RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A.28
B.26
C.18
D.109
Answer: C.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C
Question: 50 boys and 100 girls are examined in a test; 50% of the boys and 40% of the girls pass. The percentage of the total who failed is ?
A.42.5%
B.62.1%
C.56.7%
D.39.9%
Answer: C.56.7%
Explanation: Total number of students = 50+100 = 150
Number of students passed = (50% of 50+40% of 100) = 25+40 = 65
number of failures = 85*100/150 = 56.7%
Answer is C
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively?
A.Rs. 6000
B.Rs. 6300
C.Rs. 6400
D.Rs. 6480
Answer: D.Rs. 6480
Explanation: Area of the parallelogram = Length of the base * Perpendicular height
= 54 * 24 = 1296 m.
Total cost of levelling = Rs. 6480
D
Question: The radius of a cone is 4 m, height 5 m. Find the curved surface area?
A.1
B.3
C.5
D.7
Answer: C.5
Explanation: Cone curved surface area = πrl = 22/7 × 4 × 5 = 440/7 = 62 6/7
Slant height (l) = √r(power2)+h(power2) = √16+9 = √25 = 5
Question: Product of two co-prime numbers is 117. Their L.C.M should be
A.1
B.117
C.equal to their H.C.F
D.cannot be calculated
Answer: B.117
Explanation: Solution
H.C.F of co-prime numbers is 1.
So, L.C.M	= 117/1
‹=› 117.
Answer B
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
A.2888
B.2689
C.2522
D.277
Answer: C.2522
Explanation: A = 1600(21/20)3 = 2522.Answer: C
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 5.4 kilometer long bridge, at the same speed?
A.4 min
B.2 min
C.8 min
D.6 min
Answer: D.6 min
Explanation: S = 600/40 = 15 mps
S =5400/15 = 360 sec = 6 min.Answer:D
Question: The average of 6 observations is 15. A new observation is included and the new average is decreased by 1. The seventh observation is?
A.1
B.8
C.5
D.6
Answer: B.8
Explanation: Let seventh observation = X.
Then, according to the question we have
=> (90 + X) / 7 = 14
=> X = 8
Hence, the seventh observation is 8
ANSWER:B
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
A.6000
B.5000
C.5500
D.4000
Answer: B.5000
Explanation: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 â€“ 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
ANSWER B
Question: A bag contains 12 white and 18 black balls.Two balls are drawn in succession without replacement. What is the probability that first is white and second is black?
A.36/145
B.29/145
C.18/145
D.20/145
Answer: A.36/145
Explanation: The probability that first ball is white=12C1/30C1=12/30=2/5
Since.the balls is not replaced; hence the number of balls left in bag=29.
Hence the probability of second ball is black is 18C1/29C1=18/29
Required probability =(2/5)*(18/29)=36/145
The answer is option A
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
A.400 km
B.480 km
C.490 km
D.380 km
Answer: B.480 km
Explanation: B
480 km
Let the distance be x km. Then,
x/(7 1/2) - x/8 = 4
2x/15 - x/8 = 4 => x = 480 km.
Question: The average monthly salary of 20 employees in an organisation is Rs. 1700. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
A.3800
B.3890
C.88798
D.2789
Answer: A.3800
Explanation: Explanation:
Manager's monthly salary Rs. (1800 * 21 - 1700 * 20) = Rs. 3800.
Answer: A) 3800
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 20%?
A.20%
B.70%
C.29%
D.50%
Answer: A.20%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Question: Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 1250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
A.513
B.512
C.517
D.519
Answer: B.512
Explanation: Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, C, D,E The answer to be B
Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.
If x = initial number of trees = 512
Year 1 = 5/4x
Year 2 = (5/4)(5/4)x
Year 3 = (5/4)(5/4)(5/4)x
Year 4 = (5/4)(5/4)(5/4)(5/4)x
Only for Answer D: (5/4)(5/4)(5/4)(5/4) 512 = 1250
Hence, correct answer = B
Question: In a forest 170 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
A.150
B.750
C.1,250
D.1,700
Answer: D.1,700
Explanation: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 170 tagged deers comprise 10% of total # of deers --> total # of deers = 170*10 = 1,700.
