 c 2 = ( 15 * 14 ) / 2 = 105 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 105 * 28 = 2940 ( option e )"
Answer: e
Problem: a and b can do a piece of work in 10 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 30 , d ) 10 , e ) 11
Rationale: "c = 1 / 5 â € “ 1 / 10 = 1 / 10 = > 10 days answer : d"
Answer: d
Problem: a computer factory produces 6048 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 6048 / ( 28 * 24 * 2 ) = 4.5 answer c"
Answer: c
Problem: find the greatest number which on dividing 1428 and 2206 , leaves a reminder of 9 and 13 respectively
Options: a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 141
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1428 - 9 ) and ( 2206 - 13 ) = hcf ( 1419 , 2193 ) = 129 option c"
Answer: c
Problem: during 2003 , a company produced an average of 3,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 300 % over its 2003 average ?
Options: a ) 520,000 , b ) 540,000 , c ) 525,000 , d ) 530,000 , e ) 550,000
Rationale: "company produced 12 * 3000 = 36,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 36,000 . the gives the average of ( x + 36,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 36,000 + 300 % ( 36,000 ) = 144,000 . so : ( x + 36,000 ) / 4 = 144,000 x + 36,000 = 576,000 x = 540,000 the answer is b ."
Answer: b
Problem: what is the ratio of arun ' s monthly income in the year 2006 , suman ' s monthly income in the year 2007 and jyothi ' s monthly income in the year 2005 ?
Options: a ) 22 , b ) 67 , c ) 26 , d ) 18 , e ) 16
Rationale: answer : a
Answer: a
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 5 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 5 t 1 = 5 and so t 2 = 10 . the answer is c .
Answer: c
Problem: there are 2 sections a and b in a class , consisting of 40 and 20 students respectively . if the average weight of section a is 50 kg and that of section b is 40 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 46.66 kg , d ) 69.15 kg , e ) 70.89 kg
Rationale: "total weight of 40 + 20 students = 40 * 50 + 20 * 40 = 2000 + 800 average weight of the class is = 2800 / 60 = 46.66 kg answer is c"
Answer: c
Problem: on dividing 15 by a number , the quotient is 4 and the remainder is 3 . find the divisor ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "d = ( d - r ) / q = ( 15 - 3 ) / 4 = 12 / 4 = 3 a )"
Answer: a
Problem: if | 4 x + 10 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 5 , e ) 6
Rationale: there will be two cases 4 x + 10 = 46 or 4 x + 10 = - 46 = > x = 9 or x = - 14 sum of both the values will be - 14 + 9 = - 5 answer is d
Answer: d
Problem: if it takes a machine 2 ⁄ 5 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 80 , d ) 120 , e ) 300
Rationale: "1 item takes 2 / 5 min so it takes 120 min to produce x 2 x / 5 = 120 the x = 300 answer : e"
Answer: e
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 1.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 2 , 400,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 1.5 gms in 400,000 cm ^ 3 , x = 1.5 * 400,000 = 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 600,000 + 1 , 800,000 = 2 , 400,000 answer : a"
Answer: a
Problem: excluding stoppages , the speed of a bus is 82 kmph and including stoppages , it is 75 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 5.12 , b ) 4.13 , c ) 6.15 , d ) 7.5 , e ) none of these
Rationale: "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( ( 7 / 82 ) ã — 60 ) = 5.12 min . option ( a ) is correct"
Answer: a
Problem: 4 , 6 , 9 , 13.50 , 20.25 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 58 , d ) 31.528 , e ) 30.375
Rationale: "4 ( 4 ã — 3 ) ã · 2 = 6 ( 6 ã — 3 ) ã · 2 = 9 ( 9 ã — 3 ) ã · 2 = 13.50 ( 13.50 ã — 3 ) ã · 2 = 20.25 ( 40.5 ã — 3 ) ã · 2 = 30.375 answer is e"
Answer: e
Problem: during a certain season , a team won 85 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 175 , c ) 156 , d ) 150 , e ) 105
Rationale: "we are first given that a team won 85 percent of its first 100 games . this means the team won 0.85 x 100 = 85 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 85 + 0.5 t – 50 = 0.7 t 35 = 0.2 t 350 = 2 t 175 = t answer is b ."
