regisss/math_qa huggingface dataset:
Problem: a bag contains 12 red jellybeans and 12 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 3 / 10 answer : option e"
Answer: e
Problem: a candidate got 10 % of the votes polled and he lost to his rival by 16000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 20000 , c ) 2775 , d ) 5496 , e ) 6851
Rationale: "10 % - - - - - - - - - - - l 90 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 80 % - - - - - - - - - - 16000 100 % - - - - - - - - - ? = > 20000 answer : b"
Answer: b
Problem: if i walk at 8 km / h , i miss the bus by 14 minutes . if i walk at 9 km / h , i reach 16 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 3.4 km , b ) 2.9 km , c ) 2.4 km , d ) 2.6 km , e ) 2.8 km
Rationale: d = product of speed difference of time / difference of speed d = 8 x 9 / 60 [ 14 â ˆ ’ ( â ˆ ’ 16 ) / 9 - 8 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 2.4 km answer c
Answer: c
Problem: the length of a rectangle is 2 cm more than the width of the rectangle . the perimeter of the rectangle is 20 cm . find the length and the width of the rectangle .
Options: a ) l = 2 , w = 9
b ) l = 5 , w = 8
c ) l = 6 , w = 4
d ) l = 1 , w = 7
e ) l = 2 , w = 3
Rationale: let length l = x , width w = x − 2 and perimeter = p ∴ p = 2 l + 2 w = 2 x + 2 ( x − 2 ) 20 = 2 x + 2 x − 4 4 x = 24 x = 6 l = 6 cm and w = l − 2 = 4 cm answer is c .
Answer: c
Problem: a certain sum becomes 4 times itself at simple interest in 8 years . in how many years does it become 10 times itself ?
Options: a ) 24 , b ) 55 , c ) 77 , d ) 99 , e ) 01
Rationale: let the sum be rs . x , then it becomes rs . 4 x in eight years rs . 3 x is the interest on x for eight years . r = ( 100 * 3 x ) / ( x * 8 ) = 300 / 8 % if the sum becomes ten times itself , then interest is 9 x . the required time period = ( 100 * 9 x ) / ( x * 300 / 8 ) = ( 100 * 9 x * 8 ) / ( x * 300 ) = 24 years . answer : a
Answer: a
Problem: product of two natural numbers is 5 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 26 / 25 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b"
Answer: b
Problem: certain stocks in january were 20 % less than they were in february and 30 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?
Options: a ) 31 % , b ) 45 % , c ) 52 % , d ) 61 % , e ) 25 %
Rationale: "let , stock in february = 100 then , stock in january = 100 - ( 20 / 100 ) * 100 = 80 january = 30 % greater than march = 1.3 * stock in march i . e . stock in march = 90 / 1.3 = 69 approximately % decrease from february to march = ( 69 - 100 ) * 100 / 100 = 31 % approximately answer : option a"
Answer: a
Problem: if a ( a + 2 ) = 35 and b ( b + 2 ) = 35 , where a ≠ b , then a + b =
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 2 , e ) - 10
Rationale: "i . e . if a = 5 then b = - 7 or if a = - 7 then b = 5 but in each case a + b = 5 - 7 = - 2 answer : d"
Answer: d
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 10 to produce 80 units ?
Options: a ) 63 , b ) 20 , c ) 42 , d ) 65 , e ) 84
Rationale: "5 machines would produce 80 units in 40 hours . increasing the amount of machines by 2 would mean dividing 40 hours by 2 . 40 / 2 = 20 answer : b"
Answer: b
Problem: jar a has 26 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 7.6 % , b ) 8.3 % , c ) 9.6 % , d ) 10.3 % , e ) 11.5 %
Rationale: "an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 126 marbles . now , for both jars to have equal marbles we should move 13 marbles from a to b , which is 13 / 126 = ~ 10.3 % of a . answer : d ."
