RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1700. The difference between the profit shares of A and C is?
A.288
B.266
C.155
D.680
Answer: D.680
Explanation: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1700
=> 5 parts out of 15 parts is Rs. 1700
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1700) = Rs. 680
Answer:D
Question: A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is
A.7000
B.8000
C.9000
D.10000
Answer: C.9000
Explanation: Explanation :
Ratio in which profit is divided = 2:3
Assume that B's contribution to the capital = b
=> 3500*12 : b*7 = 2:3
=> 3500*12/7b = 2/3
=> b = (3500*12*3)/(2*7) = 500*6*3 = 9000. Answer : Option C
Question: How much is 80% of 40 is greater than 4/5 of 15?
A.12
B.20
C.18
D.12
Answer: B.20
Explanation: (80/100) * 40 â€“ (4/5) * 15
32 - 12 = 20
Answer:B
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 3?
A.1/8.
B.1/2.
C.1/5.
D.3/8.
Answer: A.1/8.
Explanation: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
So answer will be 1/8. Option A.
Question: A boat running upstream takes 640 min to cover a certain distance, while it takes 280 min to cover the same distance running down stream. What is the ratio between the speed of the boat and speed of water current respectively?
A.23: 7
B.22: 9
C.23: 8
D.23: 9
Answer: D.23: 9
Explanation: Let the speed of the boat=x and speed of the current=y
Relative speed in upstream=x-y and in downstream=x+y
Let the distance 'd' is to be covered in downstream and upstream, then
Time taken in upstream=d/(x-y)=640 or d=640(x-y) ----(i) and
Time taken in downstream=d/(x+y)=280 or d=280(x+y) ----(ii)
Comparing (i) & (ii), 640(x-y) = 280(x+y)
=> 16(x-y) = 7(x+y)
=> 16x -16y =7x -7y
=> 9x = 23y
=> x/y= 23/9
ANSWER:D
Question: A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 78 runs, thereby increasing his average by 6 runs. His new average is
A.18 runs
B.28 runs
C.48 runs
D.42 runs
Answer: A.18 runs
Explanation: Explanation:
Let average for 10 innings be x. Then,
(10x + 78)/11 = x + 6 => 11x + 66 = 10x + 78 => x = 12.
New average = (x + 6) = 18 runs.
Answer: A
Question: What is the greatest value of positive integer x such that 2^x is a factor of 100^90?
A.180
B.160
C.140
D.150
Answer: A.180
Explanation: Put in simple words, we need to find the highest power of 2 in 100^90
100 = 2^2*5^2
Therefore 100^90 = (2^2*5^2)^90 = 2^180*5^180
Answer : A
Question: For dinner, Cara ate 240 grams of bread which was eight times as much bread as she ate for lunch, and six times as much bread as she ate for breakfast. How much bread did Cara eat in total?
A.300
B.310
C.320
D.330
Answer: B.310
Explanation: For breakfast, Cara ate 240 / 6 = 40 grams.
For lunch, Cara ate 240 / 8 = 30 grams.
For dinner, Cara ate 240 grams.
The total is 40 + 30 + 240 = 310 grams.
The answer is B.
Question: Solution X contains 20% of material A and 80% of material B. Solution Y contains 30% of material A and 70% of material B. A mixture of both these solutions contains 22% of material A in the final product. how much solution X is present in the mixture?
A.40%
B.60%
C.80%
D.100%
Answer: C.80%
Explanation: We can assume the total weight of the mixture= 100
Conc of A in the final mixture= 22
Let weight of A in the mixture be X. Conc given= 20%=.2
Therefore, weight of B= 100-X. Conc given = 30%= .3
Now, acc to the problem, .2X+ .3(100-X)=22
Solving, we get X=80. Since we assumed the weight of the mixture = 100, Therefore presence of A in the mixture= 80%.
ANSWER:C
Question: A number of two digits has 3 for its unit’s digit, and the sum of digits is 1/7 of the number itself. The number is
A.43
B.63
C.73
D.53
Answer: B.63
Explanation: Let the ten’s digit be x.
Then, number=10x+3 and sum of digits=(x+3)
(x+3)=1/7(10x+3)
7x+21=10x+3
3x=18
X=6
The required number is 63
ANSWER B 63
Question: Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°.
If the number of convex corners in such a polygon is 25, the number of concave corners must be
A.20
B.10
C.21
D.22
Answer: C.21
Explanation: 90(25) + 270(n-25) = (n-2)*180.
=25 + 3(n-25) = (n-2)*2.
= 3n - 50 = 2n-4
= n = 46.