Answer: b
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 8 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 26 , b ) 30 , c ) 36 , d ) 38 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 8 strikes , there would be 7 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 8 ' o clock , the 8 strikes and 7 intervals will take 2 * ( 8 + 7 ) = 30 secs b"
Answer: b
Problem: a train is running at a speed of 4040 km / hr and it crosses a post in 1818 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 150 metres
Rationale: "explanation : speed = 40 km / hr = 40 km / hr = 40 ã — 518 = 1009 m / s = 40 ã — 518 = 1009 m / s time = 18 = 18 seconds distance covered = 1009 ã — 18 = 200 m = 1009 ã — 18 = 200 m therefore , length of the train = 200 m answer is c"
Answer: c
Problem: if a square mirror has a 20 - inch diagonal , what is the approximate perimeter r of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter r must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Problem: if m and n are whole numbers such that mn = 121 , the value of ( m 1 ) n + 1 is :
Options: a ) 1 , b ) 10 , c ) 121 , d ) 100 , e ) 1000
Rationale: if m and n are whole numbers such that mn = 121 , the value of ( m - 1 ) n + 1 is : a . 1 b . 10 c . 121 d . 1000 sol . - we know that 112 = 121 . putting m = 11 and n = 2 , we get : ( m - 1 ) n + 1 = ( 11 - 1 ) ( 2 + 1 ) = 103 = 1000 . answer : e
Answer: e
Problem: if the sides of a triangle are 28 cm , 26 cm and 10 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 130 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 28 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : d"
Answer: d
Problem: a train is 510 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 52 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 510 + 140 = 650 meter time = distance / speed = 650 * ( 2 / 25 ) = 52 seconds answer : c"
Answer: c
Problem: how many ounces of a 60 % salt solution must be added to 50 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: "for 60 % salt solution ( x ) and 20 % salt solution ( y ) to give 40 % = ( 60 + 20 ) / 2 salt solution , we should mix equal amounts of x and y . answer : c ."
Answer: c
Problem: a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.5 + $ 15.6 = $ 18.7 . answer : e ."
Answer: e
Problem: the ratio of red balls to blue balls is 3 : 7 . 70 % of the red balls and 30 % of the blue balls are tennis balls . how many of the balls are tennis balls ?
Options: a ) 44 % , b ) 40 % , c ) 45 % , d ) 42 % , e ) 48 %
Rationale: let total no of balls 100 , red ball 30 and blue ball 70 , so tennis ball for red and blue ball respectively 30 * 70 / 100 = 21 and 70 * 30 / 100 = 21 so total 42 tennis balls out of 100 balls . . so required % is 42 % answer : d
Answer: d
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 3 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 2 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 2 answer d ( hopefully ) ) )"
Answer: d
Problem: xy = 1 then what is ( 3 ^ ( x + y ) ^ 2 ) / ( 3 ^ ( x - y ) ^ 2 )
Options: a ) 81 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 3 ^ 4 = 81 answer a"
Answer: a
Problem: how much time does a train 125 metres long running at 60 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s
Rationale: "explanation : 60 km / hr = 60 * 5 / 18 = 16.67 m / s speed = distance / time ; v = d / t 16.67 = 125 / t t = 7.5 s answer : c"
Answer: c
Problem: if the number 517 * 324 is completely divisible by 7 , then the smallest whole number in the place of * will be :
Options: a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: sum of digits = ( 5 + 1 + 7 + x + 3 + 2 + 4 ) = ( 22 + x ) , which must be divisible by 7 . x = 6 . e
Answer: e
Problem: what is the least number which when divided by 5 , 6 , 9 and 12 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 156 , d ) 184 , e ) 196
Rationale: explanation : lcm of 5 , 6 , 9 and 12 is 180 required number = 180 + 4 = 184 answer : option d
Answer: d
Problem: sakshi can do a piece of work in 25 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 20 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 25 : x ⇒ x = ( 25 x 4 / 5 ) ⇒ x = 20 days . hence , tanya takes 16 days is complete the work . answer b"
Answer: b
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 64.54 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.54 answer : a"
Answer: a
Problem: in a bag , there are two 6 - sided dice ( numbered 1 to 6 ) , 3 12 - sided dice ( numbered 1 to 12 ) , and two 20 - sided dice ( numbered 1 to 20 ) . if 4 of these dice are selected at random from the bag , and then the 4 are rolled and we find the sum of numbers showing on the 4 dice , how many different possible totals are there for this sum ?