Answer: d
Problem: the average weight of 5 students decreases by 4 kg when one of them weighing 92 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 4 kg = > ( 92 - x ) / 5 = 4 = > x = 72 answer : d"
Answer: d
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 25 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 500 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 25 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 25 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 500 = 20 t 19 t + 500 = 20 t 500 = t there are a total of 500 students in the math class . answer is d ."
Answer: d
Problem: a 10 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 / 5 , d ) 2 / 5 , e ) 3 / 5
Rationale: "the longer wire will form a square with an area more than 4 if the wire is cut at a point within two meters of either end . the probability of this is 4 / 10 = 2 / 5 . the answer is d ."
Answer: d
Problem: an uneducated retailer marks all his goods at 55 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 155 . s . p . = 75 % of rs . 155 = rs . 116.25 . ∴ gain % = 16.25 % . answer e"
Answer: e
Problem: the sum of ages of 5 children born 4 years different each is 70 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 22 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) and ( x + 16 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) + ( x + 16 ) = 70 5 x = 30 x = 6 x + 16 = 6 + 16 = 22 answer : c"
Answer: c
Problem: the difference between simple and compound interest on rs . 1400 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.25 , b ) 3.5 , c ) 9.0 , d ) 3.15 , e ) 2.0
Rationale: "s . i . = ( 1400 * 10 * 1 ) / 100 = rs . 140 c . i . = [ 1400 * ( 1 + 5 / 100 ) 2 - 1400 ] = rs . 143.5 difference = ( 143.5 - 140 ) = rs . 3.50 answer : b"
Answer: b
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 2 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: "6 * 15 * 2 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 2 + 1 ) = ( √ 8 * 18 ) / 3 = ( √ 144 ) / 3 = 12 / 3 = 4 . answer is e"
Answer: e
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 420 m , its area is ?
Options: a ) 150 , b ) 882 , c ) 277 , d ) 210 , e ) 281
Rationale: "5 x + 12 x + 13 x = 420 = > x = 14 a = 70 , b = 168 , c = 182 s = ( 70 + 168 + 182 ) / 2 = 210 answer : d"
Answer: d
Problem: a train 500 m long , running with a speed of 180 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 10 sec , e ) 12 sec
Rationale: speed = 180 * 5 / 18 = 50 m / sec time taken = 500 * 1 / 50 = 10 sec answer : d
Answer: d
Problem: 33 1 / 3 % of 330 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 330 = 110 c )"
Answer: c
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 40 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 , b ) 800 , c ) 600 , d ) 700 , e ) 500
Rationale: "volume of pool = 40 * 150 * 10 cu . ft , 80 % full = 40 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 40 * 150 * 10 * 0.8 / 60 min = 800 min b"
Answer: b
Problem: you collect pens . suppose you start out with 7 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "solution start with 7 pens . mike gives you 22 pens : 7 + 22 = 29 pens . cindy doubles the number of pens you have : 29 × 2 = 58 pens . sharon takes 19 pens from you : 58 - 19 = 39 pens . so you have 39 at the end . correct answer : a"
Answer: a
Problem: the difference between simple and compound interest on rs . 1300 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.0 , b ) 3.25 , c ) 9.15 , d ) 3.13 , e ) 2.0
Rationale: s . i . = ( 1300 * 10 * 1 ) / 100 = rs . 130 c . i . = [ 1300 * ( 1 + 5 / 100 ) 2 - 1300 ] = rs . 133.25 difference = ( 133.25 - 130 ) = rs . 3.25 answer : b
Answer: b
Problem: the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 90 inclusive is the digital sum a multiple of 7 ?
