regisss/math_qa huggingface dataset:
Problem: there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 6 were remaining . how many people were in total ?
Options: a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 91
Rationale: sol : 45 if x persons were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 6 x × 2 / 3 × 3 / 5 × 1 / 3 = 6 x = 6 × 5 × 3 / 2 = 45 answer : a
Answer: a
Problem: in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 67 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) 1 : 1
Rationale: "required ratio = 500 : 500 = 3 : 1 answer e"
Answer: e
Problem: a 8 % stock yielding 10 % is quoted at :
Options: a ) 80 , b ) 110 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 8 , money invested = rs . ( 100 / 10 x 8 ) = rs . 80 . â ˆ ´ market value of rs . 100 stock = rs . 80 answer a"
Answer: a
Problem: if it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 50 % = 300 / 0.5 = 600 option e"
Answer: e
Problem: an error 8 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 16.64 % , c ) 15.64 % , d ) 26.64 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 8 + 8 + ( 8 × 8 ) / 100 ) % = 16.64 % answer : b"
Answer: b
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 15 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 7 + 16 x 7 ) ] = ( 225 - 210 ) = 15 years . answer c"
Answer: c
Problem: car a travels at 3 times the average speed of car b . car a started to travel at 12 : 00 o ' clock , car b started to travel at 16 : 00 o ' clock . what is the speed of car b ( in km / h ) if the total distance that both cars traveled until 18 : 00 was 1000 km ?
Options: a ) 10 . , b ) 25 . , c ) 30 . , d ) 38 , e ) 50 .
Rationale: total distance - 1000 km time ratio a : b - 3 : 1 speed ratio a : b - 3 : 1 so distance ( speed * time ) ratio will be - 3 * 3 : 1 * 1 - 9 : 1 so total distance traveled by b - 100 km time taken by b ( 18 : 00 - 16 : 00 = 2 ) - 2 hours speed of b - 50 kmph answer : e
Answer: e
Problem: there are 6 books on a shelf , of which 2 are paperbacks and 4 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 14 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Rationale: "approach 1 at - least 1 paper back = total - no paper back 6 c 4 - 4 c 4 = 14 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 4 c 3 + 2 c 2 * 4 c 2 = 14 answer is b"
Answer: b
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 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 . 931 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , 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 ) = 931 96 + 225 + 490 + 6 x = 931 6 x = 120 = > x = 20 . answer : e"
Answer: e
Problem: the average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 93 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 68 + 10 x 2.5 68 + 25 = 93 kg ans : ' b '"
Answer: b
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 176 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 154
Rationale: "set up equation : x = total number of workers 176 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 176 = 16 / 30 x x = 330 330 - 176 = 154 answer e"
Answer: e
Problem: elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 6 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 24
Rationale: "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 6 we get : 18 b + 24 f = 6 x therefore , we got 18 ounces of butter and 6 x amount of quantity when we use 24 ounces of floor . ans : e"
Answer: e
Problem: in how many w ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: w = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Problem: suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 262.8 , d ) rs . 241.7 , e ) none
Rationale: solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 128 : 125 suganya ' s share = rs . ( 30570 ã — 2 / 253 ) = rs . 241.7 . answer d
Answer: d
Problem: a space shuttle orbits the earth at about 9 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 4,800 , d ) 28,800 , e ) 32,400
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 9 * 3600 = 32,400 answer : e"
Answer: e
Problem: 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 17.5 % , b ) 17.8 % , c ) 18.1 % , d ) 18.4 % , e ) 18.7 %
Rationale: "the total amount of alcohol is 0.22 ( 7 ) + 0.11 ( 3 ) = 1.87 liters . the percentage is 1.87 / 10 = 18.7 / 100 which is 18.7 % the answer is e ."
Answer: e
Problem: a cricketer scored 136 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 55.88 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 136 - ( 12 x 4 + 2 x 6 ) = 136 - ( 60 ) = 76 now , we need to calculate 72 is what percent of 136 . = > 76 / 136 * 100 = 55.88 % answer : c"
Answer: c
Problem: by investing in 1623 % stock at 64 , one earns rs . 1700 . the investment made is
Options: a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 6528 , e ) s . 6760
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1700 , investment needed = 64 × 3 × 1700 / 50 = 6528 answer : option d"
Answer: d
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 945 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "945 = 3 * 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 9 so that there are at least three appearances of 3 ( that is : 3 , 6 , and 9 ) . the answer is c ."
