regisss/math_qa huggingface dataset:
Problem: the area of a square is equal to five times the area of a rectangle of dimensions 25 cm * 5 cm . what is the perimeter of the square ?
Options: a ) 100 , b ) 800 , c ) 500 , d ) 600 , e ) 700
Rationale: "area of the square = s * s = 5 ( 25 * 5 ) = > s = 25 cm perimeter of the square = 4 * 25 = 100 cm . answer : option a"
Answer: a
Problem: in a college , the ratio of the number of boys to girls is 8 : 4 . if there are 200 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 600 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 4 x = > 4 x = 200 = > x = 50 total students = 8 x + 4 x = 12 x = 12 ( 50 ) = 600 option c"
Answer: c
Problem: a certain bag contains 60 balls — 22 white , 18 green , 5 yellow , 6 red , and 9 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.75 , e ) 0.91
Rationale: according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 5 ) / 60 = 45 / 60 = 0.75 . answer : d .
Answer: d
Problem: a and b start a business , with a investing the total capital of rs . 50000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 1500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) 59028 , b ) 27777 , c ) 29999 , d ) 59000 , e ) 27772
Rationale: "interest received by a from b = 10 % of half of rs . 50000 = 10 % * 25000 = 2500 . amount received by a per annum for being a working partner = 1500 * 12 = rs . 18000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 2500 + 18000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 2500 + 18000 + p ) = 2 ( p ) p = 20500 total profit = 2 p + 18000 = 2 * 20500 + 18000 = 59000 . answer : d"
Answer: d
Problem: on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: 24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a .
Answer: a
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 6 full and other jar 1 / 5 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 3 , d ) 7 / 12 , e ) 2 / 3
Rationale: "same amount of water made bigger jar 1 / 6 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 6 + 1 / 6 = 2 / 6 = 1 / 3 full . answer : c ."
Answer: c
Problem: abel can complete a work in 10 days , ben in 14 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 3 days before the completion of the work . how long did the work last ?
Options: a ) 6 , b ) 7 , c ) 7 10 / 29 , d ) 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 14 + 1 / 15 ) ( t ) = 3 / 5 29 / 210 ( t ) = 3 / 5 - - - > t = 126 / 29 therefore , these 4 10 / 29 days worked plus the 3 days that carla had to work by herself add to 7 10 / 29 days answer : c"
Answer: c
Problem: what is the smallest positive integer that can be multiplied by 432 to make it a perfect square ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "432 = 2 ^ 4 * 3 ^ 2 * 3 therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3 . answer b ."
Answer: b
Problem: the price of lunch for 14 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12.85 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "clearly b is the answer i used poe here lets consider option ( b ) 14 * 12.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo b"
Answer: b
Problem: the difference between the place values of two sevens in the numeral 69758472 is
Options: a ) 0 , b ) 100 , c ) 6993 , d ) 699930 , e ) none of these
Rationale: "required difference = ( 700000 - 70 ) = 699930 answer : option d"
Answer: d
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turnon to be white , if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 3 / 8 , e ) 4 / 9
Rationale: since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b
Answer: b
Problem: 1000 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12.8 , b ) 12.6 , c ) 12.5 , d ) 12.2 , e ) 16.6
Rationale: "1000 * 20 = 1200 * x x = 16.6 . answer : e"
Answer: e
Problem: a meeting has to be conducted with 3 managers . find the number of ways in which the managers be selected from among 6 managers , if 2 managers will not attend the meeting together ?
Options: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24
Rationale: "we can either choose all 3 people from 4 manager who have no problems or choose 2 from the 4 and 1 from the 2 managers who have a problem sitting together so 4 c 3 + ( 4 c 2 * 2 c 1 ) this is 4 + 12 = 16 answer : c"
Answer: c
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is ?