Options: a ) 10 , b ) 8 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 10 ways . . a"
Answer: a
Problem: ravi and kavi start a business by investing â ‚ ¹ 3000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 24 , b ) 5 : 24 , c ) 7 : 24 , d ) 1 : 24 , e ) 3 : 24
Rationale: ratio of profit = ratio of investments = 3000 : 72000 = 1 : 24 answer : d
Answer: d
Problem: in august , a cricket team that played 120 matches won 30 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 55 , c ) 68 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 36 + x by solving we get x = 55 answer : b"
Answer: b
Problem: jim ’ s taxi service charges an initial fee of $ 2.05 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 5.20 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: let the fixed charge of jim ’ s taxi service = 2.05 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.05 + ( 3.6 / . 4 ) * . 35 = 2.05 + 9 * . 35 = 5.2 $ answer a
Answer: a
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × w , what is the value of w ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × w = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x w = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w w = 7 ^ 2 = 49 answer d"
Answer: d
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 40 miles per gallon , and from town b to town c , the car averaged 50 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 42.85 , b ) 40 , c ) 35 , d ) 41 , e ) 39
Rationale: "step 1 ) took lcm of 40 and 50 . . came as 200 . step 2 ) 200 distance between b to c . . . do 200 / 50 hence 4 gallons used step 3 ) twice distance . . hence 200 * 2 = 400 . . . do as above . . 400 / 40 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 200 + 400 = 600 miles hence . . average of whole journey = 600 / 14 which comes to 42.85 answer : a"
Answer: a
Problem: a fill pipe can fill 2 / 5 of cistern in 30 minutes in how many minutes , it can fill 4 / 5 of the cistern ?
Options: a ) 48 min , b ) 63 min , c ) 25 min , d ) 30 min , e ) 60 min
Rationale: "2 / 5 of the cistern can fill in 30 min 4 / 5 of the cistern can fill in = 30 * 5 / 2 * 4 / 5 = 60 min answer is e"
Answer: e
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 10 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 20 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 10 ) = 4 / 5 20 x = 4 ( 3 x + 10 ) 8 x = 40 x = 5 quantity of alcohol = ( 4 x 5 ) litres = 20 litres . answer is d ."
Answer: d
Problem: a car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8
Rationale: "let the time for which car averages 75 mph = t 65 * ( t + 4 ) = 45 * 4 + 75 t = > 10 t = 80 = > t = 8 total duration of the trip = 8 + 4 = 12 answer a"
Answer: a
Problem: the sum of the present age of henry and jill is 40 . what is their present ages if 8 years ago henry was twice the age of jill ?
Options: a ) 13 and 27 , b ) 16 and 24 , c ) 18 and 22 , d ) 11 and 29 , e ) none of these
Rationale: "let the age of jill 8 years ago be x , age of henry be 2 x x + 8 + 2 x + 8 = 40 x = 8 present ages will be 16 and 24 answer : b"
Answer: b
Problem: the cricket team of 11 members is 25 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: let the average age of the whole team be x years . 11 x - ( 25 + 28 ) = 9 ( x - 1 ) = > 11 x - 9 x = 44 = > 2 x = 44 = > x = 22 . so , average age of the team is 22 years . b
Answer: b
Problem: the speed of a boat in still water is 24 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 15 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 3.6 km , d ) 6.75 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 24 + 3 ) kmph = 27 kmph . distance travelled = ( 27 x 15 / 60 ) km = 6.75 km option d"
Answer: d
Problem: louie takes out a 3 - month loan of $ 2000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?
Options: a ) a ) 333 , b ) b ) 383 , c ) c ) 402 , d ) d ) 433 , e ) e ) 804
Rationale: here ' s the calculation for that case , assume monthly payment is x . after 1 st month : ( 2000 ) ( 1.1 ) - x = 2200 - x after 2 nd month : ( 2200 - x ) ( 1.1 ) - x = 2420 - 2.21 x after 3 rd month : ( 2420 - 2.21 x ) ( 1.1 ) - x = 2662 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 2662 - 3.31 x = 0 x = 2662 / 3.31 = 804 answer e
Answer: e
Problem: 50 ^ 51 ^ 52 / 11
Options: a ) 6 , b ) 4 , c ) 7 , d ) 3 , e ) 5
Rationale: "we know that 6 ^ 1 = 6 or 6 ^ 2 = 36 so for all power of 6 unit digit is 6 now que is 50 ^ 51 ^ 52 now if we divide 50 / 11 then rem is 6 means 6 ^ 51 = 6 at unit place same for 6 ^ 52 salso give 6 at unit place now finally 50 ^ 51 ^ 52 gives 6 at unit place now 6 / 11 = 6 answer : a"
Answer: a
Problem: some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 45 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "45 % is 20 % - points above 25 % and 5 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 1 : 4 . 1 / 5 of the original paint was replaced . the answer is b ."
