divelab/Sys2Bench huggingface dataset:
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 300 is required to paint the floor at the rate of Rs. 5 per sq m, then what would be the length of the floor?
Options:
A)65
B)13.42
C)18
D)16
E)14
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 300/5 = 60 sq m
l b = 60 i.e., l * l/3 = 60
l2 = 180 => l = 13.42
Answer: B
Answer: B
Question: A girl has nine jeans and 11 shirts. In how many different ways can she select a jeans and a shirts?
Options:
A)A)100
B)B)99
C)C)108
D)D)110
E)E)112
Rationale: The girl can select one jeans in nine ways.
The girl can select one shirt in 11 ways.
The number of ways in which he can select one jeans and one shirt is 9 * 11 = 99 ways.
B
Answer: B
Question: A Jar contains a mixture of AB in the ratio 3:2. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
Options:
A)18
B)15
C)16
D)20
E)25
Rationale: 10 litres of mixture that is replaced will contain 6 litres of A and 4 litres of B (as A:B = 3:2)
Let the initial volume of the mixture be 3K + 2K = 5K
So by condition ,
[ 3K-6 ]/ [ 2K-4+10 ] = 2/3 9k-18 =4k-8+20 5 k= 12+18 k = 6
Solve for K which is K = 6
So initial volume of liquid A = 3K = 18 litres
Answer : A
Answer: A
Question: A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (3D) at a speed of (2V), then a distance of (7D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?
Options:
A)3D/V
B)4D/V
C)5D/V
D)6D/V
E)7D/V
Rationale: The total time of the trip was:
3D/2V + 7D/3V + D/6V =
18D/12V + 28D/12V + 2D/12V =
48D/12V = 4D/V
The answer is B.
Answer: B
Question: The sum of two numbers is 110. Five times one number is equal to 6 times the other. The bigger of the two numbers is
Options:
A)10
B)12
C)14
D)15
E)60
Rationale: a:b 5:6
a+b=110
5x+6x=110
x=10
then two numbers are 50,60. The bigger number is 60
ANSWER:E
Answer: E
Question: If 15 oranges are bought for a rupee, how many must be sold for a rupee to gain 25%?
Options:
A)12
B)10
C)20
D)18
E)None of these
Rationale: C.P. for one orange = 1⁄15
Then S.P. = 100+25/100×1/15=125/100×15=1/12
Hence S.P. for one orange = 1⁄12
∴ 12 oranges must be sold for a rupee
Answer A
Answer: A
Question: If a*b denotes the greatest common divisor of a and b, then ((20*16)*(18*24)) = ?
Options:
A) 24
B) 12
C) 6
D) 4
E) 2
Rationale: The greatest common divisor of 20 and 16 is 4. Hence 20*16 = 4 (note that * here denotes the function not multiplication).
The greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.
Hence ((20*16)*(18*24)) = 4*6.
The greatest common divisor of 4 and 6 is 2.
Answer; E.
Answer: E
Question: A person travels equal distances with speeds of 5km/hr, 10km/hr, 15km/hr. and takes a total time of 11minutes. Find the total distance ?
Options:
A)1km
B)1500mts
C)1600mts
D)2km
E)1250mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/5)+(x/10)+(x/15) = 11/60
x=0.5
total distance = 3*0.5 = 1.5km = 1500meters
correct option is B
Answer: B
Question: If A(k)=(k+1)^2, and k=1, what is the value of A(A(A(A(k))))?
Options:
A)328359
B)557321
C)258327
D)458329
E)4422
Rationale: A(A(A(A(1))))=A(A(A(4)))=A(A(25))=A(676)= 677^2 = 458329
Thus, the answer is D.
Answer: D
Question: Revathi bought an electric cooker at 90% of the regular price. She paid $270 for the cooker. What was the regular price?