Options: a ) 60 , b ) 50 , c ) 42 , d ) 84 , e ) 61
Rationale: as ' complex - looking ' as this question might appear , it ' s actually rather simple . pay careful attention to what the specific questions asks for - the number of different possible sums from 4 dice . since we ' re dealing with some ' special ' dice ( some 12 - sided and 20 - sided dice ) , we have to adjust out math accordingly , but the possibilities are rather limited : 1 ) the minimum number on any given die is 1 2 ) the maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each . with 4 dice , we could end up with any sum between : 4 ( if we rolled 1 s on all 4 dice ) to 64 ( if we rolled two 20 s on the 20 - sided dice and two 12 s on the 12 - sided dice ) . thus , there are only 61 possible sums . e
Answer: e
Problem: convert 50 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 88000 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 50 miles = 50 * 1760 = 88000 yards answer is c"
Answer: c
Problem: a bus covers a distance of 12 km in 5 min . if it takes 5 sec to pass a telegraph post , then the length of the bus is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 200 m , e ) 280 m
Rationale: speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the bus = 40 * 5 = 200 m . answer : d
Answer: d
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 69 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 69 2 x = 14 = > x = 7 answer : d"
Answer: d
Problem: x can finish a work in 18 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 18 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 18 ) = 6 c"
Answer: c
Problem: n ^ ( n / 2 ) = 8 is true when n = 8 in the same way what is the value of n if n ^ ( n / 2 ) = 20 ?
Options: a ) 8 , b ) 14 , c ) 10 , d ) 20 , e ) 40
Rationale: n ^ ( n / 2 ) = 20 apply log n / 2 logn = log 20 nlogn = 2 log 20 = log 20 ^ 2 = log 400 logn = log 400 now apply antilog n = 400 / n now n = 20 . answer : d
Answer: d
Problem: amar takes as much time in running 12 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "d 400 m distance covered by amar = 12 / 4.8 ( 1.6 km ) = 2.5 ( 1600 ) = 400 m answer is d"
Answer: d
Problem: find the unit ’ s digit in the product ( 76 ^ 41 ) * ( 41 ^ 14 ) * ( 14 ^ 87 ) * ( 87 ^ 76 )
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: units digit of 87 ^ 76 = 1 because 87 ^ 3 n + 1 has units place as 1 units digit of 14 ^ 87 = 4 because 14 ^ ( some odd no . ) has units place as 4 units digit of 41 ^ 14 = 1 because 41 ^ ( some even no . ) has units place as 1 units digit of 76 ^ 41 = 6 because 76 ^ ( any positive no . ) has units place as 6 so , units digit of the product is = ` ` 4 ` ` ( units digit of 1 * 4 * 1 * 6 ) answer : d
Answer: d
Problem: what is the area of an equilateral triangle whose one side length is 40 ?
Options: a ) 100 √ 3 , b ) 200 √ 3 , c ) 300 √ 3 , d ) 350 √ 3 , e ) 400 √ 3
Rationale: "- > - > the area of an equilateral triangle with one side length of a is √ 3 a 2 / 4 . thus , √ 3 ( 40 ^ 2 ) / 4 = 400 √ 3 and the answer is e . correct option : e"
Answer: e
Problem: a man ate 100 bananas in 5 days , each day eating 6 more than the previous day . how many bananas did he eat on the first day ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: let the number of bannanas in first day be x for consecutive five days it will be like x , x + 6 , x + 12 , x + 18 , x + 24 the sum of those are 100 , 5 x + 60 = 100 so , x = 8 answer : c
Answer: c
Problem: what is the least value of x . so that 1894 x is divisible by 3 ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 1 + 8 + 9 + 4 + x = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . a
Answer: a
Problem: if takes 25.5 minutes to download a file using modem a . modem b work at 17 % of the speed of modem a . how long does it take to download a file using a modem b ?