Options: a ) 500 , b ) 277 , c ) 266 , d ) 188 , e ) 123
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 112 = rs . 500 answer : a"
Answer: a
Problem: the total marks obtained by a student in mathematics and physics is 90 and his score in chemistry is 30 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 90 and c - p = 30 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 90 + 30 ) / 2 = 60 . answer : e"
Answer: e
Problem: if x is less than y by 20 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 20 % ) = > 20 / ( 100 - 20 ) * 100 = 25 % answer : b
Answer: b
Problem: a picnic attracts 200 persons . there are 20 more men than women , and 20 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 65 , c ) 110 , d ) 130 , e ) 200
Rationale: adult + children = 200 let , children = y then , adult = y + 20 i . e . y + ( y + 20 ) = 200 i . e . y = 900 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 20 i . e . x + ( x + 20 ) = 2 x + 20 = 110 i . e . x = 45 i . e . men , m = 45 + 20 = 65 answer : option b
Answer: b
Problem: the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is :
Options: a ) 30 / 7 , b ) 30 / 98 , c ) 60 / 147 , d ) 50 / 294 , e ) 52 / 294
Rationale: required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a
Answer: a
Problem: what is rate of interest if principal . amount be 400 , simple interest 180 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 22.5 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 180 = 800 r / 100 r = 180 / 8 = 22.5 % answer d"
Answer: d
Problem: find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3 .
Options: a ) 131 , b ) 197 , c ) 207 , d ) 219 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3 . required number = ( lcm of 11 and 12 ) - ( common difference of divisors and remainders ) = ( 132 ) - ( 1 ) = 131 . answer : a"
Answer: a
Problem: david biked 16 1 / 3 miles in 2 hours and 20 minutes . what was his average rate of speed in miles per hour ?
Options: a ) 7 , b ) 7 2 / 3 , c ) 8 1 / 3 , d ) 9 , e ) 9 1 / 3
Rationale: d = 16 ( 1 / 3 ) = 49 / 3 t = 2 ( 1 / 3 ) = 7 / 3 s = d / t = 7 answer = a
Answer: a
Problem: if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 6 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 3 or k = 6 . all the answers are positive , so we choose k = 2 . answer = d"
Answer: d
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 50 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 50 % = 50 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 50 - c = 100 c = 10 option b ."
Answer: b
Problem: find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quartely .
Options: a ) rs . 2522 , b ) rs . 2512 , c ) rs . 2572 , d ) rs . 2592 , e ) none
Rationale: "solution principal = rs . 16,000 ; time = 9 months = 3 quarters ; amount = rs . [ 16000 x ( 1 + 5 / 100 ) ³ ] = [ 16000 x 21 / 20 x 21 / 20 x 21 / 20 ] = rs . 18522 . c . i = rs . ( 18522 - 16000 ) = rs . 2522 . answer a"
Answer: a
Problem: find the ones digit of 73 ^ 330
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 330 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer b ."
Answer: b
Problem: the mean of 50 observations was 36 . it was found later that an observation 28 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.0 , b ) 36.5 , c ) 36.1 , d ) 36.2 , e ) 36.8
Rationale: "explanation : correct sum = ( 36 * 50 + 28 - 23 ) = 1825 . correct mean = = 1805 / 50 = 36.1 answer : c ) 36.1"
Answer: c
Problem: the rate of interest on a sum of money is 9 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,125 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 9 ) / 100 = 10 p / 37 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 10 p / 37 + 4 p / 25 + p / 20 = 540 12 p / 25 = 540 p = 1125 answer : option a"
Answer: a
Problem: in a games hour 4 different types of players came to the ground ? cricket 22 , hokey 15 , football 21 , softball 19 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 62 , d ) 77 , e ) 79
Rationale: "total number of players = 22 + 15 + 21 + 19 = 77 answer is d"
Answer: d
Problem: an alloy is to contain copper and zinc in the ratio 5 : 3 . the zinc required to be melted with 40 kg of copper is ?
Options: a ) 15 kg , b ) 20 kg , c ) 8 kg , d ) 24 kg , e ) 32 kg
Rationale: let the required quantity of copper be x kg 5 : 3 : : 40 : x 5 x = 40 * 3 x = 24 kg answer is d
Answer: d
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 348 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 200 , d ) 40 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 348 = 2 x / 20 = 2 = > x = 40 answer : d"
Answer: d
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 20 percent alcohol by volume ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: "20 % is an equal distance between 10 % and 30 % . thus there should be equal parts of both solutions . we should add 200 ml of solution y . the answer is a ."
Answer: a
Problem: the ratio 6 : 3 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 200 % , e ) none
Rationale: "solution 6 : 3 = 6 / 3 = ( 6 / 3 x 100 ) % . = 200 % . answer d"
Answer: d
Problem: the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ?