Options:
A)$300
B)$200
C)$360
D)$380
E)$400
Rationale: Regular price = 270/90*100 = 300
Answer : A
Answer: A
Question: Two trains, A and B, started simultaneously from opposite ends of a 120-mile route and traveled toward each other on parallel tracks. Train A, traveling at a constant rate, completed the 120-mile trip in 6 hours; Train B, traveling at a constant rate, completed the 120-mile trip in 4 hours. How many miles had train A traveled when it met train B?
Options:
A) 28
B) 36
C) 48
D) 50
E) 54
Rationale: As the ratio of the rates of A and B is 4 to 6 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 4/(4+6)=4/10 of 120 miles: 120*4/10=48 miles.
Answer: C.
Answer: C
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 1 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Options:
A)187 km
B)480 km
C)278 km
D)120 km
E)671 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 1
2x/15 - x/8 = 1 => x = 120 km.
Answer:D
Answer: D
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)8
B)4
C)5
D)9
E)1
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: B
Question: A man sold 18 toys for Rs. 16800, gaining thereby the cost price of 3 toy find the cost price of a toy
Options:
A)Rs. 600
B)Rs. 800
C)Rs.500
D)Rs.900
E)Rs.970
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 16800.
Gain = SP – CP
3X = 16800 – 18X
21X = 16800
X = Rs. 800.
answer : B
Answer: B
Question: The percentage profit earned by selling an article for Rs. 1320 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)3000
B)1230
C)2000
D)1625
E)3400
Rationale: C.P. be Rs. x.
Then, (1320 - x)/x * 100 = (x - 1280)/x * 100
1320 - x = x - 1280
2x = 2600 => x = 1300
Required S.P. = 125 % of Rs. 1300 = 125/100 * 1300 = Rs. 1625.
ANSER D
Answer: D
Question: A sum of Rs. 350 made up of 110 coins, which are of either Rs. 1 or Rs. 5 denomination. How many coins are of Rs. 5?
Options:
A)52
B)60
C)62
D)72
E)None
Rationale: Explanation:
Let, the number of Rs.1 coins are x and Rs.5 coins are y.
Then x + y = 110
x + 5y = 350
Solving above two equations, we get y = 60. So number of Rs.5 coins are 60.
Correct Option: B
Answer: B
Question: How many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph?
Options:
A)23 sec
B)65 sec
C)25 sec
D)45 sec
E)24 sec
Rationale: D = 100 + 130 = 230
S = 36 * 5/18 = 10 mps
T = 230/10 = 23 sec
Answer:A
Answer: A
Question: If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 14 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Options:
A)25 pounds
B)46 pounds
C)92 pounds
D)100 pounds
E)140 pounds
Rationale: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*14 --> x = 140.
Answer: E.
Answer: E
Question: Two trains of length 150 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. In how much time will the trains cross each other?
Options:
A)87/7 sec
B)80/7 sec
C)80/9 sec
D)80/5 sec
E)20 sec
Rationale: Relative speed = (54 + 36)* 5/18 = 5 * 5 = 25 mps.
The time required = d/s = (100 + 150 + 250)/25
= 500/25 = 20 sec.
Answer: E
Answer: E
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money R did Bob receive?
Options:
A)20
B)22
C)24
D)26
E)52
Rationale: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ R= 20
Answer:
B
Answer: B
Question: A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit?
Options:
A)61
B)62
C)63
D)64
E)66
Rationale: If no is xy , then
10x+y = 4*(10y+x)-3= 40y +4x-3
6x-39y +3 =0
2x-13y +1 =0
13 y =2x+1
when y=1, x=6
so number is 61.
ANSWER:A
Answer: A
Question: In how many years does a sum of Rs. 4000 yield a simple interest of Rs. 16500 at 15% p.a.?
Options:
A)27.5 years
B)26.5 years
C)25.5 years
D)28.5 years
E)29.5 years
Rationale: T = (100 * 16500)/(15 * 4000) = 27.5 years
ANSWER:A
Answer: A
Question: How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
Options:
A)8881
B)2777
C)2999
D)1200
E)2788
Rationale: 50/100 * x = 30 * 20 => x
= 1200
Answer: D
Answer: D
Question: Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip, at an average speed of 60 miles per hour for the next 30 miles and at a average speed of 90 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip, Myra’s average speed in miles/hr for the entire trip was closest to
Options:
A)The average speed is 35 miles per hour.