Answer: c
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 2 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 2
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 2 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 2 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 2 = e"
Answer: e
Problem: there are 6 people in the elevator . their average weight is 160 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 97 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 160 ) = 1057 - 960 = 97 . answer a"
Answer: a
Problem: what least fraction should be added to 1 / ( 2 × 3 ) + 1 / ( 3 × 4 ) + 1 / ( 4 × 5 ) + . . . . . . . + 1 / ( 21 × 22 ) so that the result is unity ?
Options: a ) 5 / 11 , b ) 6 / 11 , c ) 4 / 11 , d ) 7 / 11 , e ) 8 / 11
Rationale: explanation : given expression = 1 / ( 2 × 3 ) + 1 / ( 3 × 4 ) + 1 / ( 4 × 5 ) + . . . . . . + 1 / ( 21 × 22 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . = ( 1 / 21 - 1 / 22 ) = 1 / 2 - 1 / 22 = 10 / 22 = 5 / 11 thus , least fraction to be added = 1 - 5 / 11 = 6 / 11 answer : option b
Answer: b
Problem: how many positive integers less than 160 are there such that they are multiples of 13 or multiples of 12 but not both ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 23 , e ) 25
Rationale: "for 13 : 13 . . . 160 = 13 * 12 for 12 : 12 . . . 156 = 12 * 13 but there is one integer 13 * 12 . so n = ( 12 - 1 ) + ( 13 - 1 ) = 23 d"
Answer: d
Problem: 24 * 22 = ? / 8
Options: a ) 4224 , b ) 2224 , c ) 5374 , d ) 2434 , e ) 4254
Rationale: "a 4224 ? / 8 = 24 * 22 ? = 24 * 22 * 8 ? = 4224"
Answer: a
Problem: how many 5 - digit numbers that do not contain the digits 4 or 7 are there ?
Options: a ) 44648 , b ) 27844 , c ) 28642 , d ) 16864 , e ) 32458
Rationale: we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c
Answer: c
Problem: evaluate 75 % of 450 + 45 % of 750
Options: a ) 632 , b ) 642 , c ) 652 , d ) 675 , e ) 572
Rationale: "explanation : = ( 75 / 100 ) * 450 + ( 45 / 100 ) * 750 = 675 option e"
Answer: e
Problem: how many positive integers i less than 20 are either a multiple of 2 , an odd multiple of 9 , or the sum of a positive multiple of 2 and a positive multiple of 9 ?
Options: a ) 19 , b ) 18 , c ) 17 , d ) 16 , e ) 15
Rationale: we ' re asked to deal with the positive integers less than 20 . there are only 19 numbers in that group ( 1 to 19 , inclusive ) . we ' re asked to find all of the numbers that fit one ( or more ) of the given descriptions . looking at the answer choices , we have every value form 15 to 19 , inclusive , so most ( if not all ) of the numbers from 1 to 19 fit one ( or more ) of the descriptions . how long would it take you to find the ones that do n ' t fit . . . . . ? the first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 ( and sums of those multiples ) . so what odd numbers are less than 9 ? 1 , 3 , 5 , 7 none of these values fit the given descriptions . that ' s 4 out of 19 that we know for sure do not fit . 19 - 4 = 15 = e
Answer: e
Problem: a train passes a station platform in 33 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 887 , d ) 195 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 33 = 15 = > x = 195 m . answer : d"
Answer: d
Problem: the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ?
Options: a ) 45 kg , b ) 38 kg , c ) 66 kg , d ) 36 kg , e ) of these
Rationale: let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d
Answer: d
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.70 per metre .
Options: a ) 2399 , b ) 6204 , c ) 2999 , d ) 5808 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.70 ) = rs . 6204 . answer : b ) 6204"
Answer: b
Problem: if x / 4 + 24 / x = 5 , what are the values of 4 x - 7 ?
