RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 12 family members in a row for the picture?
A.13!
B.11×10!
C.10×11!
D.12!/2!
Answer: C.10×11!
Explanation: The number of ways to arrange 12 people is 12!
We need to subtract the arrangement when these two people are together.
Let's think of these two people as a single unit so there are 11 units.
The number of ways to arrange 11 units is 11!
We need to multiply this by 2 since these two people could switch places.
The total number of valid arrangements is 12! - 2*11! = 11!*(12-2) = 10x11!
The answer is C.
Question: Pipes A and B can fill a tank in 4 and 2 hours. Pipe C can empty it in 8 hours. If all pipes are opened together, then the tank will be filled in?
A.3/2hr
B.1/2hr
C.8/5hr
D.9/7hr
Answer: C.8/5hr
Explanation: Net part filled in 1 hour = 1/4 + 1/2 - 1/8 = 5/8
The tank will be full in 8/5 hr
Answer is C
Question: A and B enter into partnership with capitals in the ratio 3 : 2. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 1 : 3. Find how long B remained in the business?
A.45 months
B.8 months
C.6 months
D.7 months
Answer: A.45 months
Explanation: Initially A’s investment = 3x and B’s investment = 2x
Let B remain in the business for ‘n’ months.
⇒ 3x × 10 : 2x × n = 1 : 3
∴ 3x × 10 × 3 = 2x × n × 1
⇒ n = 45
Answer A
Question: We invested a total of $1,000. We invested one part of the money at 3% and the rest of the money at 6%. The total investment with interest at the end of the year was $1,052.50. How much money did we invest at 3%?
A.$160
B.$190
C.$220
D.$250
Answer: D.$250
Explanation: Let x be the money invested at 3%.
1.03x+1.06(1000-x)=1052.50.
0.03x=1060-1052.50.
0.03x=7.50.
3x=750.
x=250.
The answer is D.
Question: If n is an integer greater than 7, which of the following must be divisible by 3?
A.n(n-5)(n-2)
B.n(n+5)(n+3)
C.n(n+2)(n-1)
D.n(n-4)(n-2)
Answer: D.n(n-4)(n-2)
Explanation: Let us start with C -> n(n+2)(n-1) = n(n+2)(n-3+2). Thus we can see that n+2 and (n-3+2) will leave the same remainder. But we need 3 terms with 3 different remainders.
Now let's look at D -> n(n-4)(n-2) = n(n-3 -1)(n-2). This represents 3 terms with 3 different remainders, and one of them will be divisible by 3.
ANSWER:D
Question: A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent .
A.10%
B.20%
C.30%
D.40%
Answer: A.10%
Explanation: Suppose , number of bananas bought = LCM of 6 and 4=12
CP=Rs.[(10/6)*12]=Rs.20 ; SP= Rs[(6/4)*12]=Rs.18
Loss%=[(2/20)*100]%=10%
ANSWER A
Question: Amar, Bhavan and Chetan divide an amount of Rs. 5600 among themselves in the ratio 3 : 6 : 5. If an amount of Rs. 400 is deducted from each of their shares, what will be the new ratio of their shares of the amount?
A.2 : 5 : 8
B.2 : 9 : 4
C.2 : 5 : 4
D.2 : 5 : 3
Answer: C.2 : 5 : 4
Explanation: Let the shares of Amar, Bhavan and Chetan be Rs. 3x, Rs. 6x and Rs. 5x respectively.
3x + 6x + 5x = 5600 => 14x = 5600 => x = 400.
Required ratio = 3x - 400 : 6x - 400 : 5x - 400
= 3x - x : 6x - x : 5x - x
= 2x : 5x : 4x => 2 : 5 : 4
Answer:C
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.3
B.7.5
C.2.25
D.1.5
Answer: D.1.5
Explanation: Explanation:
M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: Option D
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?