Hence, the required number of corners must be 46 - 25 = 21. 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.1.7
B.1.4
C.1.1
D.1.5
Answer: D.1.5
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: D
Question: For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
A.10
B.9
C.8
D.7
Answer: B.9
Explanation: "For any positive integer n , n > 1, the "length" of n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)"
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 9 the length of 512.
the answer is (B)
Question: A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: X PIPES FILL AND 8-X EMPTY
IN 1hr 1/6th is emptied so :
x/6 - (8-x)/8 = 1/6
ON SOLVING X=4 (FILL PIPES) AND 8-X=4(EMPTY PIPES)
ANSWER:D
Question: The number 49 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A.11
B.16
C.15
D.14
Answer: A.11
Explanation: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 49: 1, 4, 9, 16, 25, 36, 49..
Now, 49 should be the sum of 3 of those 7 numbers. Also to simplify a little bit trial and error, we can notice that as 49 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
We can find that 49 equals to 4+9+36=2^2+3^2+6^2=49 --> 2+3+6=11.
Answer: A.
Question: From the set of numbers {t, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
A.8
B.15
C.16
D.31
Answer: D.31
Explanation: Any letter (v, w, x, y, z) can be included or not.
Thus there are 2^5 combinations - 1 empty combination = 31 combinations
The answer is D.
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
A.4 days
B.2 days
C.6 days
D.8 days
Answer: C.6 days
Explanation: C
6 days
4/10 + 9/x = 1 => x = 15
1/10 + 1/15 = 1/6 => 6 days
Question: 325^325/125^n
A.64
B.216
C.343
D.481
Answer: B.216
Explanation: 325^325 = 325*325*325.................325 times
and 125 = 5*5*5
also 325 = 5*5*13 (2 fives)
in 325 times 325 we have 5^(2*325) which we can write in (5^3)^216
so the answer is 216
ANSWER:B
Question: An amount of Rs.1,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
A.2378
B.2697
C.250
D.5000
Answer: C.250
Explanation: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 1,000
Thus we get, 2Q + Q + Q + 4Q = 1,000
8Q = 1,000 or Q = Rs. 125
Thus, R = Rs. 125, P = 250 & S = Rs. 500
Hence, the required difference = (S – P) = (500 – 250) = Rs.250
ANSWER:C
Question: The sum of first 45 natural numbers is?
A.900
B.1000
C.1035
D.1040
Answer: C.1035
Explanation: et Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
Sn =	n	[2a + (n - 1)d]	=	45	x [2 x 1 + (45 - 1) x 1]	= 45	x 46 = (45 x 23)
2	2	2
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
Shorcut Method:
Sn =	n(n + 1)	=	45(45 + 1)	= 1035.
2	2
C)
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
A.1218
B.1219
C.1210
D.1211
Answer: C.1210
Explanation: π (232 – 122) = 1210
Answer: C
Question: A bus can hold 72 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
A.4
B.8
C.10
D.6
Answer: D.6
Explanation: No. of seats = 72/12 = 6
There are 6 seats in each row
Answer : D
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 36% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
A.35.67%
B.65.80%
C.68.57%
D.69.57%
Answer: B.65.80%
Explanation: Girls = 900, Boys = 1100
Passed = ( 36% of 1100 ) + ( 32% of 900)
= 396 + 288 = 684
Failed = 2000 - 684 = 1316
Failed % = [(1316/2000) x 100]%
= 65.8%.
ANSWER:B
Question: For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 191?
A.4450
B.5560
C.6670
D.7780
Answer: C.6670
Explanation: 100 + 102 +...+ 190 = 46*100 + (2+4...+90) = 46*100 + 2(1+2+...+45) =
46*100 + 2(45)(46)/2 = 145*46 = 6670
The answer is C.
Question: If s is a number such that –2 ≤ s ≤ 2, which of the following has the largest possible absolute value?
A.3s – 1
B.x^2 + 1
C.3 – x
D.x – 3
Answer: A.3s – 1
Explanation: Ans is A .. leads to the max value of 7 for s = -2
Question: A portion of the 80% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 50% solution of chemicals resulted. What part of the original solution was replaced?
A.1/3
B.1/2
C.1/4
D.1/5
Answer: B.1/2
Explanation: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.8(1-x)+0.2*x=0.5 --> x=1/2.
Answer: B.
Question: Replace the question mark with the correct number in the series
60 40 40 43 20 46 0 49 ?
A.-20
B.50
C.40
D.-10
Answer: A.-20
Explanation: A
-20
Its a alternate series riddle
60 40 20 0 (?)