Options: a ) 8 and 9 , b ) 8 and 24 , c ) 25 and 41 , d ) 12 and 29 , e ) 17 and 29
Rationale: i got the same thing c is the answer 25 or 41
Answer: c
Problem: a room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 126 , c ) 117 , d ) 136 , e ) 147
Rationale: let us calculate both the length and width of the room in centimeters . length = 6 meters and 72 centimeters = 672 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 672 and 432 = 48 thus , the number of square tiles required = ( 672 x 432 ) / ( 48 x 48 ) = 14 x 9 = 126 answer : b
Answer: b
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 3 : 8 , b ) 3 : 9 , c ) 3 : 4 , d ) 3 : 12 , e ) 4 : 12
Rationale: "water : soap = 3 : 4 soap : salt = 12 : 16 = > for 12 soap , salt = 16 = > for 4 soap , salt = ( 16 / 12 ) * 4 = 16 / 12 = 64 / 12 = 18 / 3 = 6 / 1 so , water : soap : salt = 3 : 4 : 6 = 3 : 4 : 6 after open container , water : soap : salt = 1.5 : 4 : 6 so , water : salt = 1.5 : 6 = 3 : 12 answer : d"
Answer: d
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 12 people were made to stand in a column , how many columns could be formed ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "16 * 30 = 12 * n n = 40 the answer is c ."
Answer: c
Problem: if x is a positive integer with fewer than 3 digits , what is the probability q that x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability q that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) .
Answer: e
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 200 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.42 % , b ) 1.9 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 200 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 200 ) / 100 + ( 1.8 * 700 ) / 100 = 14.2 gms % of liquid x in resultant mixture = ( 14.2 / 1000 ) * 100 = 1.42 % a"
Answer: a
Problem: the s . i . on a certain sum of money for 3 years at 5 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 2800 , c ) 1750 , d ) 2267 , e ) 1262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 5 ) = rs . 2800 answer : b"
Answer: b
Problem: two train each 500 m long , are running in opposite directions on parallel tracks . if their speeds are 45 km / hr and 30 km / hr respectively , the time taken by the slower train to pass the driver of the faster one is
Options: a ) 50 sec , b ) 58 sec , c ) 24 sec , d ) 22 sec , e ) 21 sec
Rationale: "explanation : relative speed = 45 + 30 = 75 km / hr = 750 / 36 m / s = 125 / 6 m / s we are calculating the time taken by the slower train to pass the driver of the faster one . hence the distance = length of the smaller train = 500 m time = distance / speed = 500 / ( 125 / 6 ) = 24 sec answer : option c"
Answer: c
Problem: if a fraction is multiplied by itself and then divided by the reciprocal of the same fraction , the result is 18 26 / 27 . find the fraction .
Options: a ) 8 / 27 , b ) 1 1 / 3 , c ) 2 2 / 3 , d ) 3 / 3 , e ) none of these
Rationale: answer if the required fraction be p according to the question ( p x p ) / ( 1 / p ) = 1826 / 27 ⇒ p 3 = 512 / 27 ∴ p = 8 / 3 = 2 2 / 3 correct option : c
Answer: c
Problem: two trains of length 100 meters and 200 meters are 630 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 630 / 45 = 14 seconds the answer is b .
Answer: b
Problem: a can do a job in 15 days and b can do it in 30 days . a and b working together will finish twice the amount of work in days ?
Options: a ) 20 , b ) 22 1 / 2 , c ) 22 1 / 0 , d ) 22 1 / 9 , e ) 22 1 / 1
Rationale: "1 / 15 + 1 / 30 = 3 / 30 = 1 / 10 10 = 10 * 2 = 20 days answer : a"
Answer: a
Problem: find the value of y from ( 12 ) ^ 3 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2450 , b ) 2560 , c ) 2650 , d ) 3500 , e ) 5184
Rationale: "given exp . = ( 12 ) 3 x 64 = ( 12 ) 3 x 64 = ( 12 ) 2 x 62 = ( 72 ) 2 = 5184 432 12 x 62 e"
Answer: e
Problem: in a graduating class , 40 percent of the students are male . in this class , 60 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.4 , b ) 0.44 , c ) 0.48 , d ) 0.52 , e ) 0.56
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.4 * 0.4 x + 0.6 * 0.6 x = 0.52 x the answer is d ."