Options: a ) 80 kg , b ) 85 kg , c ) 90 kg , d ) 88 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 6 ) kg = 48 kg . weight of new person = ( 40 + 48 ) kg = 88 kg . answer : d"
Answer: d
Problem: a and b are two partially filled buckets of water . if 8 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 8 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 88 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 8 = 1 / 3 ( b + 8 ) - - - - > 3 a - 24 = b + 8 scenario 2 b - 8 = 1 / 2 ( a + 8 ) - - - - - > 2 b - 16 = a + 8 from scenario 1 , b = 3 a - 32 substitute b with this information in stmt 2 2 ( 3 a - 32 ) - 16 = a + 8 - - - - - - > 6 a - 64 - 16 = a + 8 - - - - - - > 6 a - a = 80 + 8 - - - > 5 a = 88 a = 88 / 5 , answer choice a"
Answer: a
Problem: 16 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 20 , d ) 27 , e ) 11
Rationale: "16 * 25 = 20 * x = > x = 20 days answer : c"
Answer: c
Problem: a man traveled a total distance of 900 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 400 km , b ) 450 km , c ) 500 km , d ) 550 km , e ) 600 km
Rationale: "total distance traveled = 900 km . distance traveled by plane = 300 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 300 = 900 3 x / 2 = 600 x = 400 km the answer is a ."
Answer: a
Problem: if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 30
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 18
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 30 = 19008 / 30 = 633 , remainder = 18 e"
Answer: e
Problem: in country z , 18 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 37 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 18 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 18 % = 22 % ) . 22 % + 15 % = 37 % . therefore 37 % of the people in country z have a diploma . ans a"
Answer: a
Problem: if 0.5 of a number is equal to 0.09 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 3 : 7 , e ) 9 : 50
Rationale: sol . 0.5 a = 0.09 b â ‡ ” a / b = 0.09 / 0.50 = 9 / 50 â ˆ ´ a : b = 9 : 50 . answer e
Answer: e
Problem: two trains t 1 and t 2 start simultaneously from two stations x and y respectively towards each other . if they are 70 km apart both 3 and 6 hours after start , then find the distance between the two stations .
Options: a ) 210 km , b ) 240 km , c ) 220 km , d ) 180 km , e ) 190 km
Rationale: in first 3 hours t 1 travels r km and t 2 travels s km . after 6 hours they traveled r + s + 70 + 700 2 ( r + s ) = r + s + 140 r + s = 140 hence distance between xy is r + s + 70 = 140 + 70 = 210 answer : a
Answer: a
Problem: among 7 numbers the average of first 4 numbers is 13 and the average of last 4 numbers is 15 . the sum of last 3 numbers is 55 . the square of the fourth number is equal to the last number then what is the last number ?
Options: a ) 60 , b ) 52 , c ) 5 , d ) 25 , e ) 125
Rationale: let the numbers be a , b , c , d , e , f , g d + e + f + g = 15 * 4 = 60 e + f + g = 55 , 60 - 55 = 5 so the fourth number is 5 . the square is 25 . the answer is option d .
Answer: d
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32
Rationale: "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 12 r / 2 = 12 r = 24 the answer is c ."
Answer: c
Problem: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum q of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just q = 900 : the answer is c ."
Answer: c
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 126 . find the number of notes of rs . 50 denomination .
Options: a ) 115 , b ) 121 , c ) 117 , d ) 119 , e ) 121
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 126 - x now , 50 * x + 500 * ( 126 - x ) = 10350 50 x + 63000 - 500 x = 10350 - 450 x = - 52650 x = 117 . no . of 50 rupees note = 117 . answer : option c"
Answer: c
Problem: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 33 . find the profit percentage ?
Options: a ) 65 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 53 %
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 165 ( 33 * 5 ) profit percentage = ( 165 - 100 ) / 100 * 100 = 65 % answer : a"
Answer: a
Problem: each factor of 230 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 3 / 16 . answer : d"
Answer: d
Problem: 3 different containers contain 496 litres , 403 litres and 713 litres of mixtures of milk and water respectively . what biggest measure can measure all the different quantities exactly ?
Options: a ) 30 litres , b ) 31 litres , c ) 32 litres , d ) 33 litres , e ) 34 litres
Rationale: 403 ) 713 ( 1 403 - - - - - - - - - 310 ) 403 ( 1 310 - - - - - - - - - - 93 ) 310 ( 3 279 - - - - - - - - 31 ) 93 ( 3 93 - - - - - - - x so answer is 31 litres . . . . . . answer : b
Answer: b
Problem: 12 persons can complete the work in 18 days . after working for 6 days , 4 more persons added to complete the work fast . in how many more days they will complete the work ?