Answer: D.
Question: Fresh grapes contain 60% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kgs of raisins?
A.75 kgs
B.64kgs
C.37.5 kgs
D.65 kgs
Answer: C.37.5 kgs
Explanation: The weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-60=40% of whole weight),
so 20*0.75 = x*0.4
--> x = 37.5.
Answer: C
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
A.20
B.40
C.10
D.39
Answer: C.10
Explanation: Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) * X = 70
Solve for X
X = 70 * (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
correct answer C
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A.250
B.100
C.150
D.300
Answer: A.250
Explanation: Let amount paid to X per week = x
and the amount paid Y per week = y
x=120% of y = 120y/100 = 12y/10
22y/10=550
y=250
ANSWER A
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a negative number.
A.2 only.
B.3 only.
C.1 and 3 only.
D.2 and 3 only.
Answer: C.1 and 3 only.
Explanation: Statement I is TRUE
Statement II is not TRUE
Statement III is TRUE
Answer : C
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.17 kmph
B.40 kmph
C.18 kmph
D.13kmph
Answer: B.40 kmph
Explanation: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer:B
Question: A shopkeeper sells an article for Rs. 200 with a loss of Rs. 20 %. Find the cost price of the article.
A.220
B.250
C.280
D.260
Answer: B.250
Explanation: Explanation:
Hint:
Cost Price =	100/(100-Loss%)*S.P.
We are given that,
S.P. = Rs. 200 and loss = 20
Cost Price =	100/(100-20)*200
Cost Price =	100/80*200
Cost Price = Rs. 250
ANSWER IS B
Question: A city had 300 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 3 years. If there were 300 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2009 to 2012?
A.1200
B.2400
C.4800
D.6800
Answer: B.2400
Explanation: The population will increase in the following order:
2000: 300
2003: 600
2006: 1200
2009: 2400
2012: 4800
Difference between 2009 and 2012 = 2400
Option B
Question: To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 20%, and reduce the price it charges its consumers by 20% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?
A.1. No change
B.2. 56.25%
C.3. 100%
D.4. 300%
Answer: B.2. 56.25%
Explanation: Let,
L = 20: B = 10: H= 10 of initial box and Price = 50$
Therefore Price / cubic inch = 50 / (20*10*10) =0.025
Now, when dimensions are reduced by 50% and price also reduced by 50%
L = 16; B=8; H=8 and Price = 40$
Therefore price / cubic inch = 40 / (16*8*8) =0.039
Percentage change = (0.039 - 0.025) *100/ 0.025 = 56.25%
Answer is B
Question: If n=3*4*p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n?
A.Six
B.Seven
C.Eight
D.Nine
Answer: B.Seven
Explanation: n=3∗2^2∗p
Number of divisors = 2 * 3 * 2 = 12
The 12 divisors includes 1, n, 3, 2 and p
Number of different non prime divisors excluding 1 and n = 12 - 5 = 7
Answer: B
Question: The least number which should be added to 1789 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
A.1
B.11
C.21
D.31
Answer: B.11
Explanation: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 1789 by 60, the remainder is 49.
Number to be added = (60 - 49) = 11
B)
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 16 boys and 12 girls Will take to construct?
A.7 days
B.4 days
C.6 days
D.8 days
Answer: B.4 days
Explanation: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
16 boys + 12 girls = 16 Ã— 6/4 + 12 = 24+ 12 = 36 girls
4 days to complete the work
Answer: Option B
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 25 years and that for 40 years?
A.5:8
B.7:5
C.3:8
D.Data inadequate
Answer: A.5:8
Explanation: Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×25/100) /(P×R×40/100)]=25PR/40PR=25/40=5:8
Answer A
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11.00 a.m. ?
A.15
B.12
C.10
D.12
Answer: A.15
Explanation: A
15
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 15 times before 11.00 a.m.