Answer: d
Problem: the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 245 , b ) 77 , c ) 88 , d ) 99 , e ) 22
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 25 / 2 = > 2 ( 130 + x ) = 750 = > x = 245 m . answer : c"
Answer: c
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 8 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1240 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 8 ) = $ 320 total revenue : 1000 + 320 = $ 1320 the answer is b .
Answer: b
Problem: if n is a positive integer , what is the remainder when ( 7 ^ ( 4 n + 2 ) ) ( 6 ^ n ) is divided by 10 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 4 . c or j in this problem .
Answer: c
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 1 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 30 , c ) 15 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 1 breaks = . 3 / 1 = . 3 hrs = 30 m so answer is b ) 30 mins"
Answer: b
Problem: sahil purchased a machine at rs 11000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22500 , b ) rs . 25500 , c ) rs . 26000 , d ) rs . 28000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 11000 + 5000 + 1000 = 17000 150 % of 17000 = 150 / 100 * 17000 = 25500 option b"
Answer: b
Problem: a boat can travel with a speed of 16 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 60 km downstream .
Options: a ) 2 hours . , b ) 3 hours . , c ) 4 hours . , d ) 5 hours . , e ) 6 hours .
Rationale: "speed downstream = ( 16 + 4 ) km / hr = 20 km / hr . time taken to travel 60 km downstream = 60 / 20 = 3 hours . answer : b"
Answer: b
Problem: walking 5 / 4 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 5 / 4 = 4 : 5 time ratio = 5 : 4 1 - - - - - - - - 5 4 - - - - - - - - - ? 20 m . answer : e"
Answer: e
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 46.5 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 going up = 1 - - > total = 45 going down = 1 - - > total = 46 going up = 0.5 - - > total = 46.5 ( caught ) no of going downs = 5 . . answer : a"
Answer: a
Problem: 6000 - 5000 ÷ 20.00 = ?
Options: a ) 900 , b ) 500 , c ) 5750 , d ) 5000 , e ) none
Rationale: "answer given expression = 6000 - 5000 ÷ 20.00 = 6000 - 250 = 5750 correct option : c"
Answer: c
Problem: mahesh can do a piece of work in 50 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 50
Rationale: "work done by mahesh in 50 days = 20 * 1 / 50 = 2 / 5 remaining work = 1 - 2 / 5 = 3 / 5 3 / 5 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 5 / 3 = 50 days answer is e"
Answer: e
Problem: the area of a square is 4096 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 78
b ) 5 : 11
c ) 5 : 12
d ) 5 : 19
e ) 5 : 16
Rationale: let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4096 = 212 a = ( 212 ) 1 / 2 = 26 = 64 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 40 : 128 = 5 : 16 answer : e
Answer: e
Problem: a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 5 and peanut cookies in batches of 6 . if he makes exactly 94 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 40
Rationale: 5 c + 6 p = 94 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 5 * 8 + 6 * 9 = 40 + 54 = 94 hence e is the answer
Answer: e
Problem: when y is divided by 264 , the remainder is 42 . what is the remainder when the same y is divided by 22 ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "y = 264 * a + 42 = ( 22 * 12 ) * a + 22 + 20 the answer is e ."
Answer: e
Problem: if x < y < z and y - x > 1 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 3 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 1 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 1 , the least value for y - x must be 3 , the least value for x must be 2 , and , thus , the least possible value for y must be 3 ( y - 2 = 1 , y = 3 ) 2 < 3 < z , since z is odd , the least possible value for z is 5 z - x = 5 - 2 = 3 answer b"
Answer: b
Problem: a 12 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 150 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 12 , money invested = 100 × 12 / 8 = rs . 150 ie , market value of the stock = rs . 150 answer is d ."
