RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The “a-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
A. 3/8
B. 13/36
C. 17/36
D. 19/36
Answer: B. 13/36
Explanation: If you calculate 3^a for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Question: If p and r are integers, and p^2 = 24r, then r must be divisible by which of the following?
A.2
B.3
C.5
D.7
Answer: B.3
Explanation: Ans: D
Solution: for p to be an int 24 r must be whole square of a number.
28r= 3*2*2*2*r
to make it whole square we need 3
so r can must be divisible by 3y where y is itself a whole square.
so B is the ans
Question: A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 76 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?
A.2
B.1
C.4
D.6
Answer: B.1
Explanation: We have to work with multiples of 20 and 25.
First, we must know the limits of this multiples, so:
76/25= 3....so the max is 3
76/20=3...so the max is 3
76-75 =1
Answer : B
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 15 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
A.40
B.48
C.43
D.45
Answer: D.45
Explanation: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 45 (the only option that is a multiple of 3).
Then age of Lyn would be 15. In 15 yrs, Ele would be 60 and Lyn would be 30 - so Lyn would be half as old as Ele.
Answer (D)
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 24cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
A.1280π
B.75r
C.100r
D.24r
Answer: C.100r
Explanation: Interesting to note that the larger wheel has a diameter of 40 (8*5) while the smaller one has a diameter of 24 (8*3)...
If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 40pi and 28pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.66 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.66 = 16.6 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.66 = 1000 revolutions per hour.
If r = 10, then the answer choice must be b.
C. 100r
Question: If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.150 then sum is
A.s.15000
B.s.15100
C.s.15800
D.s.16000
Answer: A.s.15000
Explanation: p(r/100)^2=C.I-S.I
P(10/100)^2=150
15000
ANSWER:A
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.88
B.20
C.99
D.18
Answer: B.20
Explanation: Explanation:
C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer:B
Question: Three people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
A.1/2
B.2/7
C.3/2
D.4/7
Answer: A.1/2
Explanation: Original share of 1 person = 1/3
New share of 1 person = 1/2
Increase = (1/2 - 1/3	= 1/6)
Therefore, Required fraction = (1/6)/(1/3)	= (1/6)x (3/1)	= 1/2
Answer is A.
Question: If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca
A.50
B.30
C.20
D.94
Answer: A.50
Explanation: (a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER A 50
Question: The letters E,A,W,D,S and R are rearranged to form the word 'Rewads'. Find its probability.
A.1/120
B.1/720
C.1/680
D.1/760
Answer: B.1/720
Explanation: Explanation :
There are total 6 letters. The probability that E gets the first position is 1/6.
The probability that A is in the second position is 1/5.
Likewise, probability for W,D,R and S are 1/4, 1/3,1/2 and 1/1.
Hence, the required probability is:-
=> (1/6) x (1/5) x (1/4) x (1/3) x (1/2) x 1.
=> 1/720.
Answer : B
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 11 books, how many shelves does the bookcase have?
A.8
B.6
C.4
D.3
Answer: A.8
Explanation: Let x be the number of shelves.
No of books in the beginning =11*x
After taking out 21 books No of remaining books = 11x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+11
11x-21=8(x-1)+11
3x=24
x=8. Answer A
Question: A square carpet with an area 169 m2 must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room?
A.180 m2
B.164 m2
C.152 m2
D.143 m2
Answer: D.143 m2
Explanation: Side of square carpet = √Area=√169=13m
After cutting of one side,
Measure of one side = 13 – 2 = 11 m
and other side = 13 m (remain same)
∴ Area of rectangular room = 13 × 11 = 143 m2
Answer D
Question: One-third less than 20% of 180 is equal to:
A.24
B.30
C.35
D.40
Answer: A.24
Explanation: Lots of ways to tackle this.
20% of 180 =36
1/3 of 36= 12
So, 1/3,less than 36 is equal to 36- 12 = 24
Answer: A
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on $4000 for 2 years at 10% per annum. The sum placed on simple interest is:
A.$1750
B.$2250
C.$1250
D.$1500
Answer: A.$1750
Explanation: Compound Interest = (4000 x (1 + 10/100)^2 - 4000)
= 4000 x 11/10 x 11/10 - 4000 = 840
Therefore the sum is 420 x 100/(3 x 8) = 1750.
