RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 70 percent of the pollutant?
A. $200,000
B. $100,000
C. $50,000
D. $10,000
Answer: A. $200,000
Explanation: To remove 90% of pollutant
C= 100,000(90)/(100-90) = 900,000
To remove 70% of pollutant
C' = 100,000(70)/(100-70) = 700,000
Difference = C - C' = 200,000
Answer - A
Question: A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?
A)
B)
C)
D)
E)
A.1/6
B.7/216
C.1/36
D.9/216
Answer: C.1/36
Explanation: The sum of 16 is obtained if the dices show: (6, 5, 5) or (6, 6, 4).
Each can occur in 3!/2!=3 ways, for example we can get (6, 5, 5) in 3 ways: (6, 5, 5), (5, 6, 5), (5, 5, 6), permutation of three items (6, 6, 5) out of which 2 5's are identical.
So, # of favorable outcomes is 2*3=6;
Total # of outcomes is 6*6*6=216;
P=favorable/total=6/216=1/36.
Answer: C
Question: How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/7!?
A.1
B.3
C.5
D.6
Answer: B.3
Explanation: 7! = 7*6*5*4*3*2*1
= 5040
1/7! = 1/5040
=[1/(5.04)] * 10^-3
1/(5.04) will be approximately lesser than .2
Number of leading zeros will be 3
Answer B
Question: How many 6's are there in the following number sequence which are immediately preceded by 9 but not immediately followed by 4 ?
5 6 4 3 2 9 6 3 1 6 4 9 6 4 2 1 5 9 6 7 2 1 4 7 4 9 6 4 2
A.1
B.3
C.2
D.5
Answer: C.2
Explanation: Answer: C . 2
Question: Find the unknown term X,8,6,2,-4, -12
A.2
B.4
C.6
D.8
Answer: D.8
Explanation: X,8,6,2,-4, -12
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - 6 = -4
-4 - 8 = -12
ANSWER:D
Question: How many even integers n, such that 20<=n<=250 are of the form 3k+4, where k is any natural number?
A.33
B.36
C.39
D.42
Answer: C.39
Explanation: The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 250 = 16+6(39)
There are 39 numbers in the list.
The answer is C.
Question: A girl swims downstream 48 km and upstream 16 km taking 8 hours each time; what is the speed of the current?
A.2.0
B.2.1
C.2.2
D.2.3
Answer: A.2.0
Explanation: 48 --- 8 DS = 6
? ---- 1
16 ---- 8 US = 2
? ---- 1 S = ?
S = (6 - 2)/2 = 2
Answer:A
Question: In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 2:3, If Rs 15,0000 was their profit, how much amount did B receive.
A.12653
B.14587
C.36975
D.75000
Answer: D.75000
Explanation: Explanation:
A:B = 2:3= 2:3
=> A:C = 2:1 = 2:1
=> A:B:C = 2:3:1
B share = (3/6)*150000
= 75000
Option D
Question: What least number must be added to 1170, so that the sum is completely divisible by 23 ?
A.3
B.5
C.7
D.9
Answer: A.3
Explanation: 51*23 = 1173
1173 - 1170 = 3
Answer : A
Question: Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps: the original square of side a is divided into n smaller squares, not necessarily of the same size, then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is
A.1:1
B.sqrt 2 : 1
C.n(4-π) / (4n - π)
D.(4n − π) / n (4 - π)
Answer: A.1:1
Explanation: Explanation :
Consider the square of side x, then its area will be x2.
The area of largest circle = π(x/2)2
which can be cut from square πx2/4 .
Therefore, area scrapped = x2 - πx2/4 = x2 (1 - π/4).
Hence,
=> the area scrapped / Area of square
=> x2 (1 - π/4) / x2
=> 1 - π/4 =constant.
As this ratio is constant, whether we cut a circle from smaller square or larger square, scrapped area will be a fixed percentage of square. Therefore, in this case where two squares are pf the same size, the ratio will be 1 : 1.
Answer : A
Question: If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 17 days. If he works at reduced efficiency, he can work without break and finish that same job in 17 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?