Answer: d
Problem: the toll for crossing a certain bridge is $ 0.75 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 13.00 and then pay only $ 0.10 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : a"
Answer: a
Problem: 9 people are planning to share equally the cost of a rental van . if one person withdraws from the arrangement and the others share equally the cost of the rental van , then the share of each of the remaining people will increase by . . . ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7
Rationale: let p = total cost of the rental van . the original share per person is p / 9 . the new share per person is p / 8 . p / 8 = p / 9 * 9 / 8 = ( 1 + 1 / 8 ) * original share the answer is b .
Answer: b
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 50 % ?
Options: a ) 125 % , b ) 150 % , c ) 100 % , d ) 90 % , e ) 85 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 50 % increase a surface = 6 * ( ( 1.5 a ) ^ 2 ) = 6 * 2.25 * a ^ 2 the increase in the surface area = ( 6 * 2.25 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.25 - 1 ) ) / ( 6 * a ^ 2 ) = 2.25 - 1 = 1.25 = 125 % answer : a"
Answer: a
Problem: there is a 5 % chance that tigers will not win at all during the whole season . there is a 5 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %
Rationale: "there is a 5 % chance that tigers will not win at all during the whole season we can infer that there is 95 % chance tigers will win . similarly there is a 5 % chance that federer will not play at all in the whole season we can also infer that there is 95 % chance that federer will play . answer e"
Answer: e
Problem: at a florist shop on a certain day , all corsages sold for either $ 25 or $ 40 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 40 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 300
Rationale: "i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 25 = x , no . of corsages @ $ 40 = y and revenue = r so , 25 x + 40 y = r . . . . . . . . . ( 1 ) now , given the situation , 25 ( x + 8 ) + 40 ( y - 8 ) = r - . 4 r = > 25 x + 200 + 40 y - 320 = . 6 r = > 25 x + 40 y = . 8 r + 120 . . . . . . . . . . . . ( 2 ) so , r = . 6 r + 120 = > r = 300 the answer is e ."
Answer: e
Problem: in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
Options: a ) 900 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2100
Rationale: "let v be the total number of votes . 0.4 v = 480 v = 1200 the answer is b ."
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 38 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 260 + 120 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"
Answer: c
Problem: pipe a that can fill a tank in an hour and pipe b that can fill the tank in 15 are opened simultaneously when the tank is empty . pipe b is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 40 mins , b ) 35 mins , c ) 30 mins , d ) 32 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe a was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 4 = 5 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 5 = 3 / 20 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : c
Answer: c
Problem: john has exactly 31 pens , and each pen is either bule , black , or red . if he has 5 more black pens than red pens , and twice as many blue pens as black pens , how many blue pens does john has ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) 17
Rationale: x = the number of blue pens y = the number of black pens z = the number of red pens from the first sentence we have equation # 1 : x + y + z = 31 . . . he has 5 more black pens than red pens . . . equation # 2 : y = 5 + z . . . twice as many blue pens as black pens . . . equation # 3 : x = 2 y solve equation # 1 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 5 ) = 31 4 y - 5 = 31 4 y = 36 y = 9 there are 9 black pens . this is 5 more than the number of red pens , so z = 4 . hence the answer is . x = 18 , and just for check 18 + 9 + 4 = 31 . answer = 18 , ( b )
Answer: b
Problem: what is the average ( arithmetic mean ) of the numbers 5 , 6 , 7 , 7 , 8 , and 9 ?
Options: a ) 4.2 , b ) 6.5 , c ) 6 , d ) 7 , e ) 8
Rationale: "{ 5 , 6 , 7 , 7 , 8 , 9 } = { 7 - 2,7 - 1 , 7 , 7,7 + 1,7 + 2 } - - > the average = 7 . answer : d ."
Answer: d
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 500 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 1288 , d ) rs . 16108 , e ) rs . 12000
Rationale: "explanation : manager ' s monthly salary rs . ( 2000 * 21 - 1500 * 20 ) = rs . 12000 . answer : e"
Answer: e
Problem: a rectangular tiled patio is composed of 50 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 50 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "r * c = 50 and ( 6 + 4 ) ( 7 - 2 ) = 50 - - > r = 6 and c = 7 . answer : b ."