A.1/10
B.1/5
C.2/5
D.3/5
Answer: C.2/5
Explanation: In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability = 1- 3/5 = 2/5. Thus C is the correct answer
Question: Jane makes toy bears. When she works with an assistant, she makes 62 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
A.20%
B.80%
C.100%
D.180%
Answer: B.80%
Explanation: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 64.8 bears per 36 hours a week or 1.8 bears/hr ([40 bears * 1.62] / [40 hrs * .90]).
[(1.8 - 1)/1] * 100% = 80%
ANSWER:B
Question: A hall 36m long and 15m broad is to be paved with stones, each measuring 6dm by 5 dm. The number of stones required is:
A.180
B.1800
C.18
D.18000
Answer: B.1800
Explanation: Area of the hall= 3600*1500
Area of each stone= (60*50)
Therefore, number of stones= (3600*1500/ 60*50)= 1800
ANSWER:B
Question: What is the average of first 21 multiples of 7 ?
A.22
B.77
C.88
D.21
Answer: B.77
Explanation: Required average = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 77
Answer:B
Question: A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his
average after 17th match
A.36
B.37
C.38
D.39
Answer: D.39
Explanation: Explanation:
Let the average after 17th match is x
then the average before 17th match is x-3
so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39
Answer: Option D
Question: If X can run 48m and Y 42m, then in a race of 1km, X beats Y by:
A.140m
B.125m
C.100m
D.110m
Answer: B.125m
Explanation: Explanation:
When X runs 48m, Y runs 42m.
Hence, when X runs 1000m, Y runs (1000 * 42) / 48 = 875m
X beats Y by 125m.
ANSWER:B
Question: A 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A.230m
B.240m
C.250m
D.260m
Answer: D.260m
Explanation: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 240 + x
therefore, D= speed*time
thus 240 + x = 500/9 * 9
x= 500-240=260 m
ANSWER:D
Question: In a store, the total price for 25 shirts is $400 and the total price for 75 sweaters is $1500. By how much does the average (arithmetic mean) price of a sweater exceed that of a shirt in this store?
A.$1
B.$2
C.$3
D.$4
Answer: D.$4
Explanation: The average price of a shirt is: $400 / 25 = $16.
The average price of a sweater is: $1500 / 75 = $20.
The difference in price is: $20 - $16 = $4.
The answer is D.
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?
A.98
B.40
C.28
D.27
Answer: B.40
Explanation: 760 ---- 22
760 ---- 20
x ----- 19
x*19 = 760*20
x = 800
760
-------
40
Answer: B
Question: The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 2 seconds?
A.4
B.55
C.15
D.48
Answer: B.55
Explanation: Given: z=s^2+2s for 0≤s≤7
z(2) = 2^2 + 2*2 = 8
z(7) = 7^2 + 2*7 = 63
Therefore z(7) - z(3) = 63 - 8 = 55 km/hr
Option B
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 9 minutes less than they can row it in still water. How long would they take to row down with the stream
A.45 or 23 minutes
B.63 or 12 minutes
C.60 minutes
D.19 minutes
Answer: B.63 or 12 minutes
Explanation: speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-9))
giving t = 66 close to B
ANSWER:B
Question: A reduction of 10% in the price of salt enables a lady to obtain 20kgs more for Rs.400, find the original price per kg?
A.2.0
B.2.8
C.2.2
D.2.5
Answer: C.2.2
Explanation: Answer:	400*(10/100) = 40 --- 20
? --- 1 => Rs.2
400 --- 360
? --- 2 => Rs.2.22.Answer: C
Question: In how many different ways can 4 boys and 2 girls sit on a bench such that the girls always sit together?
A.240
B.280
C.320
D.360
Answer: A.240
Explanation: We can think of the girls as one unit.
The number of ways to arrange 5 units in order is 5!
The girls can have different arrangements, so we multiply this by 2!
The number of ways to sit is 5!*2!=240
The answer is A.