B)The average speed is 40 miles per hour.
C)The average speed is 45 miles per hour.
D)The average speed is 50 miles per hour.
E)The average speed is 55 miles per hour.
Rationale: Here, Myra traveled at three speeds for one-third distance each.
Average Speed = 3abc/(ab + bc + ca) = 3*30*60*90/(30*60 + 60*90 + 30*90)
Average Speed = 3*2*90/(2 + 6 + 3) = 540/11
Answer (D)
Answer: D
Question: The simple form of the ratio 5/3:2/5 is?
Options:
A)10:6
B)10:3
C)25:6
D)25:3
E)30:3
Rationale: 5/3 : 2/5 = 25:6
ANSWER:C
Answer: C
Question: How many numbers between 0 and 1770 have a prime tens digit and a prime units digit?
Options:
A)266
B)272
C)278
D)284
E)290
Rationale: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1700, there 16*17 = 272 such numbers.
From 1701 to 1770, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 272+12 = 284
The answer is D.
Answer: D
Question: If 4<(1-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
Options:
A)II only
B)III only
C)I and II only
D)II and III only
E)I, II and III
Rationale: 12<7-x
x<-5
x+5<0
1.5<x...not possible
2.True.....Check for values x=-6,-7,-8....... etc
3.True.. Since x+5<0 -(x+5) will always be positive
Hence, Ans is E..
Answer: E
Question: If two numbers are in the ratio 2:3. If 12 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)12
B)B)18
C)C)20
D)D)24
E)E)26
Rationale: 2:3
2x + 12 : 3x + 12 = 3 : 4
4[2x + 12] = 3[3x + 12]
8x + 48 = 9x + 36
9x - 8x = 48 - 36
x = 12
Then smallest number is = 2
2x = 24
Correct Option D
Answer: D
Question: A train covers a certain distance at a speed of 400kmph in 3 hours. To cover the same distance in 2 2/3 hours, it must travel at a speed of
Options:
A)480km/hr
B)450km/hr
C)550km/hr
D)750km/hr
E)650km/hr
Rationale: Explanation:
Distance = 400Ã—3 = 1200km
Required speed = (1200Ã— 3/8) = 450km/hr
Answer: Option B
Answer: B
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 5 out of 7 consecutive days in Rwanda?
Options:
A)4/7
B)3/7
C)21/128
D)4/28
E)28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
7C5 (1/2)^5 (1/2)^r
which is 21/128
Answer is C.
Answer: C
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)18 sec
B)16 sec
C)87 sec
D)17 sec
E)11 sec
Rationale: Speed = 63 * 5/18
= 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
Answer: B
Answer: B
Question: 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days
Answer is D.
Answer: D
Question: Sandy had $224 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?
Options:
A)$260
B)$290
C)$320
D)$350
E)$380
Rationale: Let the money Sandy took for shopping be x.
0.7x = 224
x = 320
The answer is C.
Answer: C
Question: Of the families in City X in 1992, 30 percent owned a personal computer. The number of families in City X owning a computer in 1999 was 50 percent greater than it was in 1992, and the total number of families in City X was 5 percent greater in 1999 than it was in 1994. what percent of the families in City X owned a personal computer in 1999?
Options:
A)43%
B)42.85%
C)45.25%
D)46.23%
E)41.66%
Rationale: Say a 100 families existed in 1992 then the number of families owning a computer in 1992 - 30
Number of families owning computer in 1999 = 30 * 150/100 = 45
Number of families in 1999 = 105
The percentage = 45/105 * 100 = 42.85%.
ANSWER:B
Answer: B
Question: How many positive integers will divide evenly into 320?