40 43 46 49 (+3)
Question: 108.	Triangle A’s base is 9% greater than the base of triangle B, and A’s height is 9% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
A. 9 % less
B. 1 % less
C. Equal to each other
D. 1.3 % more
Answer: D. 1.3 % more
Explanation: Wish the question specified that we are talking about corresponding height.
Base of A = 10/9 * Base of B
Height of A = 8/9 * Height of B
Area of A = (1/2) * Base of A * Height of A = 10/9 * 8/9 * Area of B = 80/81 * Area of B
Area of A is 1.3% more than the area of B.
Answer (D)
Question: Find the missing in the series: 70, 56, 45, 41,___
A.22
B.287
C.2679
D.276
Answer: D.276
Explanation: Answer:D
Question: If S and T are positive integers, and the remainder obtained when S is divided by T is the same as the remainder obtained when T is divided by S, which of the following is a possible value of ST?
A. 64
B. 55
C. 42
D. 36
Answer: A. 64
Explanation: I am not too sure on this. I guess it is possible only when S and T are both same. If they are both same, ST must be a perfect square.
64 is a perfect square.
Ans:A
Question: All the six members of a family A, B, C, D, E and F are travelling together. B is the son of C but C is not the mother of B. A and C are a married couple. E is the brother of C. D is the daughter of A. F is the brother of B. Who is the mother of B ?
A.C
B.V
C.R
D.A
Answer: D.A
Explanation: Explanation:
B is the son of C but C is not the mother of B means C is the father of B. A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C
Clearly. A is the mother of B.
Answer: D
Question: A cubical block of metal weighs 3 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
A.48
B.32
C.24
D.18
Answer: C.24
Explanation: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 3 pounds
If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 3 pounds = 24 pounds
So answer is C
And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3
we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
3 * 8 = 24
So answer is C
Question: If a, b, t are integers, 33 = abt, and a < b < t, what is the smallest possible value of a?
A.-33
B.-3
C.1
D.3
Answer: A.-33
Explanation: Given : a * b * t = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Question: For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
A.9
B.18
C.27
D.36
Answer: C.27
Explanation: f(x) = -3(x - 10)(x - 4) = -3x2*square* + 42x - 120 : expand and obtain a quadratic function
h = -b/2a = -42/-6 = 7 : h is the value of x for which f has a maximum value
f(h) = f(7) = 27 : maximum value of f.
correct answer C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?
A.1 : 1
B.2 : 1
C.2 : 3
D.3 : 2
Answer: D.3 : 2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27 x meters, and
length of the second train = 17 y meters.
(27 x + 17 y) / (x + y) = 23
=> 27 x + 17 y = 23 x + 23 y
=> 4 x = 6 y
=> x/y = 3/2.
Answer : D
Question: If -1 < h < 3, which of the following has the greatest value?
A.a) 1-h
B.b) 1+h
C.c) 1+h^2
D.d) 1-1/h
Answer: B.b) 1+h
Explanation: easiest way of solving this would be to substitute a value.
lets say h= - 1/2
a) 3/2
b) 1/2
c) 5/4
d) 3
e) - 3
the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.
Answer is B.
Question: A hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 18 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
A.7.5
B.12.5
C.17.5
D.22.5
Answer: C.17.5
Explanation: In 5 minutes, the cyclist travels a distance of (5/60)*18 = 1.5 km.
The time it takes the hiker to complete this distance is 1.5/4 hours = 22.5 minutes
The cyclist needs to wait 22.5 - 5 = 17.5 minutes
The answer is C.
Question: A bag holds 4 red marbles and 4 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
A.1/7
B.1/5
C.3/14
D.2/7
Answer: C.3/14
Explanation: probability of selecting first red marble = 4/8
probability of selecting second red marble without replacement = 3/7
final probability = 4/8 * 3/7 = 3/14
The correct answer is C.
Question: If goods be purchased for $840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A.35 1/3%
B.30 2/3%
C.33 1/3%
D.38 1/2%
Answer: C.33 1/3%
Explanation: C
33 1/3%
1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
A.7 min
B.9 min
C.4 min
D.9 min
Answer: B.9 min
Explanation: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer:B
Question: A 9% stock yields 8%.The market value of the stock is :
A.Rs. 72
B.Rs. 92
C.Rs. 112.50
D.Rs. 116.50
Answer: C.Rs. 112.50
Explanation: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 9, investment = Rs.(100/8X9)= Rs. 112.50
∴ Market value of Rs. 100 stock = Rs.112.50
Answer C
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour?