Answer A) $1750
Question: Average monthly income of a family of 4 earning members was Rs. 782. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
A.Rs. 1178
B.Rs. 820
C.Rs. 990
D.Rs. 1385
Answer: A.Rs. 1178
Explanation: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 782 x 4 - 650 x 3 Rs.
= 1178 Rs.
Correct Option: A
Question: At the start of the fall shopping season, a pair of boots cost $700. By the end of the season, the price was reduced to $420. If you waited to purchase the boots at the lower price, what percentage of the original price will you have paid?
A. 25%
B. 33%
C. 50%
D. 60%
Answer: D. 60%
Explanation: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Here, we're told that the original price of the boots is $700 but that the purchase price is $420. We're asked what PERCENTAGE OF the original price is the purchase price.
Original Price = $700
Purchase Price = $420
The percentage of the original price of the boots:
$420/$700 = 3/5 = 60%
D
Question: Factor: 5x2 – 15x – 20.
A.5(x-4)(x+1)
B.-2(x-4)(x+5)
C.-5(x+4)(x-1)
D.5(x+4)(x+1)
Answer: A.5(x-4)(x+1)
Explanation: Solution:
5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
Answer: (A).
Question: with the digits 1,2,3,4,5,6 make all 6 digit nos which r not divisible by 5. The no of such 6 digit no's is ?
A.37,880
B.38,880
C.39,880
D.38,890
Answer: B.38,880
Explanation: 6c1*6c1*6c1*6c1*6c1*5c1 = 6*6*6*6*6*5
= 38,880
ANSWER:B
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all
A.15.5
B.15
C.16
D.17
Answer: D.17
Explanation: Explanation:
As number of girls and boys is not given so result cant be computed
Option D
Question: In case R is the only individual sewing on committee B, which among the following shouldserve on committee A?
A.V and U
B.V and T
C.U and S
D.T and S
Answer: D.T and S
Explanation: T and S should serve on A
ANSWER:D
Question: An unbiased die is tossed. Find the probability of getting a multiple of 6
A.A)1/6
B.B)2/5
C.C)1/4
D.D)2/3
Answer: A.A)1/6
Explanation: Here S = {1,2,3,4,5,6}
E = event of getting a multiple of 3
E = {6}
P(E) = 1/6
Answer is A
Question: Ravish has to secure 40% marks to clear his board exam of class 10th.
He got 40 marks and failed by 40 marks.
What is the maximum marks ?
A.150
B.135
C.160
D.200
Answer: D.200
Explanation: D
200
To pass the exam ravish needs 40 + 40 = 80 marks.
=> (80/40) *100 = 200
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/7 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
A.7/10
B.2/5
C.3/5
D.4/5
Answer: A.7/10
Explanation: Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 3/4 * 4/7 X = 3/7 X
% loaded by day crew = X/(X + 3/7X) = 7/10
Answer A
Question: In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase?
A.16.66%
B.17%
C.15.8%
D.12%
Answer: A.16.66%
Explanation: Explanation :
Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66%
Answer : A
Question: 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?
A. 3.40%
B. 4.40%
C. 5.40%
D. 6.40%
Answer: D. 6.40%
Explanation: 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.
Question: A and B start a business with Rs.3000 and Rs.9000 respectively. Hoe should they share their profits at the end of one year?
A.3:5
B.1:5
C.1:3
D.3:1
Answer: C.1:3
Explanation: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
3000 : 9000 => 1:3,Answer: C
Question: What is the ratio between perimeters of two squares one having 7 times the diagonal then the other?
A.3: 8
B.3: 6
C.3: 7
D.7: 1
Answer: D.7: 1
Explanation: d = 7d d = d
a√2 = 7d a√2 = d
a = 7d/√2 a = d/√2 => 7: 1
Answer:D
Question: Its a very poor village so sahara group organized a beneficiary cricket match for these people.
The event raised Rs300000.
Tickets were priced as follows:
Rs 748 for males
Rs 712 for ladies
Rs 45 for kids
How many males,ladies and kids were there ?
A.100 males , 209 ladies & 52 kids
B.120 males , 359 ladies & 72 kids
C.149 males , 259 ladies & 92 kids
D.150 males , 256 ladies & 92 kids
Answer: C.149 males , 259 ladies & 92 kids
Explanation: C
149 males , 259 ladies & 92 kids
Question: At what rate percent on simple interest will Rs.750 amount to Rs.1200 in 5 years?