Options: a ) 130 minutes , b ) 140 minutes , c ) 150 minutes , d ) 160 minutes , e ) 170 minutes
Rationale: let speed of modem a be k so speed of modem b is 17 / 100 * k time taken by modem a = 25.5 minutes let time taken by modem b = x k * 25.5 = 17 / 100 * k * x 0.17 * x = 25.5 x = 25.5 / 0.17 = 150 minutes answer : c
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 9 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 9 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 9 x = 9 answer : a"
Answer: a
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent w of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before w = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Problem: what annual installment will discharge a debt of $ 100 due in 3 years at 10 % simple interest ?
Options: a ) 25.6 , b ) 50.2 , c ) 30.3 , d ) 45 , e ) 56
Rationale: let each installment be x [ x + ( x * 10 * 1 / 100 ) ] + [ x + ( x * 10 * 2 / 100 ) ] + x = 100 11 x / 10 + 12 x / 10 + x = 100 x = 30.3 answer is c
Answer: c
Problem: a boat can travel with aspeed of 20 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 125 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: speed downstream = ( 20 + 5 ) km / hr = 25 km / hr . time taken to travel 125 km downstream = 125 / 25 hrs = 5 hrs . answer : e
Answer: e
Problem: john bought 9.25 m of cloth for $ 397.75 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 43
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 397.75 cost per metre = 397.75 ÷ 9.25 the cost of the cloth per metre = $ 43 answers : e"
Answer: e
Problem: a sum fetched total simple interest of 4016.25 at the rate of 13 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 6178.85 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 65 % of p = 4016.25 or , p = 6178.85 answer a"
Answer: a
Problem: what could be the range of a set consisting of odd multiples of 3 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 70
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 3 * ( 2 n + 1 ) where n is any positive integer . range = 3 * ( 2 m + 1 ) - 3 * ( 2 n + 1 ) = 3 * 2 * ( m - n ) = 6 * ( m - n ) . m , n - any positive integers the answer must be divisible by 6 , which is only 24 . the correct answer is b"
Answer: b
Problem: i walk a certain distance and ride back taking a total time of 37 minutes . i could walk both ways in 55 minutes . how long would it take me to ride both ways ?
Options: a ) 12 mins , b ) 10 mins , c ) 19 mins , d ) 15 mins , e ) 20 mins
Rationale: let the distance be x km . then , ( time taken to walk x km ) + ( time taken to ride x km ) = 37 min . ( time taken to walk 2 x km ) + ( time taken to ride 2 x km ) = 74 min . but , the time taken to walk 2 x km = 55 min . time taken to ride 2 x km = ( 74 - 55 ) min = 19 min . ans : c
Answer: c
Problem: a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 15 % next year . this year , the total amount paid for type a products was $ 4000 and the total price paid for type b products was $ 5300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 11,495 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: cost of type a products next year = 1.35 * 4000 = 5400 cost of type b products next year = 1.15 * 5300 = 6095 total 5400 + 6095 = 11495 answer : b
Answer: b
Problem: the area of a parallelogram is 242 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 11 , e ) 2
Rationale: "2 x * x = 242 = > x = 11 answer : d"
Answer: d
Problem: a part - time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9.09 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.1 x now we need to find number of hours worked so that x * y = 1.1 x * z i . e z = x * y / 1.1 x = 1 / 1.1 y % decrease = ( y - 1 / 1.1 y ) / y * 100 = 1 - 1 / 1.1 * 100 = 9.09 % thus my answer is a .