Options:
A)8
B)12
C)16
D)18
E)20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 8
Option A
Answer: A
Question: There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
Options:
A)520
B)720
C)425
D)625
E)420
Rationale: Let the original average expenditure be Rs. x. Then,
42(x-1)-35x=42
7x= 84
x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420.
Answer is E.
Answer: E
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Monday. They were very happy. What day of the week would come on 14 Feb. 2011?
Options:
A)monday
B)tuesday
C)sunday
D)wednesday
E)thursday
Rationale: feb 14 2005 - monday
feb 14 2006 - tuesday
feb 14 2007 - wednesday
feb 14 2008 - thursday
feb 14 2009 - saturday [since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - sunday
feb 14 2011 - monday
Feb 14 2012 - Tuesday
ANSWER:B
Answer: B
Question: A Fisher man can row 4 km against the stream in 30 minutes and returns in 20 minutes. What is the speed of the current?
Options:
A)1 km/hr
B)2 km/hr
C)3 km/hr
D)4 km/hr
E)5 km/hr
Rationale: Explanation:
Speed up stream = (4/30) × 60 = 8 km/hr
Speed down stream = (4/20) × 60 = 12 km/hr
Speed of current = 1/2 (12 - 8) = 4/2 = 2 km/hr
Answer: Option B
Answer: B
Question: An automobile financier claims to be lending money at simple interest, but he includesthe interest every six months for calculating the principal. If he is charging an interest of10%, the effective rate of interest becomes:
Options:
A)10%
B)10.25%
C)10.5%
D)none of these
E)Cannot be determined
Rationale: Explanation:
Let the sum be Rs. 100. Then,
S.I. for first 6 months = Rs.[ (100 x 10 x 1)/(100 x 2) ]= Rs.5
S.I. for last 6 months =Rs.[(102 x 10 x 1)/(100 x 2) ] = Rs.5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%
Answer: B
Answer: B
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
A)345
B)340
C)342
D)346
E)341
Rationale: 400*(90/100)*(95/100) = 342
Answer:C
Answer: C
Question: If 5 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Options:
A)280
B)63
C)120
D)160
E)1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 5c2
for vertical 8c2
total parallelogram is 5 c2*8c2=10*28
=280
ANSWER:A
Answer: A
Question: A man invests Rs. 5,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Options:
A)Rs. 1200
B)Rs. 1300
C)Rs. 2500
D)Rs. 2000
E)None of these
Rationale: Explanation :
Interest on Rs.5000 at 5% per annum = ( 5000 × 5 × 1) / 100 = Rs. 250
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (5000 + x) × 6 × 1/100.
=> 250 + 2x/25 = (5000 + x) × 6 × 1/100.
=> 25000 + 8x = (5000 + x) × 6.
=> 25000 + 8x = 30000 + 6x.
=> 2x=5000.
=> x=2500.
Answer : C
Answer: C
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options:
A)17/28
B)17/25
C)17/17
D)17/19
E)17/12
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50
= 17/25.
Answer:B
Answer: B
Question: A train is 360 meter long is running at a speed of 47 km/hour. In what time will it pass a bridge of 140
meter length.
Options:
A)28.3 seconds
B)38.3 seconds
C)48.3 seconds
D)58.3 seconds
E)None of these
Rationale: Explanation:
Speed = 47 Km/hr = 47*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500/ 13 = 38.3 seconds
Answer: B
Answer: B
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 100 metres?
Options:
A)18
B)17
C)22
D)20
E)13
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 100 m = 100/5 = 20 seconds.
Answer: D
Answer: D
Question: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders W will be:[/b]
Options:
A)3, 3, 2
B)3, 4, 2
C)5, 4, 3
D)W=5, 5, 2
E)W=6, 4, 3
Rationale: Let the original number be X. Then by the successive dividing we have followings :
X=5A+2
A=7B+3
B=8C+4.
So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.
Now by dividing X by 8, 7, 5 successively we have followings :
X=8*(5*7C+19)+5
5*7C+19=7*(5C+2) + 5
5C+2=5C+2.