Question: A and B walk around a circular track. They start at 1 p.m from the same point in the opposite directions. A and B walk at a speed of 4 rounds per hour and 6 rounds per hour respectively. How many times shall they cross each other before 4 p.m
A.15
B.20
C.25
D.30
Answer: D.30
Explanation: Explanation:
Relative speed = (4+6) =10 rounds per hour
So, they cross each other 30 times in three hours hence, they cross 30 times before 4 p.m
Answer: Option D
Question: Between 1800 and 1850 a population of a country increased from 12 million to 15 million. Between 1850 and 1900 its population increased from 15 million to 22 million. By what percent did the rate of population growth increase from the period 1800-1850 to the period 1850-1900?
A.75%-100%
B.101%-125%
C.126%-150%
D.151%-175%
Answer: A.75%-100%
Explanation: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of population growth to initial population for the two periods. The first ratio will be for the period 1800-1850, and the second ratio will be for the period 1850-1900. Because the populations are in millions, we do not have to express all the trailing zeros in our ratios.
1800-1850
growth/initial population = 3/12 = 1/4
1850-1900
growth/initial population = 7/15
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
1800-1850
growth/initial population = (1/4) x 60 = 15
1850-1900
growth/initial population = (7/15) x 60 = 28
We can plug 15 and 28 into our percent change formula:
(new – old)/old x 100
[(28 – 15)/15] x 100
13/15 x 100
At this point we can stop and consider the answer choices. 13/15 x 100 is greater than 75% but less than 100%.
Answer A.
Question: Sam invested Rs. 8000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
A.3200.0
B.11520.0
C.8820.0
D.7354.0
Answer: C.8820.0
Explanation: P = Rs. 8000 ; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [8000 * (1 + 5/100)2]
= (8000 * 21/20 * 21/20)
= Rs.8820.00
Answer:C
Question: The value of x is to be randomly selected from the integers from 1 to 7, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
A.1/5
B.2/7
C.1/7
D.3/7
Answer: C.1/7
Explanation: y will only be negative for x=2.
(We can check the values from 1 to 7 to be certain.)
P(y is negative) = 1/7
The answer is C.
Question: Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
A.333
B.383
C.402
D.433
Answer: C.402
Explanation: Let say she pays $X per month.
interest for month 1 = 1000*10/100
= 100
interest for month 2 = (1000+100 -X)*10/100
= (1100 - X)*10/100
= 110 - X/10
interest for month 3 = (1100 -X + 110 - X/10 - X)*10/100
= 121 - 21/100 X
Total interest = 3X-1000
So 3X-1000 = 100 + 110 - X/10 + 121 - 21/100 X
=>331X = 133100
=>X = 402.11
ANSWER:C
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (2, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
A. 1/2
B. 1
C. 3/2
D. 2
Answer: B. 1
Explanation: b=2k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=2k+1
k=1
Answer : B
Question: A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
A.16 km
B.87 km
C.89 km
D.67 km
Answer: A.16 km
Explanation: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 3.5
=> x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x
= 16 km.
Answer:A
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
A.45
B.49
C.20
D.82
Answer: C.20
Explanation: M = 15
S = 5
DS = 15 + 5 = 20
Answer:C
Question: In a shop X number of kinds of fruits are there and 40 number of kinds of vegetables are there, then 1% of vegetable is equal to 20% of fruits then how many kinds of fruits are there
A.20
B.35
C.70
D.90
Answer: A.20
Explanation: 1/100(400) = 2/10(x)
X = 20..
Option A.
Question: The width of a rectangular hall is ½ of its length. If the area of the hall is 200 sq.m, what is the difference between its length and breadth?