Answer: a
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 150,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 50,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 5 a * 1 + a * 5 ) / 6 = 10 a / 6 = 50000 answer is c . $ 50,000"
Answer: c
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 2304 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40
b ) b . 100
c ) c . 400
d ) d . 1,800
e ) e . 10,000
Rationale: the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 2304 pi r = 12 so area = 4 . pi . r ^ 2 = 576 . pi = 576 x 3.14 = 1800 ( approx ) d
Answer: d
Problem: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 35 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 35
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that ' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e ."
Answer: e
Problem: if 2 x - y = 4 then 6 x - 3 y = ?
Options: a ) 15 , b ) 12 , c ) 18 , d ) 10 , e ) 14
Rationale: 6 x - 3 y = 3 * ( 2 x - y ) = 3 * 4 = 12 answer : b
Answer: b
Problem: find 3486 / 189
Options: a ) 18.44 , b ) 18.48 , c ) 18.42 , d ) 18.49 , e ) 18.41
Rationale: first we make the denominator 200 . i . e . , we are introducing an error of 11 which is 11189 = 11711189 = 117 th of the denominator . now 3486200 = 17.433486200 = 17.43 but this answer is less than actual answer . so we have to increase it by 1 / 17 th part of it . 117 × 17.43 ≃ 1117 × 17.43 ≃ 1 so final answer = 17.43 + 1 = 18.43 actual answer = 18.44 answer : a
Answer: a
Problem: mary and mike enter into a partnership by investing $ 600 and $ 400 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 mary received $ 1000 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 8500 , b ) $ 9500 , c ) $ 7000 , d ) $ 7500 , e ) $ 6500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6 : 4 . i . e . , 60 % of 2 x would go to mary and 40 % of 2 x would go to mike . hence , mary would get ( 60 - 40 ) % of 2 x more than mike or 20 % of 2 x = $ 1000 i . e . , ( 20 / 100 ) * 2 x = 1000 or 2 x = 5000 . hence , the profit made by the company during the year $ 3 x = $ 7500 . answer : d"
Answer: d
Problem: a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 27 percent , what is the discount rate on mysteries ?
Options: a ) 10 % , b ) 11 % , c ) 12.5 % , d ) 13 % , e ) 14 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.27 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.125 = 12.5 % c"
Answer: c
Problem: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 200 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 50 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 200 + 120 = 320 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 320 / 0.8 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 200 / 400 ) * 100 = 50 % option c"
Answer: c
Problem: find the ones digit of 73 ^ 356
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 356 will be the same as the units digit of 3 ^ 356 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 356 = 356 + 0 = ( multiple of 4 ) + 0 , then the units digit of 3 ^ 356 will be thus 1 . answer : a ."
Answer: a
Problem: a classroom has 3 electric lamps . from a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps . find the probability that the room is lighted .
Options: a ) 1 / 6 , b ) 4 / 120 , c ) 29 / 30 , d ) 1 / 9 , e ) none of these
Rationale: explanation : out of 10 electric bulbs , 3 are selected in 10 c 3 ways . so , number of possible outcomes = t = 10 c 3 = 120 . the room is lighted i . e at least one fo the 3 bulbs chosen at random is a good bulb . wherever ' at least one ' is present , it is easier to do the problem using complement of the event ( i . e room is dark and all 3 bulbs are bad ) . p ( room is dark ) = f / t = p ( none of the bulbs is good ) = > 4 c 3 / 120 . [ since 4 bulbs are bad ] . p ( room is lighted ) = 1 - ( 4 c 3 / 120 ) . [ room is lighted if at least one bulb is good ] . or p ( at least one ) = 1 - ( 4 / 120 ) . = 29 / 30 . answer : c
Answer: c
Problem: if a population of women in a town is 90 % of men . what is the population of men as a % of population of women ?