A.6/5
B.1/5
C.9/5
D.12/5
Answer: D.12/5
Explanation: We're told that there are 2 ways for Dale to complete a job:
1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 17 days.
2) Reduced Efficiency: 17 straight days with no days off.
Working at Full Efficiency creates the following pattern:
2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2+1+2+1+2= 17 days
Totals: 12 days on, 5 days off
Reduced Efficiency means that Dale will do 12 days of work in 17 days, thus those Reduceddaysare 12/5 of Full Efficiency.
Answer : D
Question: You collect coins. Suppose you start out with 11. Since his mother makes coins, Miguel decides to double your coins. Since you're nice, you give Mary 12 coins. How many coins do you have at the end?
A.9
B.10
C.11
D.12
Answer: B.10
Explanation: Solution
Start with 11 coins.
Miguel doubles the number of coins you have: 11 × 2 = 22 coins.
Mary takes 12 coins from you: 22 - 12 = 10 coins.
So you have 10 at the end.
Correct answer: B
Question: From his monthly salary a man spends 10% of his salary for house rent, 20% on food, 25% for all other expenses and saves Rs 2520 per month. His monthly salary is?
A.Rs 4400
B.Rs 5000
C.Rs 5600
D.Rs 6200
Answer: C.Rs 5600
Explanation: Explanation: Total salary = 100%
His spending are on house rent 10%, on food 20% and for other expenses 25%.
Total expenditure = 10 % + 20% + 25% = 55%
His savings are => Income – Expenses
=> 100% - 55% => 45% = Rs 2520
Hi salary is 1005 => 2520 45
x 100
= Rs 5600
C
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.7.8. The true discount is
A.Rs.72
B.Rs.65
C.Rs.54
D.Rs.50
Answer: B.Rs.65
Explanation: Solution
T.D	= [B.G x 100 / R x T]
= Rs.(7.8 x 100 / 12 x 1)
= Rs.65.
Answer B
Question: A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?
A.33m
B.34m
C.35m
D.36m
Answer: C.35m
Explanation: A runs 25% as fast as B.
That is, if B runs 100m in a given time, then A will run 125m in the same time
In other words, if A runs 5m in a given time, then B will run 4m in the same time.
Therefore, if the length of a race is 5m, then A can give B a start of 1m so that they finish the race in a dead heat.
Start:length of race :: 1:5
we know that the start is 7m. length of the race will be 7/x=1/5. i.e.7*5=35m.
ANSWER:C
Question: If a wholesaler distributes items to several outlets (A, B, C and D) in the ratio of 1/10 : 1/11 : 1/15 : 1/16, then find the total number of items the wholesaler distributes?
A.945
B.745
C.845
D.145
Answer: C.845
Explanation: Here, A : B : C : D = 1/10 : 1/11 : 1/15 : 1/16
1) L.C.M of 10, 11, 15,16 is 2640
2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/10) x 2640 = 264
B = (1/11) x 2640 = 240
C = (1/15) x 2640 = 176
D = (1/16) x 2640 = 165
3) Total number of toys = (264 x + 240 x + 176 x + 165 x) = 845 x
Minimum number of pens (x) = 1
Therefore, total number of items = 845 items.
Correct option :C
Question: A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
A.20
B.3
C.6
D.12
Answer: C.6
Explanation: B is 6 years younger to C.
B and D are twins.
Hence C is 6 years elder to D.
ANSWER:C
Question: A man was born on January 1st, 23 B.C. and died January 2nd, 23 A.D. How old did he live to be?
A.25
B.35
C.45
D.55
Answer: C.45
Explanation: 45 years old.
There is no year 0 so you can add 23 to 23 but you must subtract one to take year 0 out of consideration: 23 + 23 - 1 = 45 years old. In some cultures people are born 1 years old, in this case they would be 46 years old when they die.
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
A.14300
B.14400
C.14500
D.14600
Answer: B.14400
Explanation: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 × 120/100 = 14400
B)
Question: Pradeep has to obtain 20% of the total marks to pass. He got 160 marks and failed by 25 marks. The maximum marks are
A.1925
B.600
C.925
D.1325
Answer: C.925
Explanation: Explanation :
Let their maximum marks be x.