A.12
B.3
C.14
D.5
Answer: A.12
Explanation: 450 = (750*5*R)/100
R = 12%.Answer: A
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
A.38
B.39
C.40
D.41
Answer: C.40
Explanation: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
To illustrate consider adding:
*7
*7
...
77
77
----
=350
So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
Answer: C.
Question: Best friends Sprite and Icey have are playing a game of marbles. They invite 4 of their friends to play with them. There are 36 marbles in the bag. If all 6 people are playing, how many marbles does each person get?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: Answer= D
36 / 6 = 6
Answer= D
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.12
B.13
C.11
D.10
Answer: D.10
Explanation: Explanation:
Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
ANSWER IS D
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:
A.57.5 km/hr.
B.77.5 km/hr.
C.87.5 km/hr.
D.97.5 km/hr.
Answer: C.87.5 km/hr.
Explanation: C
87.5 km/hr.
Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
Let the speed of two trains be 7x and 8x km/hr.
--> x = 100/8 = 12.5
--> Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Question: (1^2+2^2+3^2+.....+9^2)=?
A.330
B.285
C.365
D.385
Answer: B.285
Explanation: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=9
=(1/6x9x10x19)
=285
Answer is B.
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 24km/hr, then find the area of square field.
A.125
B.225
C.256
D.425
Answer: C.256
Explanation: Explanation :
D = 24*3/2 = 36 km. So side of square is 16km, so area – 256km^2
Answer – C
Question: Jill has 7 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
A.3
B.6
C.9
D.12
Answer: D.12
Explanation: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 7 1 3/4w = 7w=4The total number of jars = 3w =12Answer: D
Question: When a certain number X is divided by 95, the remainder is 31. What is the remainder when X is divided by 19?
A.10
B.11
C.12
D.15
Answer: C.12
Explanation: Let possible value of x is 126
least possible value of x/19 is 126/19 =>6 quotient with remainder 12
Thus answer is (C) 12
Question: The lowest number which should be added to 5915 so that the sum is exactly divisible by 3, 5, 8 and 7 is:
A.705
B.825
C.805
D.905
Answer: C.805
Explanation: L.C.M. of 3, 5, 8 and 7= 840.
On dividing 5915 by 840, the remainder is 35.
Number to be added = (840 - 35) = 805. Answer: Option 'C'
Question: Ajay spends 20 per cent of his salary on house rent, 5 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajayâ€™s income?
A.Rs.60000
B.Rs.80500
C.Rs.54000
D.Rs.70500
Answer: C.Rs.54000
Explanation: Explanation:
Savings = Income â€“ expenditure
100 â€“ (20+5+15+10) = 50%
50% of income = Rs.27000
:. Income = 27000 x 100/50 = Rs. 54000.
Answer: Option C
Question: Of the 350 people attending a conference, 150 have signed up for the Marketing workshop and 320 have signed up for the Accounting workshop. If 60 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
A.180
B.220
C.245
D.260
Answer: A.180
Explanation: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:
Total = Gp.1 + Gp.2 - Both + Neither
350 = 150 + 320 - Both + 60
350 = 530 - Both
Both = 180
Final Answer:
A
Question: Average of 10 matches is 34, How many runs one should should score to increase his average by 4 runs.
A.A)70
B.B)76
C.C)78
D.D)80
Answer: C.C)78
Explanation: Explanation:
Average after 11 innings should be 38
So, Required score = (11 * 38) - (10 * 34)
= 418 - 340 = 78
Answer: Option C
Question: John makes $65 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
A.7.69%
B.16.66%
C.17.8%
D.19%
Answer: A.7.69%
Explanation: Increase = (5/65)*100 = (1/13)*100 = 7.69%.
A
Question: Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly?
A.6
B.7
C.8
D.9
Answer: B.7
Explanation: i got two equations:
3x-2y=25
x+y=6
3x-2(6-x)=25
3x-12+2x=25
5x=37
x=7.4 or between 7 and 8. (ANS B)
Question: How many cubes of 8cm edge can be cut out of a cube of 16cm edge
A.36
B.2
C.8
D.48
Answer: C.8
Explanation: Explanation:
number of cubes=(16 x 16 x 16) / (8 x 8 x 8) = 8
Answer: C
Question: If Y < X and XM > YM, what must be true?
A.M < X.
B.M >0.
C.X < 0.
D.M < 0.