Answer: b
Problem: the tax on a commodity is diminished by 20 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 8 %
Rationale: "explanation : 100 * 100 = 10000 80 * 115 = 9200 10000 - - - - - - - 800 100 - - - - - - - ? = 8 % e )"
Answer: e
Problem: the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 15 of her stamps , the ration of the number of kaye had to the number of alberto had was 4 : 3 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 70 , d ) 60 , e ) 90
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 15 a 2 = 3 x + 15 k 2 / a 2 = 7 / 5 ( 5 x - 15 ) / ( 3 x + 15 ) = 4 / 3 3 * ( 5 x - 15 ) = 4 * ( 3 x + 15 ) 15 x - 45 = 12 x + 60 3 x = 105 x = 35 k 2 = 5 * 35 - 15 = 160 a 2 = 3 * 35 + 15 = 90 k 2 - a 2 = 70 answer : c"
Answer: c
Problem: find the area of a parallelogram with base 24 cm and height 10 cm ?
Options: a ) 240 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 200 cm 2 , e ) 297 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 10 = 240 cm 2 answer : a"
Answer: a
Problem: what is the unit digit in 7 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "unit digit in 7 ^ 100 = unit digit in [ ( 7 ^ 4 ) ^ 25 ] but unit digit in 7 ^ 4 = 1 unit digit 7 ^ 100 = 1 answer is b"
Answer: b
Problem: beginning in town a , biker bob rides his bike 8 miles west , 5 miles north , 4 miles east , and then 15 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 25 miles , b ) 20.4 miles , c ) 30 miles , d ) 32 miles , e ) 33 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 8 - 4 = 4 m now this third side or the distance between town a and town b = 20 ^ 2 + 4 ^ 2 = sq root 416 = 20.4 miles answer : b"
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 44 ft , b ) 88 ft , c ) 74 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft"
Answer: c
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 140 ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 140 5 x - 20 = 140 5 x = 160 x = 32 the answer is e ."
Answer: e
Problem: a chemical supply company has 60 liters of a 45 % 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 ) 6 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 45 % hno 3 solution means hno 3 = 27 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 27 + x = 50 % of ( 60 + x ) or x = 6 . hence , a"
Answer: a
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 40 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 11.2 % , d ) 7 % , e ) 13 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 40 % more ie . , 140 recliners hence her sales tields 140 * 80 = $ 11200 increase in sales = 11200 - 10000 = $ 1120 so % increase = 1120 * 100 / 10000 = 11.20 % c is the answer"
Answer: c
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 8.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 2,100 , d ) $ 2,150 , e ) $ 2,700
Rationale: cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 8 = $ 4000 profit : 4000 - 1900 = $ 2100 option c is correct
Answer: c
Problem: rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 50000 + y so y = 20000 then x = 50000 - 20000 = 30000 first part = 30000 answer : a"
Answer: a
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 20 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 77 , d ) 40 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 20 km with stoppages . stoppage time = time take to travel ( 60 - 20 ) km i . e 40 km at 60 km / hr . stoppage time = 40 / 60 hrs = 40 min . answer : d"
Answer: d
Problem: find the remainder when 2 ^ 31 is divided by 5 .
Options: a ) 3 , b ) 7 , c ) 1 , d ) 9 , e ) none of them
Rationale: 2 ^ 10 = 1024 . unit digit of 2 ^ 10 x 2 ^ 10 x 2 ^ 10 is 4 [ as 4 x 4 x 4 gives unit digit 4 ] . unit digit of 231 is 8 . now , 8 when divided by 5 , gives 3 as remainder . hence , 231 when divided by 5 , gives 3 as remainder . answer is a .
Answer: a
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 25 kmph and prasanna moves southward at a speed of 35 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 60 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 25 kmph x 1 hr = 25 km total southward prasanna ' s distance = 35 kmph x 1 hr = 35 km total distance between prasanna and laxmi is = 25 + 35 = 60 km . answer : c"
Answer: c
Problem: john was thrice as old as tom 6 years ago . john will be 15 / 13 times as old as tom in 6 years . how old is tom today ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 15 / 13 * ( t + 6 ) 13 j + 78 = 15 t + 90 13 ( 3 t - 12 ) + 78 = 15 t + 90 24 t = 168 t = 7 the answer is b .