Then, 20% of x = 160 + 25
=>20/100x= 185
x = (18500/20)
x= 925.
Answer : C
Question: The area of a sector of a circle of radius 5 cm formed by an arc of length 4.5 cm is?
A.8.78
B.11.25
C.8.75
D.8.98
Answer: B.11.25
Explanation: (5 * 4.5)/2
= 11.25
Answer:B
Question: Given that on 27th February 2003 is Thursday. What was the day on 27th February 1603?
A.Monday
B.Thursday
C.Sunday
D.Tuesday
Answer: B.Thursday
Explanation: Solution:
After every 400 years, the same day occurs.
Thus, if 27th February 2003 is Thursday, before 400 years i.e., on 27th February 1603 has to be Thursday.
Answer B
Question: If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even?
A.1/2
B.2/3
C.3/4
D.4/5
Answer: A.1/2
Explanation: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 3/6*2/5 = 1/5
P(X and Y are both odd) = 3/6*3/5 = 3/10
P(X+Y is even) = 1/5 + 3/10 = 1/2
The answer is A.
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 24 seconds, the speed of each train (in km/hr) is
A.18
B.36
C.28
D.20
Answer: A.18
Explanation: Explanation:
Distance covered = 120+120 = 240 m
Time = 24 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/24 = 10 m/s
Speed of each train = v = 10/2 = 5 m/s
= 5×36/10 km/hr = 18 km/hr
Answer: Option A
Question: 3, 5, 7, 11, 13, 17, 19, ____
A.25
B.36
C.23
D.49
Answer: C.23
Explanation: The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23....
Answer : C.
Question: Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
A.20 hours 30 min
B.25 hours 30 min
C.30 hours 30 min
D.40 hours 30 min
Answer: A.20 hours 30 min
Explanation: A
20 hours 30 min
1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Question: 9548 + 7314 = 5362 + (?)
A.8300
B.8400
C.11500
D.8700
Answer: C.11500
Explanation: 9548 16862 = 5362 + x
+ 7314 x = 16862 - 5362
----- = 11500
16862
-----
C)
Question: Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many W minutes it takes John to reach the station?
A.5 min
B.6 min
C.7 and 1/2 min
D.8 min
Answer: C.7 and 1/2 min
Explanation: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence, W=6(5/4)=15/2 minutes. The correct answer is C.
Question: A milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
A.4%
B.6(1/4)%
C.20%
D.25%
Answer: C.20%
Explanation: Explanation:
Let C.P. of 1 litre milk be Re. 1
Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.
C.P. of 1 litre mixture = Re. 100	x 1 =	4
125	5
By the rule of alligation, we have:
Ratio of milk to water =	4/5 : 1/5 =4:1.
Hence, percentage of water in the mixture =(1/5 x 100)%=20%
ANSWER IS C
Question: If integers x and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. xb + b^2
II. (x + b)^2
III. x + b
A.I only
B.II only
C.III only
D.I and II only
Answer: B.II only
Explanation: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. xb + b^2 --> if x=1 and b=2 then xb + b^2=6, which is a factor of 30. OK;
II. (x + b)^2 --> (x + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. x + b --> if x=1 and b=2 then x + b=3, which is a factor of 30. OK.
Answer: B.
Question: If r and s are negative integers, which of the following statements must be true?
I. (-r)^s is positive.
II. (-r)^(-s) is positive.
III. r^(-s) is positive.
A.None
B.II only
C.I and II
D.I and III
Answer: C.I and II
Explanation: Let's r = -2 and s = -3
I. (-r)^s = (2)^(-3) = 1/(2^3) --> Positive
II. (-r)^(-s) is positive. = 2^3 --> Positive
III. r^(-s) is positive. = -2^3 --> Negative
Answer: C
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 168 km downstream
A.3 hours
B.4 hours
C.5 hours
D.6 hours
Answer: D.6 hours
Explanation: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 168 km
Time taken = distance/speed = 168/28 = 6 hours
Answer: Option D
Question: A portion of the 85% solution of chemicals was replaced with an equal amount of 30% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced?