Options: a ) 108 % , b ) 105 % , c ) 111 % , d ) 112 % , e ) 114 %
Rationale: we ' re told that the number of women in a town is equal to 90 % of the number of men in that town . if . . . . men = 10 women = 9 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 9 = 1 1 / 9 = 1.111111 = 111 % answer : c
Answer: c
Problem: two trains 135 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.18 , b ) 7.12 , c ) 7.3 , d ) 7.45 , e ) 7.51
Rationale: "t = ( 135 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.45 answer : d"
Answer: d
Problem: 4 numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .
Options: a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112
Rationale: answer : a
Answer: a
Problem: rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is :
Options: a ) rs 200 , b ) rs 300 , c ) rs 400 , d ) rs 500 , e ) rs 600
Rationale: let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) x 700 ) = 400 answer : c
Answer: c
Problem: a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 24 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : e"
Answer: e
Problem: find the greatest number that will divide 150 , 230 and 175 leaving 50 , 5 and 25 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 32 , d ) 9 , e ) 8
Rationale: explanation : answer will be hcf of ( 150 - 50 , 230 - 5 , 175 - 25 ) hcf of ( 100 , 225 , 150 ) = 32 option c
Answer: c
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 16.8 , b ) 17.8 , c ) 15.9 , d ) 13.2 , e ) 12.4
Rationale: "d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec answer a"
Answer: a
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum x of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum x = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Problem: in track last week , the boys ran 27 laps . the girls ran 9 more laps . each lap is a 3 - fourth of a mile . how many miles did the girls run ?
Options: a ) 24 miles , b ) 25 miles , c ) 26 miles , d ) 27 miles , e ) 28 miles
Rationale: the girls ran 27 + 9 = 36 laps . 36 x 3 / 4 = 108 / 4 , which reduces to 27 . the girls ran 27 miles correct answer d
Answer: d
Problem: if tim had lunch at $ 50.20 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 60.24
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.20 = ( 20 / 100 ) * 50.20 = $ 10.04 total spent 50.20 + 10.04 = $ 60.24 correct answer e"
Answer: e
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 8 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 640 , e ) 760
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 8 € 40 = 2 * 8 * 40 = 640 hence , answer is d"
Answer: d
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 24,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,500 , e ) s . 7,200
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 24000 x 3 / 10 = rs . 7,200 . e"
Answer: e
Problem: every year an amount increases by 1 / 6 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 87111 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 81022
Rationale: "64000 * 7 / 6 * 7 / 6 = 87111 answer : a"
Answer: a
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 305 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 440 , c ) 550 , d ) 625 , e ) 700
Rationale: let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 305 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 605 a + b + c = 55 per hour so for eight hrs = 55 * 8 = 440 = answer = b
Answer: b
Problem: how many odd numbers between 10 and 1200 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 33 which includes 15 numbers . the answer is d ."
Answer: d
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 5 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 30 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 5 x = 961 5 x = 150 = > x = 30 . answer : b"
Answer: b
Problem: 300 liters of a mixture contains milk and water in the ratio 3 : 2 if 15 liters of this mixture be replaced by 15 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 12 : 8 , b ) 12 : 4 , c ) 13 : 8 , d ) 14 : 5 , e ) 13 : 5
Rationale: "quantity of milk in 300 liters if mix = 300 * 3 / 5 = 180 liters quantity of milk in 315 liters of new mix = 180 + 15 = 195 liters quantity of water in it = 315 - 195 = 120 liters ratio of milk and water in new mix = 90 : 20 = 13 : 8 answer isc"
Answer: c
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 12 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 492 km
Rationale: "the total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 = sum of 12 terms in ap whose first term is 30 and last term is 52 = 12 / 2 [ 30 + 52 ] = 492 km . answer : e"
Answer: e
Problem: a chemical supply company has 60 liters of a 25 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 25 % hno 3 solution means hno 3 = 15 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 15 + x = 50 % of ( 60 + x ) or x = 30 . hence , e"
Answer: e
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 140 m . then , a wins by
Options: a ) 60 m , b ) 40 m , c ) 20 m , d ) 10 m , e ) 50 m
Rationale: "solution to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers ( 4 / 3 x 360 ) m = 480 m thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . ∴ a wins by 20 m . answer c"
Answer: c