Answer: b
Problem: if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 2 , b ) 7 / 2 , c ) 10 / 3 , d ) 15 / 4 , e ) 25 / 3
Rationale: "n = 3 d / 5 j = n / 3 = d / 5 the average of november and january is ( n + j ) / 2 = 4 d / 5 / 2 = 2 d / 5 d is 5 / 2 times the average of november and january . the answer is a ."
Answer: a
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross - section is 640 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 28 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 10 + 6 ) = 640 d = 80 answer : d"
Answer: d
Problem: the jogging track in a sports complex is 528 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 3.84 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 528 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 528 m apart , they take ( 100 / 825 * 528 / 1000 ) hrs = ( 528 / 8250 * 60 ) min = 3.84 min . answer : b"
Answer: b
Problem: a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2500 so 200 * x + 230 * x = 2500 = > 430 x = 2500 = > x is approximately equal to 6 . so total people is 2 * 6 = 12 we are not taking 12 as answer because say 11 th person has minimum of 180 weight then 200 * 6 + 230 * 6 = 2580 ( which is more than 2500 ) answer e ."
Answer: e
Problem: the ratio of two quantities is 7 to 12 . if each of the quantities is divided by 3 , what is the ratio of these 2 new quantities ?
Options: a ) 3.5 : 6 , b ) 14 : 24 , c ) 7 : 12 , d ) 2.3 : 4 , e ) it can not be determined from the information given
Rationale: "if both sides of a ratio are divided by the same number there is no change in the ratio . 5 : 6 means 7 x : 12 x . . . the ratio starts as 7 / ( 1 ) : 12 / ( 1 ) . so when you diveide by three it becomes 7 / ( 3 ) : 12 / ( 3 ) . . so if the xs are equal the ratio does not change . . answer : c"
Answer: c
Problem: if 45 % of z is 72 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 120 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 72 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 72 / 100 ) * ( 3 / 4 ) x i . e . z = ( 72 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.2 ) x = ( 120 / 100 ) x i . e . z is 120 % of x answer : option b"
Answer: b
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 70 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 40 %
Rationale: let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 70 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 40 mins ( @ 60 miles / hr ) = ( 70 / 70 ) * 40 = 40 miles fuel used to travel 80 miles = ( 80 / 40 ) = 2 gallon i . e . used fuel = ( t - 8 ) = 2 gallon i . e . t = 10 gallons i . e . used fuel = ( 2 / 10 ) * 100 = 20 % d
Answer: d
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 420 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 620 , c ) 500 , d ) 520 , e ) 840
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 420 ) = 2 + 2 ( extra ) = > 2 x - 840 = x = > x = 840 . answer : e"
Answer: e
Problem: population of a city in 20004 was 1200000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 1300650
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1300650 e"
Answer: e
Problem: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: t = ( 111 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 6.85 answer : c
Answer: c
Problem: working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 2 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 5 per hour hillary = 1 / 2 per hour rate when working together : mary = 1 / 5 + ( 1 / 3 * 1 / 5 ) = 1 / 4 per hour hillary = 1 / 2 - ( 1 / 2 * 1 / 2 ) = 1 / 4 per hour together they work 1 / 4 + 1 / 4 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Problem: the two lines y = x and x = - 2 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 8 √ 2 , c ) 8 , d ) √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 2 , - 2 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 2 × 2 ) = 2 ; so z = 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 2 . clearly s = √ 2 , oranswer choice ( d ) ."