Options: a ) 10 days , b ) 9 days , c ) 8 days , d ) 7 days , e ) 6 days
Rationale: total work 12 * 18 = 216 units after 6 days work finished 6 * 12 = 72 units remaining work 216 - 72 = 144 units remaing days = 144 ( 12 + 4 ) = 9 days answer : b
Answer: b
Problem: there are 870 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 145
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e"
Answer: e
Problem: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 14
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 5 x = 35 = > x = 7 hence , b ' s age = 2 x = 14 years . answer : e"
Answer: e
Problem: a and b invests rs . 10000 each , a investing for 9 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 21000 , find their shares ?
Options: a ) 1300,1500 , b ) 9000,12000 , c ) 7290,8000 , d ) 15000,12000 , e ) 72821,75000
Rationale: "the ratio of their profits a : b = 9 : 12 = 3 : 4 share of a in the total profit = 3 / 7 * 21000 = rs . 9000 share of b in the total profit = 4 / 7 * 21000 = rs . 12000 answer : b"
Answer: b
Problem: a batsman scored 150 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 66.66 % , e ) 70 %
Rationale: "explanation : number of runs made by running = 150 - ( 5 x 4 + 5 x 6 ) = 150 - ( 50 ) = 100 now , we need to calculate 100 is what percent of 150 . = > 100 / 150 * 100 = 66.66 % option d"
Answer: d
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7380 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 937.1 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7380 / 18 + 7380 / 14 = 410 + 527.1 = 937.1 hours answer : option b"
Answer: b
Problem: a jar of 220 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: 220 = 20 * 11 = 22 * 10 there are 20 people in the group today . the answer is a .
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train ?
Options: a ) 100 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : a"
Answer: a
Problem: a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 20 ) / ( 20 - 0 ) = 2 / 1 1 / x = 2 / 1 x = 1 / 2 answer : c"
Answer: c
Problem: if a and b are the roots of the equation x 2 - 4 x + 4 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 24 , c ) 17 , d ) 8 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 4 product of roots = ab = 4 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 16 - 8 = 8 answer d"
Answer: d
Problem: if a town of 75,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 76000 , b ) b . 77000 , c ) c . 78000 , d ) d . 79000 , e ) e . 80000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Problem: the total cost of 100 paper plates and 200 paper cups is $ 4.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 80 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 4.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 0.80 therefore oa is a"
Answer: a
Problem: which greatest possible length can be used to measure exactly 15 meter 75 cm , 11 meter 25 cm and 7 meter 65 cm
Options: a ) 45 cm , b ) 255 cm , c ) 244 cm , d ) 55 cm , e ) 280 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1575 cm , 1125 cm , 765 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 255 . option b"
Answer: b
Problem: if ( m - 8 ) is a factor of m ^ 2 - sm - 24 , then s =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - sm - 24 a = - 3 s = 8 + a = 5 = d = b"
Answer: b
Problem: a dice has one of the first 4 prime number on each its 6 sides , with no two sides having the same number . the dice is rolled 10 times and the results added . the addition is most likely to be closet to
Options: a ) 41 , b ) 43 , c ) 60 , d ) 68 , e ) 70
Rationale: if die is rolled then avg score = ( 2 + 3 + 5 + 7 ) / 4 = 41 / 4 so , most likely sum for 10 times = 41 / 4 * 10 = 43 answer : b
Answer: b
Problem: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.7 % , what fraction of the products was checked by worker y ?
Options: a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 8 , d ) 4 / 5 , e ) 5 / 8
Rationale: x : 0.5 % is 0.2 % - points from 0.7 % . y : 0.8 % is 0.1 % - points from 0.7 % . therefore the ratio of products checked by y : x is 2 : 1 . thus , worker y checked 2 / 3 of the products . the answer is a .
Answer: a
Problem: 40 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
Options: a ) 25 cm , b ) 20 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 4 x 40 ) m 3 = 160 m 3 rise in water level = 160 / 40 ã — 20 = 0.2 m = 20 cm answer : b"
Answer: b
Problem: if a is thrice as fast as b and together can do a work in 18 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 24 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 18 = 3 + 1 / 3 x = 4 / 3 x = 1 / 18 x = 18 * 4 / 3 = 24 answer : c"
Answer: c
Problem: what is the average of first 21 multiples of 4 ?
Options: a ) a ) 44 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82
Rationale: "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 4 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 44 a"
Answer: a
Problem: a factory produces 3400 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 575 toys , b ) 375 toys , c ) 680 toys , d ) 475 toys , e ) 675 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 3400 / 5 = 680 toys correct answer c"
Answer: c
Problem: if the cost price is 99 % of selling price then what is the profit percentage .