A.5/11
B.6/11
C.7/11
D.9/11
Answer: D.9/11
Explanation: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.85(1-x)+0.3*x=0.4 --> x=9/11.
Answer: D.
Question: Three friends Dhoni, Rahul and Aswin divide $1540 amongs them in such a way that if $10, $12 and $18 are removed from the sums that Dhoni, Rahul and Aswin received respectively, then the share of the sums that they got will be in the ratio of 15: 17: 18. How much did Aswin receive?
A.$560
B.$562
C.$564
D.$558
Answer: D.$558
Explanation: A+B+C = 1540
Given ratio 15:17:18
Let us say the shares of A,B,C deducting 10,12,18 be a,b,c
a+b+c = 1540-40= 1500 = 50K
c share = (1500X18)/50 = 540
C = Aswin share = 540+18= 558
Option D
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
A.32:21
B.12:17
C.17:12
D.21:32
Answer: D.21:32
Explanation: Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000×6+15000×6)
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
=(30000×4+50000×4)
Suresh : Kiran
=(20000×6+15000×6) :(30000×4+50000×4)
=(20×6+15×6):(30×4+50×4)
=(20×3+15×3):(30×2:50×2)
=105:160
=21:32
Answer is D.
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km?
A.43 kmph
B.65 kmph
C.24 kmph
D.14 kmph
Answer: C.24 kmph
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer:C
Question: I chose a number and divide it by 2. Then I subtracted 100 from the result and got 4. What was the number I chose?
A.200
B.208
C.400
D.500
Answer: B.208
Explanation: Let x be the number I chose, then
x/2−100=4
x/2=104
x=208
Answer is B.
Question: A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is
A.83.33 ml
B.83.03 ml
C.93.33 ml
D.63.03 ml
Answer: A.83.33 ml
Explanation: Explanation:
Profit (%) = 9.09 % = \inline \frac{1}{11}
Since the ratio of water and milk is 1 : 11,
Therefore the ratio of water is to mixture = 1:12
Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml]
Answer: A) 83.33 ml
Question: If the LCM of two integers c, d (where d> c and c>1) is c*d, then which of the following can not be true?
A.Both c and d can be consecutive integers.
B.Both c and d can be Prime Numbers.
C.All Prime factors of c must be Prime factors of d.
D.c and d do not have a common factor.
Answer: C.All Prime factors of c must be Prime factors of d.
Explanation: If LCM of two numbers C and D is the product CD then both numbers are Co- prime.
(Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).
Numbers that can be Co-Prime are :
1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.
With above four statements it can be concluded that Options A, B, D and E are all true.
Only Option C cannot be true.
Hence answer is C
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6647, how much amount did Raghu invest ?
A.2300
B.2887
C.2000
D.1129
Answer: A.2300
Explanation: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 6647
= x= 6647/2.89 = 2300
Therefore, amount invested by Raghu is Rs. 2300.
Answer: A
Question: At what time between 9 and 10 o’clock will the hands of a watch be together?
A.49 1/11 min. past 9
B.40 min. past 9
C.45 min. past 9
D.50 min. past 9
Answer: A.49 1/11 min. past 9
Explanation: Sol.
To be together between 9 and 10 o’clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gined in 60 min.
45 min. spaces are gained in [60 / 55 * 45] min. or 49 1/11 min.
∴ The hands are together at 49 1/11 min. past 9.
Answer A
Question: A sum of Rs. 427 is to be divided among A, B and C such that 3 times A’s share, 4 tunes B’s share and 7 times C’s share are all equal. The share of C is :
A.84
B.140
C.140
D.240
Answer: A.84
Explanation: Explanation:
3A = 4B = 7C = k,Then A = k/3, B = k/4 and C= k/7.
A : B : C = k/3 : k/4 : k/7 = 28:21 :12.
Cs share = Rs. [427 x (12/61)] = Rs. 84
Answer: A
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 900 gm and 850 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?
A.3.84
B.1.75
C.3.52
D.2.72
Answer: C.3.52
Explanation: 1L A = 900 gm
1L B = 850 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Each "part" is 4/5 of a liter.