Answer: d
Problem: sum of two numbers is 15 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "explanation : x + y = 15 2 x – 3 y = 5 x = 10 y = 5 a )"
Answer: a
Problem: some of 50 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: 30 % is 10 % - points above 20 % and 20 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 2 : 1 . 2 / 3 of the original paint was replaced . the answer is c .
Answer: c
Problem: two women started running simultaneously around a circular track of length 1800 m from the same point at speeds of 10 km / hr and 20 km / hr . when will they meet for the first time any where on the track if they are moving in opposite directions ?
Options: a ) 72 , b ) 74 , c ) 76 , d ) 78 , e ) 80
Rationale: time taken to meet for the first time anywhere on the track = length of the track / relative speed = 1800 / ( 30 + 60 ) 5 / 18 = 1800 * 18 / 90 * 5 = 72 seconds . answer : a
Answer: a
Problem: the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 20 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 46 , c ) 88 , d ) 33.33 , e ) 12
Rationale: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 200 . total score of the batsman in the 30 matches = 1000 . average score of the batsman = 1000 / 30 = 33.33 answer : d"
Answer: d
Problem: a goods train runs at the speed of 72 kmph and crosses a 240 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 643 m , d ) 280 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 240 / 26 = 20 x + 240 = 520 x = 280 . answer : d"
Answer: d
Problem: if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 2 a + 22 b ?
Options: a ) - 4 , b ) - 70 , c ) 0 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 70 , 9 a - b = - 12 b - 2 a , 10 b + 70 = - 12 b - 2 a manipulating the second equation gives us 10 b + 70 = - 12 b - 2 a = = > 2 a + 22 b = - 70 answer is b"
Answer: b
Problem: how much time will a train of length 300 m moving at a speed of 72 kmph take to cross another train of length 500 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 80 , c ) 88 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 300 + 500 = 800 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 800 / 10 = 80 sec . answer : b"
Answer: b
Problem: a certain number when divided by 39 leaves a remainder 17 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 4
Rationale: "explanation : 39 + 17 = 56 / 13 = 4 ( remainder ) answer : e"
Answer: e
Problem: a tank contains 8,000 gallons of a solution that is 4 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 3.40 % , b ) 4.40 % , c ) 5.40 % , d ) 6.40 % , e ) 7.40 %
Rationale: "we start with 8,000 gallons of a solution that is 4 % sodium chloride by volume . this means that there are 0.04 x 8,000 = 320 gallons of sodium chloride . when 3,000 gallons of water evaporate we are left with 5,000 gallons of solution . from here we can determine what percent of the 5,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 320 / 5,000 ) x 100 = ? 0.064 x 100 = ? = 6.4 % answer is d ."
Answer: d
Problem: x , y and z , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2000 , what will be z ' s share of the earnings ?
Options: a ) $ 1080.90 , b ) $ 1000.90 , c ) $ 1070.90 , d ) $ 1050.90 , e ) $ 1090.90
Rationale: the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2000 = $ 1090.90 hence : e
Answer: e
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 504 , b ) 536 , c ) 544 , d ) 548 , e ) 568
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"
Answer: d
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 30 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 30 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 30 for cristina = c = 5 * t @ t = 15 , n = 75 c = 75 right answer ans : a"
Answer: a
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6.6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 7040
Rationale: number of bricks = volume of wall / volume of bricks = 800 x 660 x 22.5 / 25 x 11.25 x 6 = = 7040 answer : e
Answer: e
Problem: the total number of students in grades 1 and 2 is 30 more than the total number of students in grades 2 and 5 . how much lesser is the number of students in grade 5 as compared to grade 1 ?
Options: a ) 20 , b ) 30 , c ) 10 , d ) 40 , e ) 15
Rationale: ( grade 1 + grade 2 ) - ( grade 2 + grade 5 ) = 30 grade 1 - grade 5 = 30 answer : b
Answer: b
Problem: a football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be
Options: a ) 14 , b ) 16 , c ) 18 , d ) 10 , e ) 21
Rationale: "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 21 goals if . . . . total goals = 21 goals 5 th game = 5 goals 1 st 4 games = 16 goals avg . for 1 st 4 games = 16 / 4 = 4 goal / game avg . for all 5 games = 21 / 5 = 4.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer ."