Options: a ) 1 , b ) 1.11 , c ) 1.01 , d ) 1.1 , e ) 1.21
Rationale: "selling price = rs 100 : then cost price = rs 99 : profit = rs 1 . profit = { ( 1 / 99 ) * 100 } % = 1.01 % answer is c ."
Answer: c
Problem: g ( a ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( y ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b
Answer: b
Problem: j is 25 % less than p and 20 % less than t . t is w % less than p . what is the value of w ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( w / 100 ) ] * p i . e . 100 - w = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . w = 6.25 answer : option d"
Answer: d
Problem: how many litres of pure acid are there in 4 litres of a 35 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.4
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 8 * 20 / 100 = 1.4 answer : option e
Answer: e
Problem: last year department store x had a sales total for december that was 7 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 7 / 18 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 70 year total = 11 * 10 + 70 = 180 answer = 70 / 180 = 7 / 18 = d"
Answer: d
Problem: a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is :
Options: a ) 1 : 2 , b ) 2 : 5 , c ) 6 ' ' 2 , d ) 3 : 1 , e ) 4 : 7
Rationale: explanation : let speed upstream = x hen , speed downstream = 2 x speed in still water = 2 x + x / 2 speed of the stream = 2 x - x / 2 speed in still water : speed of the stream = 3 x / 2 : x / 2 = 3 : 1 answer : d
Answer: d
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 20
Rationale: "age of the 15 th student = 15 * 15 - ( 14 * 5 + 16 * 9 ) = 225 - 214 = 11 years answer is b"
Answer: b
Problem: a shopkeeper sold an article at $ 100 with 10 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 72 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 110 = $ 91 ( approximately ) answer is c"
Answer: c
Problem: how many factors does 25 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 4 * 2 = 8 answer b ."
Answer: b
Problem: a glass was filled with 12 ounces of water , and 0.03 ounce of the water evaporated each day during a 22 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 5.002 % , b ) 5.5 % , c ) 0.5 % , d ) 5 % , e ) 20 %
Rationale: "in 22 days 22 * 0.03 = 0.66 ounces of water evaporated , which is 0.66 / 12 â ˆ — 100 = 5.5 of the original amount of water . answer : b ."
Answer: b
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 38 of gas ?
Options: a ) 212 , b ) 256 , c ) 304 , d ) 372 , e ) 460
Rationale: "38 / 4 = 9.5 gallons 9.5 * 32 = 304 miles the answer is c ."
Answer: c
Problem: if x + y = 20 , x - y = 10 , for integers of x and y , x = ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 13 , e ) 42
Rationale: "x + y = 20 x - y = 10 2 x = 30 x = 15 answer is a"
Answer: a
Problem: molly ' s age in 18 years will be 5 times her age 6 years ago . what is molly ' s present age ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: let x be molly ' s present age . x + 18 = 5 ( x - 6 ) x = 12 the answer is d .
Answer: d
Problem: in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ?
Options: a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264
Rationale: total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c
Answer: c
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 90 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 90 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 900 gm ) of tea and 1 / 2 kg ( 900 gm ) of coffee ( equal quantities ) = 90 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 90 = > x = 90 thus proved . . . option d ."
Answer: d
Problem: a dealer purchased an article at 3 / 4 of its list price and sold 50 % more than the list price . find his gain percent ?
Options: a ) 108 % , b ) 300 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: mp = 100 cp = 75 sp = 150 - - - - - - 75 - - - - 75 100 - - - - ? = > 100 % answer : c
Answer: c
Problem: 4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 24 . what is half of that number ?
Options: a ) 670 , b ) 750 , c ) 945 , d ) 375 , e ) 315
Rationale: "let no . be x 4 / 15 * 5 / 7 * x - 4 / 9 * 2 / 5 * x = 8 by further solving 20 x / 105 - 8 x / 45 = 8 4 x / 315 = 24 x = 1890 we have to find x / 2 = 1890 / 2 = 945 answer : c"
Answer: c
Problem: a driver just filled the car ' s gas tank with 54 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 2.7 , e ) 3
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 54 ) + x = 0.1 ( 54 + x ) 0.9 x = 5.4 - 2.7 = 2.7 x = 3 liters the answer is e ."