So if we have 3 parts A, we have 900*3*(4/5) = 2160
If we have 2 parts B, we have 850*2*(4/5) = 1360
2160 + 1360 = 3520
Solving for units gives us 3.52
So the answer is C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%?
A.20%
B.35%
C.13 1/30%
D.12%
Answer: B.35%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 90
2/3 SP1 = 90
SP1 = 135
100 --- 35 => 35%
ANSWER:B
Question: While planning their outing, Abhishek understood that their boat could travel with a speed of 12kmph in still water.The group decided to travel 24 minutes downstream. Aarti had prior experience in that route and mentioned that the speed of stream was 4kmph.How many kms will the group travel downstream?
A.6.4
B.3.2
C.4
D.4.8
Answer: A.6.4
Explanation: downstream speed = speed of the boat + speed of the river
12+4 = 16
distance travelled = 16x24/60 = 6.4
ANSWER:A
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, ?, 8, 2, 1
A.1
B.3
C.5
D.48
Answer: D.48
Explanation: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
D
Question: What is the solution of the equations x - y = 0.08 and 1(x + y)-1 = 2 ?
A.x = 3.2, y = 2.3
B.x = 1, y = 0.1
C.x = 2, y = 1.1
D.x = 0.065, y = 0.735
Answer: D.x = 0.065, y = 0.735
Explanation: Answer
x - y = 0.8 ...(i)
and 1(x + y)-1=2
⇒ 1/ (x + y) = 2
⇒ 2(x + y) =1
⇒ x + y = 1/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 0.065
and y = 0.735
Correct Option: D
Question: John purchased a grinder and a mobile for Rs. 15000 &Rs. 10000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
A.s. 400
B.s. 120
C.s. 420
D.s. 450
Answer: A.s. 400
Explanation: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 10000(1 + 10/100) = 10000 + 1000
Total SP - Total CP = r + m - (15000 + 10000) = -600 + 1000 = Rs. 400
As this is positive, an overall profit of Rs. 400 was made.
A
Question: There are A girls in a class, and their average height is M inches. In the same class, there are Y boys with an average height of N inches. What is the average height of all the students in the class?
A.(X + Y)/(M + N)
B.(M + N)/(X + Y)
C.(XM + YN)/(M + N)
D.(AM + YN)/(A + Y)
Answer: D.(AM + YN)/(A + Y)
Explanation: Total height = AM+YN
No of students = X+Y
Avg = (AM+YN)/(A+Y)
Answer is D
Question: Sum of the squares of three numbers is 179 and the sum of their products taken two at a time is 131. Find the sum?
A.20
B.22
C.26
D.28
Answer: B.22
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 179 + 2* 131
a + b + c = √441 = 21
B
Question: There are 6 ladies and 5 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.
A.85400
B.86400
C.36400
D.65600
Answer: B.86400
Explanation: First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.
Now there are 6 spaces (space in between two ladies) and we have to seat 5 gents there.
First select 5 places out of 6 available places. can be done in 6C5 ways. Then arrange 5 gents there in 5! ways.
Total: 5!*6C5*5! = 86400
B is the answer.
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
A.3
B.9
C.3^5
D.5^3
Answer: C.3^5
Explanation: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 3^5
Ans:C
Question: In a class, there are 15 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
A.10
B.12
C.18
D.24
Answer: A.10
Explanation: Explanation:
Let the number of boys be x. Then, (3/4)x = 15 or x = 15 x(4/3) = 20.
If total number of students is y, then (2/3) y = 20 or y = 20 x (3/2) = 30.
Therefore Number of girls in the class = (30 - 20) = 10.
Answer: A
Question: The average earning of amechanic for the first 4days of a week is Rs.60 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
A.s. 10
B.s. 44
C.s. 30
D.s. 40
Answer: B.s. 44
Explanation: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 60 + 4 x 22 -20
= Rs. 308
âˆ´ Average earning = 308/ 7
= Rs. 44
B
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
A.Rs.525
B.Rs.500
C.Rs.550
D.Rs.555
Answer: B.Rs.500
Explanation: 70 = (P*4*7/2)/100
P = 500
Answer:B