Answer: e
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 22 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 3 / 5 . hence , d is the correct answer ."
Answer: d
Problem: a jeep takes 4 hours to cover a distance of 620 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 148 kmph , b ) 152 kmph , c ) 106 kmph , d ) 103 kmph , e ) 165 kmph
Rationale: "time = 4 distance = 620 3 / 2 of 4 hours = 4 * 3 / 2 = 6 hours required speed = 620 / 6 = 103 kmph d )"
Answer: d
Problem: the mean of 50 observations was 36 . it was found later that an observation 60 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 60 - 23 ) = 1837 . correct mean = 1837 / 50 = 36.7 answer : a"
Answer: a
Problem: in a party every person shakes hands with every other person . if there were a total of 105 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 105 n ( n - 1 ) / 2 = 105 â ˆ ´ n = 15 answer : a"
Answer: a
Problem: at a certain organisation , the number of male members went up by 12 % in the year 2001 from year 2000 , and the number of females members went down by 4 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: "men increase by 12 % = = > 1.12 m = males in 2001 women decrease by 4 % = = > 0.96 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.12 m + 0.96 f = 1.012 * ( m + f ) 1.12 m + 0.96 f = 1.012 m + 1.012 f 1.12 m - 1.012 m = 1.012 f - 0.96 f 0.108 m = 0.052 f m / f = ( 0.052 ) / ( 0.108 ) = 52 / 108 = 1 / 2 answer = ( a )"
Answer: a
Problem: what least value should be replaced by * in 842 * 124 so the number become divisible by 9
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 8 + 4 + 2 + * + 1 + 2 + 4 ) = 21 + * should be divisible by 9 , 21 + 6 will be divisible by 9 , so that least number is 6 . answer : option d"
Answer: d
Problem: there are 7 players in a bowling team with an average weight of 76 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 78 kg . , b ) 70 kg . , c ) 75 kg . , d ) 70 kg . , e ) 72 kg .
Rationale: "the new average will be = ( 76 * 7 + 110 + 60 ) / 9 = 78 kgs a is the answer"
Answer: a
Problem: ratio between rahul and deepak is 4 : 3 , after 2 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 2 = 26 = > x = 6 so deepak age is = 3 ( 6 ) = 18 option b"
Answer: b
Problem: the sum of all consecutive odd integers from − 25 to 35 , inclusive , is
Options: a ) 130 , b ) 135 , c ) 155 , d ) 195 , e ) 235
Rationale: "the sum of the odd numbers from - 25 to + 25 is 0 . let ' s add the remaining numbers . 27 + 29 + 31 + 33 + 35 = 5 ( 31 ) = 155 the answer is c ."
Answer: c
Problem: a train crosses a platform of 130 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 887 , c ) 167 , d ) 197 , e ) 230
Rationale: "length of the train be ‘ x ’ x + 130 / 15 = x + 250 / 20 20 x + 2600 = 15 x + 3750 5 x = 1150 x = 230 m answer : e"
Answer: e
Problem: one computer can upload 100 megabytes worth of data in 4 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 20 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 2.5 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4 * 5 = 20 seconds it can upload 5 * 100 = 500 megabytes worth of data , hence the second computer in 20 seconds uploads 1300 - 500 = 800 megabytes worth of data . the second computer can upload 100 megabytes of data in 2.5 seconds . answer : b ."
Answer: b
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 500 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 8 = 256 < 500 , then the greatest possible length of integer z is 8 . the answer is c ."
Answer: c
Problem: after decreasing 50 % in the price of an article costs rs . 620 . find the actual cost of an article ?