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
A.18 years
B.12 years
C.5 years
D.9 years
Answer: A.18 years
Explanation: Answer: Option A
Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
A.320
B.350
C.340
D.360
Answer: C.340
Explanation: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(912-9-90*2)/3=340
Answer : C
Question: The compound interest on $ 30,000 at 7% p.a is $. 4347.Find out the period (in years) ?
A.1
B.1.5
C.2
D.2.5
Answer: C.2
Explanation: Amount = 30,000 + 4347
= 34347 ......... Now by using compound interest formula we get, 30,000 * (107/100)^n = 34347 ====> n = 2 years Ans - C
Question: In 2 Kg mixture of copper and aluminium, 30% is copper. How much aluminium powder should be added to the mixture so that the proportion of copper becomes 20%
A.800 gm
B.600 gm
C.1200 gm
D.900 gm
Answer: B.600 gm
Explanation: Mixture = 2 kg = 2000g.
Copper = 30% of 2000 = 600g.
To make copper 20% of mixture, we should need to mix 1000g of Aluminum.
As,
2000 + 1000 = 3000g mixture.
And 20% of 3000 = 600g.
ANSWER : B
Question: In an election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
A.15000
B.15500
C.16800
D.17500
Answer: C.16800
Explanation: Let the number of votes enrolled be x. Then ,
Number of votes cast =75% of x. Valid votes = 98% of (75% of x).
75% of (98% of (75%of x)) =9261.
[(75/100)*(98/100)*(75/100)*x] =9261.
X = [(9261*100*100*100)/(75*98*75)] =16800.
ANSWER C
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
A.3.5 years
B.4years
C.4.5years
D.5years
Answer: B.4years
Explanation: Explanation:
Time = (100 x 81)/(450 x 4.5) years
= 4 years.
Answer: B
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 500 shares of the company's stock?
A.$260
B.$96
C.$26
D.$120
Answer: A.$260
Explanation: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*500 --> $260
answer is A
Question: If the radius of a circle is decreased by 50%, find the percentage decrease in its area.
A.25 %
B.50 %
C.75 %
D.95 %
Answer: C.75 %
Explanation: Let original radius = R. New radius =(50/100) R = (R/2)
Original area=22/7( R )2= and new area=  ((R/2))2= ( ( R )2)/4
Decrease in area =((3(22/7) (R )2 )/4 X (1/(22/7)( R)2) X 100) % = 75%
Answer is C.
Question: I sold a book at a profit of 10%. Had I sold it for $90 more, 15% would have been gained. Find the cost price?
A.$1800
B.$2500
C.$3000
D.$3120
Answer: A.$1800
Explanation: 115% of cost - 110% of cost = $90
5% of cost = $90
cost = 90*100/5 = $1800
Answer is A
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
A.12211
B.22777
C.29777
D.14000
Answer: D.14000
Explanation: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer:D
Question: Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 2 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
A.20%
B.17%
C.5.5%
D.3.3%
Answer: C.5.5%
Explanation: 33.33/6=5.5
Answer : C
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
A.3
B.87
C.42
D.767
Answer: C.42
Explanation: Explanation:
required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154 = 42 sq cm.
Answer: C) 42
Question: If 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
A.176
B.253
C.342
D.458
Answer: B.253
Explanation: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.
The number of ways to select 2 lines from 23 lines is 23C2 = 253
The answer is B.
Question: Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
One chicken lays two eggs in three days. How many eggs do three chickens lay in nine days?
A.11
B.17
C.18
D.20
Answer: C.18
Explanation: C
18
1 chicken lays 2 eggs in 3 days, so 3 chickens lay 3×2=6 eggs in 3 days. In 9 days, these 3 chickens lay 3 times as much eggs as in 3 days. Conclusion: three chickens lay 3×6=18 eggs in nine days.