The remainders are, therefore, 5, 5, 2.
The answer is (D).
Answer: D
Question: One boss decided to increase the salary of an employee by 5%. How much will he get if his salary was Rs.2000?
Options:
A)2200
B)2000
C)2100
D)2300
E)None
Rationale: Solution:
Actual salary is 2000 Rupees
5 % of 2000 = 2000 *5/100 = 100
So 100 Rupees increased
=2000+100 =2100
He will get salary of 2100
Answer C
Answer: C
Question: Sonika bought a V.C.R. at the list price of 18,800. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
Options:
A)20,304
B)19,780
C)19,680
D)19,380
E)None of these
Rationale: Sol. List price of V.C.R. =18,800
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,800
= 8⁄100 × 18800 = 1504
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,800 + 1504
= 20,304. Answer A
Answer: A
Question: If (1+m)n=n, which of the following must be true?
Options:
A)m=-1 or n=0
B)m=0 or n=0
C)m=1 or n=1
D)m=-1 or n=-1
E)m=0 or n=1
Rationale: By only having mn=0, we cannot say answer is B as A and E options also satisfy the condition mn=0. ans B
Answer: B
Question: A certain quantity of 50% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)3/5
Rationale: Let's say that the total original mixture A is 100 ml
The original mixture A thus has 50 ml of alcohol out of 100 ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 25%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 15%. Therefore, 15 out of 25 is 3/5 and E is the answer.
Answer: E
Question: The average age of a committee of 8 members is 52 years. A member aged 65 years retired and his place was taken by another member aged 42 years . The average age of
present committee is;
Options:
A)39 years
B)38 years
C)36 years
D)35 years
E)49.1 years
Rationale: Total age of the committee = 52*8 = 416,
Total age when a member is retired
and a new one was joined = 416-65 +42, =393
Average age of present committee = 393/8 = 49.1.
ANSWER:E
Answer: E
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)87 m
B)17 m
C)26 m
D)28 m
E)78 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: B
Question: There are 25 balls which are red, blue or green. If 8 balls are blue and the sum of green balls and blue balls is less than 17, at most how many green balls are there?
Options:
A)8
B)5
C)6
D)7
E)10
Rationale: r+g+b=25
b=8
b + g < 17
=> 8 + g < 17
=> g < 9
=> at most 8 green balls
ANSWER:A
Answer: A
Question: An outlet pipe can empty 2/3 of a cistern in 20 minutes. In 8 minutes, what part of the cistern will be emptied?
Options:
A)1/2
B)1/3
C)2/9
D)4/15
E)9/20
Rationale: 8/20 * 2/3 = 4/15
The answer is D.
Answer: D
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 45 times, A has killed:
Options:
A)50 birds
B)72 birds
C)30 birds
D)80 birds
E)20 birds
Rationale: Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of	(5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x	=(3/16)x
3x/16= 45 or x =(45 x 16)/3= 240.
Birds killed by A =(5x/24)	=(5/24*240)= 50.
Answer is A
Answer: A
Question: Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, thirty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 40 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?
Options:
A)20%
B)40%
C)50%
D)60%
E)80%
Rationale: Let I be the number of incandescent bulbs.
Let F be the number of fluorescent bulbs.
0.3I + 0.8F = 0.4(I+F)
0.4F = 0.1I
F = 0.25I
This means that for every 4 incandescent bulbs, there is 1 fluorescent bulb.
The percent of bulbs that are switched on which are incandescent is:
0.3I / (0.3I + 0.8F) = 0.3I / (0.3I + 0.8*0.25I) = 0.3I / 0.5I = 3/5 = 60%.
The answer is D.
Answer: D
Question: Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes?
Options:
A)60.3
B)70.3
C)81.3
D)85.3
E)94.3
Rationale: X = 83
Y =76
Z =85
so to find the average of x,y,z
(x+y+z)/3=244/3
ans is 81.33
ANSWRE:C
Answer: C