Options: a ) 1400 , b ) 1240 , c ) 1200 , d ) 1100 , e ) 1500
Rationale: "cp * ( 50 / 100 ) = 620 cp = 12.4 * 100 = > cp = 1240 answer : b"
Answer: b
Problem: a cube has a volume of 27 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 216 , b ) 48 , c ) 64 , d ) 80 , e ) 100
Rationale: "volume = 27 = side ^ 3 i . e . side of cube = 3 new cube has dimensions 6 , 6 , and 6 as all sides are twice of teh side of first cube volume = 6 * 6 * 6 = 216 square feet answer : option a"
Answer: a
Problem: if the compound interest on a certain sum of money for 7 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 2100 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 7 yrs = ( 3000 x 10 x 7 ) / 100 = 2100 / - answer : d ."
Answer: d
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 4 + 3 and * 4 + 4 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 4 would be divisible by all numbers from 1 to 4 . = > * 4 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 4 is divisible by 3 ) in fact adding anyprimenumber between 1 to 4 to * 4 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 4 + 3 and * 4 + 11 then the answer would be 1 . for * 4 + 3 and * 4 + 13 , it is 2 and so on . . . a"
Answer: a
Problem: in the hillside summer camp there are 50 children . 85 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 20 . , b ) 45 . , c ) 50 . , d ) 30 . , e ) 25 .
Rationale: given there are 50 students , 84 % of 50 = 42 boys and remaining 8 girls . now here 84 % are boys and 16 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 8 % . . if we add 50 to existing 45 then the count will be 92 and the girls number will be 8 as it . now boys are 92 % and girls are 8 % . ( out of 100 students = 92 boys + 8 girls ) . imo option c is correct .
Answer: c
Problem: 4 , 5 , 7 , 11 , 19 , ( . . . )
Options: a ) 32 , b ) 22 , c ) 35 , d ) 27 , e ) 28
Rationale: "4 4 × 2 - 3 = 5 5 × 2 - 3 = 7 7 × 2 - 3 = 11 11 × 2 - 3 = 19 19 × 2 - 3 = 35 answer is c"
Answer: c
Problem: a set s = { x , - 8 , - 5 , - 2 , 2 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) - 1 , e ) can not be determined
Rationale: "median of the set = ( - 2 + 2 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 17 - 15 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c"
Answer: c
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many acres q were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn q = 4 * 94 = 376 correct option - c
Answer: c
Problem: a sum fetched a total simple interest of $ 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8925
Rationale: "e 8925 principal = $ 100 x 4016.25 / 9 x 5 = $ 401625 / 45 = $ 8925 ."
Answer: e
Problem: a train running at 1 / 2 of its own speed reached a place in 8 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 4 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: time taken if run its own speed = 1 / 2 * 8 = 4 hrs time saved = 8 - 4 = 4 hrs answer : c
Answer: c
Problem: the ratio 6 : 5 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 120 % , d ) 125 % , e ) none
Rationale: "solution 6 : 5 = 6 / 5 = ( 6 / 5 x 100 ) % . = 120 % . answer c"
Answer: c
Problem: find the area of a parallelogram with base 20 cm and height 16 cm ?
Options: a ) 198 cm 2 , b ) 320 cm 2 , c ) 279 cm 2 , d ) 128 cm 2 , e ) 297 cm 2
Rationale: "area of a parallelogram = base * height = 20 * 16 = 320 cm 2 answer : b"
Answer: b
Problem: a part of certain sum of money is invested at 10 % per annum and the rest at 16 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 8 : 5 , b ) 4 : 9 , c ) 4 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: 16 : 10 = 8 : 5 answer : a
Answer: a
Problem: the h . c . f of two numbers is 12 and their l . c . m is 6600 . if one of the numbers is 288 , then the other is ?
Options: a ) 255 , b ) 260 , c ) 265 , d ) 270 , e ) 275
Rationale: "other number = ( 12 * 6600 ) / 288 = 275 . answer : e"
Answer: e
Problem: the unit digit in the product ( 624 * 708 * 913 * 463 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 8 * 3 * 3 ) = 8 answer : d"
Answer: d
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 450 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 678 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is b : 678 solution : total number of students studying both are 450 + 226 - 134 = 542 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 542 , so 100 % is approx . 678 ."