Answer: e
Problem: a store owner estimates that the average price of type a products will increase by 30 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount paid for type a products was $ 3200 and the total price paid for type b products was $ 5800 . 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 ) $ 15,325 , c ) $ 11,129 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.3 * 3200 = 4160 cost of type b products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 answer : c"
Answer: c
Problem: 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60
Rationale: 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . so , 20 % * employees = 40 % * fair haired employees ( because both are equal to the number of fair haired women employees ) ( 1 / 2 ) * employees = fair haired employees answer ( c )
Answer: c
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 168,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: "increase = 168000 - 120000 = 48000 % increase = 48000 * 100 / 120000 = 40 % answer : option d"
Answer: d
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 250 , and the total cost is $ 16,000 , what is the value of n ?
Options: a ) 10 , b ) 24 , c ) 60 , d ) 70 , e ) 85
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 10,000 + n * $ 250 - - > n = 24 . answer : b ."
Answer: b
Problem: in a sports club with 30 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "17 + 19 = 36 but where as total number is 30 - 2 = 28 therefore answer is 36 - 28 = 8 hence answer is e"
Answer: e
Problem: a boy want to make a cuboid of dimension 5 m , 6 m , 7 m from small cubes of . 04 m 3 . later he realized he can make same cuboid by making it hollow . then it takes some cubes less . what is the no . of these cubes ?
Options: a ) 2150
b ) 2250
c ) 2350
d ) 2850
e ) 3250
Rationale: volume of cuboid = 5 * 6 * 7 = 210 m 3 volume of inner cuboid = ( 5 - 1 ) * ( 6 - 1 ) * ( 7 - 1 ) = 120 m 3 therefore , volume of hollow cuboid = 210 - 120 = 90 m 3 no of cubes required = 90 / . 04 = 2250 cubes answer : b
Answer: b
Problem: a fill pipe can fill 1 / 2 of cistern in 10 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 1 min , b ) 4 min , c ) 6 min , d ) 10 min , e ) 25 min
Rationale: "required time = 10 * 2 * 1 / 2 = 10 minutes answer is d"
Answer: d
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 3 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 3 / 8 * ( 1 - 3 / 5 ) = 14 / 40 = 3 / 20 . answer : d ."
Answer: d
Problem: the average weight of 10 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 100 kg , b ) 102.5 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 10 x 3.5 ) kg = 35 kg . weight of new person = ( 65 + 35 ) kg = 100 kg . answer : a"
Answer: a
Problem: the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 90 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 92 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 90 ) / 10 avg = 100 - 8 = 92 answer is c"
Answer: c
Problem: what will be remainder when ( 67 ^ 67 + 67 ) is divided by 68 ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 71 , e ) 72
Rationale: ( xn + 1 ) will be divisible by ( x + 1 ) only when n is odd . ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder . b )
Answer: b
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1000 , what is the reduced price for kg ?
Options: a ) s . 50 , b ) s . 46 , c ) s . 49 , d ) s . 41 , e ) s . 42
Rationale: "1000 * ( 25 / 100 ) = 250 - - - - 5 ? - - - - 1 = > rs . 50 answer : a"
Answer: a
Problem: the perimeters of 2 squares are 60 cm and 48 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ?
Options: a ) 20 cm
b ) 28 cm
c ) 36 cm
d ) 48 cm
e ) 40 cm
Rationale: side of the 1 st square = 60 / 4 = 15 cm side of the 2 nd square = 48 / 4 = 12 cm area of the 3 rd square = 15 ^ 2 - 12 ^ 2 = 81 cm ^ 2 side of the 3 rd square = 9 cm required perimeter = 9 * 4 = 36 cm answer is c
Answer: c
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 4 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 ) 5 , 500,000
b ) 2 , 400,000
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 4 gms in 400,000 cm ^ 3 , x = 4 * 400,000 = 1 , 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 = 1 , 600,000 + 1 , 800,000 = 2 , 400,000 answer : b
Answer: b
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 20 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 20 minutes , e ) 2 hours 10 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 20 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 20 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 20 + 60 ) = 80 minutes on the road . d . 1 hour 20 minutes"
Answer: d
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 300 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 60 % , e ) 30 %
Rationale: price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 300 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 300 ) * 100 / 500 = 60 % answer : option d
Answer: d
Problem: what is the 10 th digit to the right of the decimal point in the decimal equivalent of 124 / 22 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 6
Rationale: "124 / 22 = 5.6363 . . . . 63 is non - terminating repeating decimal . the 10 th digit to the right of decimal point will be 3 . answer b"
Answer: b