A.8m
B.10m
C.12m
D.15m
Answer: B.10m
Explanation: Let the length of the hall be x m
Breadth of the hall = 1x/2 m
Area of the hall = Length * Breadth
200 = x * 1x/2
x² = 400
x =20
Difference between the length and breadth of the hall = x - 1x/2 = x/2
=20/2 = 10m
ANSWER:B
Question: A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 1.5 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
A.2/7
B.3/10
C.5/11
D.6/13
Answer: D.6/13
Explanation: The rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour
The rate of the advanced system is 1/1.5 = 2/3 of a room per hour
The combined rate is 13/6 rooms per hour.
The time to ventilate one room is 6/13 of an hour.
The answer is D.
Question: If n is an integer and 102n^2 is less than or equal to 8100, what is the greatest possible value of n?
A.7
B.8
C.9
D.10
Answer: B.8
Explanation: 102 * n^2 <=8100
n^2 <=8100/102 which will be less than 81 since 8100/100 = 81 which is the square of 9
Next closest value of n where n^2<=81 is 8
Ans B
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 23 gallons of gasoline?
A.190
B.284.6
C.300
D.280
Answer: D.280
Explanation: so 12.2 * 23 = 280..
IMO option D is correct answer..
Question: Vasya wrote down several consecutive integers. Which of the following could not be the percentage of even numbers among them?
A. 40
B. 45
C. 48
D. 50
Answer: A. 40
Explanation: what you have to check is if the (answer given: 100-answer given) is either equal or two consecutive values..
reason for this is that there are only three possiblities of numbers of odd numbers in consecutive integers
1) equal to number of even numbers
2)one more than number of even numbers
3)one more than number of even numbers
(A) 40:60=2:3possible
(B) 45:55=9:11not possible
(C) 48:52=12:13possible
(D) 50:50=1:1possible
(E) 60:40=3:2possible
ans A
Question: Jar X is 1/4 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?
A.2/5
B.1/4
C.1/3
D.1/2
Answer: D.1/2
Explanation: Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/2*P/2=P/4
Then the total amount in Jar X is P/4+P/4=P/2
The answer is D.
Question: Two goods trains each 2000 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.228
B.278
C.192
D.27
Answer: C.192
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 2000 + 2000 = 4000 m.
Required time = 4000 * 6/125 = 192 sec.
Answer:C
Question: If r and t are positive integers, rt + r + t cannot be
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Let rt + t + r = x
Add 1 on both sides:
rt + t + r + 1 = x + 1
t(r + 1) + r + 1 = x + 1
(r + 1)(t + 1) = x + 1
Minimum value of (r + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> rt + t + r cannot be 6
Answer: B
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
A.5760 lr
B.6000 lr
C.6500 lr
D.4000 lr
Answer: A.5760 lr
Explanation: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
ANSWER A
Question: A person walking at a constant rate of 6 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour. the cyclist stops to wait for the person 10 minutes after passing her, while the person continues to walk at her constant rate, how many minutes must the cyclist wait until the person catches up?
A.15min
B.11min
C.20min
D.40min
Answer: B.11min
Explanation: After passing the person the cyclist travels for 10 minutes at a rate of 10 miles/hour.
In those 10 mins the cyclist travels a distance of 5/3 miles.
In those 10 mins the person travels a distance of 1 miles.
So the person still has to cover 2/3 miles to meet the waiting cyclist.
The person will need 1/9 hours or 11 mins to cover the remaining 2/3 miles.
The answer is B
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A.80%
B.70%
C.60%
D.50%
Answer: B.70%
Explanation: Explanation:
Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: B
Question: Look at this series: 28, 25, 30, 27, 32, 29, ... What number should come next?
A.32
B.34
C.30
D.31
Answer: B.34
Explanation: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option B
Question: 0.35 represents what percent of 7?
A.0.05%
B.0.5%
C.5%
D.500%
Answer: C.5%
Explanation: One more method
0.35 represents what percent of 7?
Divide by 7
0.05 represents what percent of 1?
Answer = 0.05*100 = 5% = C
Question: How many integers between 5000 and 6000 that have distinct digits and increase from left to right ?