Answer: b
Problem: the volume of the sphere q is ( 37 / 64 ) % less than the volume of sphere p and the volume of sphere r is ( 19 / 27 ) % less than that of sphere q . by what is the surface area of sphere r less than the surface area of sphere p ?
Options: a ) 77.77 %
b ) 75 %
c ) 67.5 %
d ) 87.5 %
e ) none of these
Rationale: explanation : let the volume of sphere p be 64 parts . therefore volume of sphere q = > 64 − ( 37 / 64 ) % of 64 . = > 64 − 37 = 27 parts . the volume of r is : - = > 27 − ( 19 / 27 ) × 27 . = > 27 − 19 = 8 parts . volume ratio : = > p : q : r = 64 : 27 : 8 . radius ratio : = > p : q : r = 4 : 3 : 2 . the surface area will be 16 : 9 : 5 . surface area of r is less than the surface area of sphere p . = > 16 k − 4 k = 12 k . now , = > ( 12 k / 16 k ) × 100 . = > 75 % . hence , the surface area of sphere r is less than the surface area of sphere p by 75 % . answer : b
Answer: b
Problem: what is the radius of a circle that has a circumference of 3.14 meters ?
Options: a ) 2.5
b ) 2
c ) 1.5
d ) 1
e ) 0.5
Rationale: circumference of a circle = 2 π r . given , circumference = 3.14 meters . therefore , 2 π r = circumference of a circle or , 2 π r = 3.14 . or , 2 ? 3.14 r = 3.14 , [ putting the value of pi ( π ) = 3.14 ] . or , 6.28 r = 3.14 . or , r = 3.14 / 6.28 . or , r = 0.5 . answer : 0.5 meter . correct answer e
Answer: e
Problem: the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 8 , b ) 15 , c ) 14 , d ) 12 , e ) 10
Rationale: since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let the ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 * 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer a
Answer: a
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "first ratio = 3 / 20 = 15 % second ratio = ( 3 + 12 ) / ( 9 + 108 ) = 15 / 117 = 12,8 % decrease = 2,2 % 2,2 % / 15 % = 15 % approximately . answer : b"
Answer: b
Problem: the difference of two numbers is 11 and one fifth of their sum is 9 . the numbers are :
Options: a ) 31 , 20 , b ) 30 , 19 , c ) 29 , 18 , d ) 28 , 17 , e ) none
Rationale: "x − y = 11 , x + y = 5 × 9 x − y = 11 , x + y = 45 , y = 17 , x = 28 answer : d"
Answer: d
Problem: an internet recently hired 8 new network , in addvertisement 20 network already employed . all new network cam from university a . in addition 75 % of computer addvertisement came from same university a . what fraction of original 20 network addvertisement came from same univerity a ? pls help to solve
Options: a ) 13 / 20 , b ) 15 / 20 , c ) 14 / 20 , d ) 12 / 20 , e ) 11 / 20
Rationale: new networks = 8 already employed networks = 20 total networks = 28 computer advt . from uni . a = 28 * ( 75 / 100 ) = 21 out 28 networks 21 came from uni . a among these 21 we know 8 are newly hired so 21 - 8 = 13 networks among previously employed networks came from uni . a answer is : 13 / 20 answer : a
Answer: a
Problem: dividing by 3 ⁄ 9 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 5 / 2 , e ) 5 ⁄ 16
Rationale: "say x / 3 / 9 * 5 / 6 = x * 9 / 3 * 5 / 6 = x * 5 / 2 d"
Answer: d
Problem: if it takes a machine 1 ⁄ 3 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 80 , d ) 120 , e ) 360
Rationale: "1 item takes 1 / 3 min so it takes 120 min to produce x x / 3 = 120 the x = 360 answer : e"
Answer: e
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many s apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons s = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c