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
A.1hour
B.2hour
C.3hour
D.4hour
Answer: A.1hour
Explanation: Let the duration of the flight be x hours
Then 600/x - 600/x (1/2) = 200
= 600/x - 1200/2x+1 =200
=x(2x+1) =3
=2xsquare + x -3 = 0
=(2x+3)(x-1) = 0
= x= 1 hr ( neglecting the -ve value of x)
Answer: Option A
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 72. what is sum of the numbers?
A.42
B.56
C.76
D.84
Answer: A.42
Explanation: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 72
=> 12x = 72
=> x = 72/12 = 6
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 6 = 42
Answer: Option A
Question: In how many E ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
A.6
B.12
C.18
D.24
Answer: C.18
Explanation: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning E= 24 - 6 = 18
Answer: C
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
A.6 2/3%
B.6 2/8%
C.7 2/3%
D.6 5/3%
Answer: A.6 2/3%
Explanation: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%
Answer:A
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
A.338
B.277
C.585
D.676
Answer: C.585
Explanation: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer:C
Question: In an exam, Amar scored 49 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
A.344
B.826
C.207
D.269
Answer: A.344
Explanation: Average mark scored by all the three boys =
[49/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 344
Answer: A
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
A.3:1
B.2:1
C.2:5
D.2:3
Answer: B.2:1
Explanation: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 45000 * 12: 30000 * 9
= 45 * 12: 30 * 9
= 3*12: 2 * 9
= 2:1
Answer is B
Question: With both inlets open, a water tank will be filled with water in 36 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
A.9,000
B.4,500
C.1,750
D.1,000
Answer: B.4,500
Explanation: The work Done by Inlet A and B together in 1 min = 1/36
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/36)- (1/120) =1/51
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/51)- (1/120) = 50 Cubic meter
i.e.4500 Cubic Meter
Answer: option B
Question: The difference between the simple and the compound interest compounded every six months at the rate of 10% p.a. at the end of two years is 124.05. What is the sum?
A.10,000
B.6,000
C.12,000
D.8,000
Answer: D.8,000
Explanation: Let the sum be x.
Then, [x(1+5/100)4−x]−[x×10×2/100]=124.05
Solving the above eqns, we get x = 8,000.
Answer D
Question: Maria sold 10kg of apples in her first hour at the market, but only 2kg of apples in the second hour. On average, how many kg of apples did she sell in two hours at the market?
A.6 kg
B.5 kg
C.12 kg
D.24 kg
Answer: A.6 kg
Explanation: (10 kg + 2kg)/2 = 6 kg
Correct answer is: A
Question: If 3 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King, one of them will be Queen and one of them will be Jack?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
A.96/5525
B.48/5525
C.16/5525
D.8/16575
Answer: C.16/5525
Explanation: Let K,Q and J represent King, Queen and Jack respectively.
One possible combination is KQJ and this can be arranged in 3! ways.
Probability of KQJ = (4/52)*(4/51)*(4/50)
Total probability = 3! * (4/52)*(4/51)*(4/50) . No need for final calculation. Reduce this to simpler form and you only have 1 option with 16 in the numerator. C is the correct answer.
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time will they meet?
A.10.30 a.m
B.11 a.m
C.10 a.m
D.12 noon
Answer: B.11 a.m
Explanation: Explanation:
Assume that they meet x hours after 8 a.m.
Then,train1,starting from A , travelling towards B, travels x hours till the trains meet
⇒Distance travelled by train1 in x hours = Speed ×Time = 60x
Then, train2, starting from B , travelling towards A, travels (x-1) hours till the trains meet
⇒Distance travelled by train2 in (x-1) hours = Speed ×Time = 75(x-1)
Total distance travelled = Distance travelled by train1 + Distance travelled by train2
=> 330 = 60x + 75(x-1)
=> 12x + 15(x-1) = 66
=> 12x + 15x - 15 = 66
=> 27x = 66 + 15 = 81
=> 3x = 9
=> x = 3
Hence the trains meet 3 hours after 8 a.m., i.e. at 11 a.m.
Answer: Option B
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
A.1136
B.1268
C.1244
D.1296
Answer: D.1296
Explanation: Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)^2
= 36^2
=1296
Ans-D