Answer: b
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 50 % profit on the first article and 50 % loss on second article . find the net profit or loss percent ?
Options: a ) 500 , b ) 768 , c ) 276 , d ) 280 , e ) 279
Rationale: "profit on first article = 50 % of 1000 = 500 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : a"
Answer: a
Problem: a can complete a project in 10 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 15 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 10 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 10 ) + ( x / 30 ) - 1 ) = 1 4 x / 30 = 2 x = 15 therefore , the answer is b : 15 ."
Answer: b
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 8 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 8 / 8 * c : ( b + c ) / 2 = ( 8 / 8 ) * c b = ( 1 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 * c ) / 2 = ( 1 / 2 ) * c median = ( a + c ) / 2 = ( 1 / 2 * c + c ) / 2 = ( 3 / 2 ) * c / 2 = ( 3 / 4 ) * c ( answer e )"
Answer: e
Problem: a car traveling at a certain constant speed takes 10 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 65 , e ) 78
Rationale: time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 10 = 55 seconds = 55 / 3,600 hours = 1 / 65 hours ; so , we get that to cover 1 kilometer 1 / 65 hours is needed - - > regular speed 65 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : d
Answer: d
Problem: a bus trip of 210 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "the time is the distance / speed . the time difference is 1 hour . 210 / v - 210 / ( v + 5 ) = 1 210 ( v + 5 ) - 210 v = ( v ) ( v + 5 ) 1050 = ( v ) ( v + 5 ) 30 * 35 = ( v ) ( v + 5 ) v = 30 mph the answer is b ."
Answer: b
Problem: if the 5 th date of a month is tuesday , what date will be 3 days after the 3 rd friday in the month ?
Options: a ) 17 , b ) 18 , c ) 20 , d ) 22 , e ) 33
Rationale: b 18 5 th date of a month is tuesday friday will be on = 5 + 3 = 8 th of a month 1 st friday is on 1 st of a month 2 nd friday is on 8 th of a month 3 rd friday will be on 15 th of a month 3 days after 15 th = 15 + 3 = 18
Answer: b
Problem: what is the dividend . divisor 19 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 176 , e ) e ) 160
Rationale: "d = d * q + r d = 19 * 9 + 5 d = 171 + 5 d = 176 answer d"
Answer: d
Problem: 30 % of a number is more than 60 % of 150 by 120 . find the number ?
Options: a ) 770 , b ) 712 , c ) 720 , d ) 740 , e ) 700
Rationale: "( 30 / 100 ) * x – ( 60 / 100 ) * 650 = 190 2 / 7 x = 210 x = 700 answer : e"
Answer: e
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] + 5 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = c = 6 f ( x ) = 3 x – 5 2 * [ f ( x ) ] + 5 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) + 5 = 3 ( 3 x - 6 ) - 5 6 x - 5 = 9 x - 23 x = 6"
Answer: c
Problem: one day a car rental agency rented 3 / 4 of its cars , including 2 / 3 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "the cars with cd players which were not rented is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 1 / 5 ) / ( 1 / 4 ) = 4 / 5 the answer is d ."
Answer: d
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is ?
Options: a ) 128 , b ) 177 , c ) 199 , d ) 178 , e ) 150
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : e"
Answer: e
Problem: an investor deposited $ 5,000 to open a new savings account that earned 12 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5300.50 , b ) $ 5304.50 , c ) $ 5405.50 , d ) $ 5604.50 , e ) $ 5805.50
Rationale: "the amount in the account after 6 months is 1.03 * 1.03 ( $ 5,000 ) = $ 5304.50 . the answer is b ."
Answer: b
Problem: a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in ?
Options: a ) 8 , b ) 4 , c ) 6 , d ) 12 , e ) 10
Rationale: ( a + b + c ) ' s 1 day work = 1 / 6 ; ( a + b ) ' s 1 day work = 1 / 8 ( b + c ) ' s 1 day work = 1 / 12 ( a + c ) ' s 1 day work = ( 2 * 1 / 6 ) - ( 1 / 8 + 1 / 12 ) = ( 1 / 3 - 5 / 24 ) = 1 / 8 so , a and c together will do the work in 8 days . answer a
Answer: a