A.10
B.48
C.60
D.20
Answer: D.20
Explanation: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
545_ --> 4
546_ --> 3
547_ --> 2
548_ --> 1
556_ --> 3
557_ --> 2
558_ --> 1
567_ --> 2
568_ --> 1
578_ --> 1
Number of integers =20
D
Question: 3 and 9 are the first two terms in a geometric sequence. What is the arithmetic difference between the 7th term and the 5th term?
A.3*3^2
B.3* 3^13 - 5 * 3^11
C.3^13
D.8 * 3^6
Answer: D.8 * 3^6
Explanation: Common ratio = 9/3 =3
7th term = 3*3^7
5th term = 3*3^5
Difference = 3 * (3^7 - 3^5) = 3 * 3^5 *(3^2 - 1)
= 3 * 3^5 * 8
= 8 * 3^6....
D
Question: How many positive integers t less than 30 have no common prime factor with 30?
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: t=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
A.4 : 3
B.8 : 7
C.4 : 1
D.6 : 5
Answer: B.8 : 7
Explanation: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
ANSWER:B
Question: There were totally 100 men.83 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
A.11
B.12
C.13
D.14
Answer: C.13
Explanation: 100-(100-83)-(100-75)-(100-85)-(100-70)
= 100-17-25-15-30=100-87=13
ANSWER:C
Question: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
A.1/3
B.7/22
C.1/9
D.7/66
Answer: D.7/66
Explanation: Total No of Rocks = 45
Probability of choosing 1st Slate Rock = 15/45
Probability of choosing 2nd Slate Rock = 14/44 (Without replacement)
So combined probability = 15/45*14/44 = 7/66
So, ANSWER D.
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
A.350
B.288
C.277
D.2912
Answer: B.288
Explanation: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.Answer: B
Question: A boy has six trousers and 9 shirts. In how many different ways can he select a trouser and a shirt?
A.186 ways
B.78 ways
C.56 ways
D.54 ways
Answer: D.54 ways
Explanation: The boy can select one trouser in six ways.
The boy can select one shirt in 9 ways.
The number of ways in which he can select one trouser and one shirt is 6 * 9 = 54 ways.
Answer:D
Question: A baseball player hit the following number of home runs in consecutive years: 35, 38, 39, 43, and 44. If the player had hit 3 additional home runs in the last year, which of the following statements best describes the change in the mean and the median of the home runs?
A. The mean and the median will remain unchanged.
B. The mean will remain unchanged but the median will increase.
C. The mean will increase but the median will remain unchanged.
D. The mean and the median will increase by the same amount.
Answer: C. The mean will increase but the median will remain unchanged.
Explanation: Old set = {35, 38, 39, 43, 44}.
New set = {35, 38, 39, 43, 47} --> the median (middle term) will remain the same and the mean will increase.
Answer: C.
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages.
A.20,35,45
B.8,20,28
C.16,28,36
D.16,28,46
Answer: A.20,35,45
Explanation: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 76
20K = 100
K = 5
Therefore, then present ages are 20,35,45.
ANSWER:A
Question: Bipin is 6 times old as Alok. Bipin's age will be twice of Chandan's age after 10 years. If Chandan's 7th birthday was celebrated 3 years ago, what is Alok's present age ?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: let the present ages of bipin, alok, chandan are b,a,c respectively
given conditions are
1)b=6a
2)(b+10)=2*(c+10)
3)chandans present age=c=10 years
therefore b=30
so a=5
ANSWER:D
Question: At a school, three-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is two-thirds the number of females, what fraction of the students speak a foreign language?
A.11/25
B.14/25
C.16/25
D.18/25
Answer: C.16/25
Explanation: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(2/5)x = (6/25)x
The number of females who speak a foreign language is (2/3)(3/5)x = (2/5)x
The total number of students who speak a foreign language is (6/25)x + (2/5)x = (16/25)x
The answer is C.