Answer: B.M >0.
Explanation: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when ve is multiplied on both sides. That means M is ve
B is the answer
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 12 : 1 ?
A.6 months
B.3 months
C.2 months
D.8 months
Answer: C.2 months
Explanation: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 12. or x = (85000 * 12) / (42500 * 12) = 2.
So, B joined for 2 months.
Answer: C
Question: The average age of boys in a class is 16 years and that of the girls is 15 years. What is the average age for the whole class?
A.15
B.16
C.17
D.Insufficient Data
Answer: D.Insufficient Data
Explanation: We do not have the number of boys and girls. Hence we cannot find out the answer.
Answer is D.
Question: A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
A.90
B.2,700
C.3,300
D.5,400
Answer: C.3,300
Explanation: Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies.
Answer: C.
Question: If 96 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
A.16
B.14
C.20
D.18
Answer: A.16
Explanation: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (96 *4/24) = 16
ANSWER:A
Question: The ratio 4:20 expressed as percent equals to
A.20 %
B.25 %
C.55 %
D.65 %
Answer: A.20 %
Explanation: Explanation:
Actually it means 4 is what percent of 20, which can be calculated as,
(4/20)*100 = 4*5 = 20
Answer: Option A
Question: What do you get if you add 3 to 300 five times?
A.305
B.310
C.320
D.303
Answer: D.303
Explanation: D
303 , 303 , 303 , 303 , 303
Question: Three days ago, yesterday was the day before Sunday. What day will it be tomorrow?
A.monday
B.thursday
C.sunday
D.tuesday
Answer: B.thursday
Explanation: Three days ago, yesterday was the day before Sunday, so three days ago was itself Sunday.
That means today is Wednesday, so tomorrow is Thursday
Question: Which one of the following can't be the square of natural number ?
A.465456
B.656565
C.521213
D.143642
Answer: D.143642
Explanation: The square of a natural number nerver ends in 2.
143642 is not the square of natural number.
Correct Option is D
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 75 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
A.26 : 15
B.12 : 7
C.13 : 7
D.15 : 6
Answer: A.26 : 15
Explanation: Sol. Distance travelled by Car A = 65 Ã— 8 = 520 km
Distance travelled by Car B = 75 Ã— 4 = 300 km
Ratio = 520/300 = 26 : 15
A
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ?
A.118
B.290
C.119
D.139
Answer: C.119
Explanation: Number of words which can be formed
= 5! - 1 = 120 - 1
= 119.
Answer:C
Question: A farmer has 100337 seeds to plant throughout 9 acres. To evenly distribute the seeds, how many would he need to remove?
A.9
B.3
C.4
D.0
Answer: C.4
Explanation: For this solution you need to add the digits of the total seeds and find the closest number divisible by 9. 100337=14. 9 is divisible by 9. 14-5=9 Therefore the farmer would need to remove 4 seeds to divide the seeds evenly between the acres. Correcr answer C.
Question: Which of the following integers is a divisor of(15!+15)?
A.15
B.14
C.13
D.7
Answer: A.15
Explanation: When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 15) = 15 (1*2*3*4*5*...*12*13*14 + 1) We obtain this by taking 15 common.
Hence 15 is definitely a divisor of (15! + 15).
A
Question: At a certain university, 7 students from the 10-student history department and 5 students from the 7-student English department will be selected to form a 12-student committee. At a neighboring university, 2 students from a 10-person math department and 3 students from a 7-student science department will be selected to form a 5-student focus group. What is the ratio of the number of ways in which the 12-student committee can be formed to the number of ways in which the 5-student focus group can be formed?
A.25/16
B.8/5
C.12/5
D.16/5
Answer: B.8/5
Explanation: Number of ways of selecting a 12 member student committee = 10C7 * 7C5
Number of ways of selecting a focus group of 5 students = 10C2 * 7C3
Ratio of 12 member student committee to 5 member focus group = 10C7∗7C5/10C2∗7C3= 8585
Answer: B
Question: The speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 95 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10 kmph
B.11 kmph
C.25 kmph
D.18 kmph
Answer: C.25 kmph
Explanation: Speed of the boat in still water = (45+95)/2 = 70 kmph. Speed of the stream = (95-45)/2 = 25 kmph.Answer: C
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
A.2999
B.2778
C.6000
D.2889
Answer: C.6000
Explanation: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
Answer:C