A.38
B.47
C.50
D.53
Answer: D.53
Explanation: Suppose food eaten in first hour : x
The AP is : x, x+3, x+6, .... [Number of terms 'n' = 9]
Therefore,
9/2[2 x + (9-1)*3] = 450.
Solving for x, x = 38.
Now, 6th term will be : x + (6-1)*d = 38 + 5*3 = 53.
Hence D !!
Question: A man whose speed is 6 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?
A.7
B.5.6
C.6
D.9
Answer: B.5.6
Explanation: M = 6.0
S = 1.5
DS = 7.5
US = 4.5
AS = (2 * 7.5 * 4.5) /12 = 5.6
Answer:B
Question: A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in?
A.8
B.4
C.6
D.12
Answer: A.8
Explanation: (A + B + C)'s 1 day work = 1/6;
(A + B)'s 1 day work = 1/8
(B + C)'s 1 day work = 1/12
(A + C)'s 1 day work = (2 * 1/6) - (1/8 + 1/12)
= (1/3 - 5/24) = 1/8
So, A and C together will do the work in 8 days.
ANSWER A
Question: The contents of a bag of marbles consist of 12 green marbles and 20 blue marbles. How many blue marbles must be removed so that 40% of the marbles in the bag will be green?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: We can use simple arithmetic to solve this problem by testing our answers.
Lets test B:
If we only remove 1 blue marble:
12 green marbles and 19 blue marbles for a total of 31 marbles
12/31=37.5% not quite our answer.
Lets test C:
If we remove 2 blue marbles:
12 green marbles and 18 blue marbles for a total of 30 marbles
12/30=40%
C is our answer!
Question: What will come in place of the x in the following Number series? 25, 100, 400, X, 6400
A.6400
B.6900
C.1600
D.7500
Answer: C.1600
Explanation: (C)
25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -.
A.1/26
B.3/52
C.15/26
D.11/26
Answer: A.1/26
Explanation: Explanation:
Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
ANSWER IS A
Question: (7/10^2)*(8/10^2)*(6/10^2)=?
A.0.000336
B.0.336
C.0.0336
D.0.00337
Answer: A.0.000336
Explanation: 7/10^2=0.07
8/10^2=0.08
6/10^2=0.06
=0.07*0.08*0.06 multiply the whole number (i.e) 7*8*6=336
Move the place depend upon the decimal places (i.e) 0.000336
Option A is answer
Question: How many multiples of 10 are there between 100 and 10000 (both are inclusive)?
A.456
B.789
C.991
D.1020
Answer: C.991
Explanation: the answer is (10000-100)/10+1=991
Answer is C
Question: A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current.
A.1.5 km/hr
B.1 km/hr
C.1.5 km/min
D.0.5 km/hr
Answer: A.1.5 km/hr
Explanation: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.
Rate of current=1/2(10-7)km/hr=1.5 km/hr.
Answer is A.
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is?
A.35
B.50
C.88
D.22
Answer: A.35
Explanation: Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x
= 35 km/hr.Answer:A
Question: 11 persons are sittingin a row. how many ways can 11 persons be arranged in a row such that 3 persons should always be together?
A.7!×2!
B.10!×1!
C.9!×3!
D.8!×2!
Answer: C.9!×3!
Explanation: Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person.
Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways.
We had grouped three persons together. These three persons can be arranged among themselves in 3! ways.
Hence, required number of ways
=9!×3!
C
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
A.30
B.40
C.50
D.70
Answer: B.40
Explanation: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B)
Question: The average age of 30 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.
A.46
B.55
C.43
D.39
Answer: A.46
Explanation: Explanation:
If teacher's age is 15 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 16.
Age of teacher = Average age of all + Total increase in age
= 16 + (1 x 30 ) = 46 years
Answer:A
Question: In a certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?
A.11/18
B.12/18
C.13/18
D.10/18
Answer: A.11/18
Explanation: Let the total no of workers be x
No of women =x/3
No of men =x-(x/3)=2x/3
No of women having children =1/3 of ½ ofx/3=x/18
No of men having children=2/3 of ¾ of2x/3=x/3
No of workers having children = x/8 +x/3=7x/18
Workers having no children=x-7x/18=11x/18=11/18 of all wprkers
Answer is A.
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 12, and 8 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
A.5/2
B.7/4
C.8/5
D.10/3
Answer: D.10/3
Explanation: The time it takes printer X is 16 hours.
The combined rate of Y and Z is 1/12 + 1/8 = 5/24
The time it takes Y and Z is 24/5
The ratio of times is 16 / (24/5) = 5*16/24 = 10/3
The answer is D.