RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The work done by a man, a woman and a child is in the ratio of 3:2:1. There are 20 men, 30 women & 48 children in a factory. Their weekly wages amount to Rs.840, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women & 30 children for 2 weeks?
A.Rs.1000
B.Rs.1050
C.Rs.1170
D.Rs.1900
Answer: C.Rs.1170
Explanation: sax Ratio of wages of 20 men, 30 women
and 45 chﬂdren perweek
: (3 x 2o):(2 x 30) (1 x 43) 5
Total wages or 20 men per week
= R5 300
Therefore, wages of a man per week : Rs 15,
sirmlarly, wages of woman per week
: Rs 10 and wages ofchwld perweek Rs 5
Total wages of (15 men, 21 women and 30
chﬂdrenj perweek
= 15x15 + 21x10 + 30x5 = 585
Total wages for 2 weeks = Rs.1170
C
Question: 5^100 is divided by 18. Then what is the remainder?
A.10
B.11
C.13
D.15
Answer: C.13
Explanation: Here N = 18=2×32
ϕ(18)=18(1−12)(1−13) = 6
So 56 when divided by 18, remainder is 1.
So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49
Now 49 when divided by 18, remainder is 13.
C
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $920 in total compensation, how many total hours did he work that week?
A.36
B.50
C.44
D.48
Answer: B.50
Explanation: For 40 hrs = 40*16=640
Excess = 920-640=280
For extra hours =.75(16)=12+16=28
Number of extra hrs =280/28=10
Total hrs =40+10=50
Answer B 50
Question: The bankerâ€™s gain on a sum due 3 years hence at 10% per annum is Rs. 120. The bankerâ€™s discount is
A.Rs.960
B.Rs.840
C.Rs.520
D.Rs.760
Answer: C.Rs.520
Explanation: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(120x100/10 x 3)
= Rs.400.
B.D
=Rs(400+ 120)
= Rs.520.
Answer C
Question: Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 610 or over 780. If the individual ranges of the three people's scores in those 4 practice tests were 50, 80 and 90, what is the difference between the maximum and minimum possible ranges of all their scores put together.
A.70
B.80
C.90
D.100
Answer: B.80
Explanation: According to the information in the question the maximum range would be between 610 and 780(170). The minimum range would be the greatest range for any one individual, which is listed in the problem as 90. So the difference between these would be 170-90 or 80.
Answer: B
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 8 more than the average expenditure of all the nine. The total money spent by all of them was
A.36
B.40
C.29.25
D.27
Answer: A.36
Explanation: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 8 = 9x
⇒ x = 4
∴ Total money spent = 9x = 9 × 4 = 36
Answer A
Question: At 12:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 3:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
A.5:00 p.m.
B.6:00 p.m.
C.7:00 p.m.
D.8:00 p.m.
Answer: B.6:00 p.m.
Explanation: By the time Jim starts, Tom has already covered = 3 hr * 10 mph = 30 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 30 miles which can be covered in = 30/10= 3hours
If Jim leaves at 3 pm, he will catch Tom at 6 pm
Answer: B
Question: The difference between C.I. and S.I. on an amount of $10,000 for 2 years is $49. What is the rate of interest per annum?
A.5%
B.6%
C.7%
D.8%
Answer: C.7%
Explanation: $49 is the interest on the first year of interest.
Let x be the interest rate.
The interest after the first year is 10000*x.
The interest on the first year's interest is 10000*x*x
10000*x^2 = 49
x = 0.07
The answer is C.
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 32% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
A.20%
B.30%
C.50%
D.55%
Answer: A.20%
Explanation: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.32N
x = 0.8N
The percentage of rooms which permit smoking is 1 - 0.8 = 20%
The answer is A.
Question: A single discount equivalent to the discount series of 30%, 10% and 5% is?
A.31.5
B.31.8
C.40.1
D.31.3
Answer: C.40.1
Explanation: 100*(70/100)*(90/100)*(95/100)
= 59.9
100 - 59.9 = 40.1
Answer:C
Question: A completes a work in 6 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be
A.8 days
B.9 days
C.10 days
D.4.8 days
Answer: D.4.8 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 6 × 24/ 30 = 4.8 days.
D
Question: How many total number of ways in which a distinct objects can be put into two different boxes is
A.n2
B.2a
C.2n
D.3n
Answer: B.2a
Explanation: Let the two boxes be B1 and B2. There are two choices for each of the a objects. So, the total number of ways is
2 × 2 ×.....× 2 (a times ) = 2a
Answer B
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 20% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
A.119.45%
B.129.56%
C.138.24%
D.141.92%
Answer: C.138.24%
Explanation: 0.8*1.2^3 = 1.3824
The answer is C.
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 30 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
A.22 %
B.30%
C.42 6/7%
D.70%
Answer: C.42 6/7%
Explanation: Expensive item = $100;
Cheap item = $70;
We must increase $70 to $100, so by $30, which is approximately 40% increase: (100-70)/70 = 3/7 = ~0.42.
Answer: C.
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
A.18:11
B.18:16
C.18:17
D.18:18
Answer: A.18:11
Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer:A
Question: Find a sum for first 3 prime number'ss?
A.25
B.10
C.15
D.12
Answer: B.10
Explanation: Required sum = (2 + 3 + 5) = 10
Note: 1 is not a prime number
Option B
Question: Father is aged square times more than his son john. After 3 years, he would be three times of John's age. what would be the age of John's Father after 15 years ?
A.18
B.36
C.40
D.57
Answer: D.57
Explanation: Let Father's age be J and John's' age be D...
Given J + 3 = 3(D + 3 ) => J - 6 = 3D -> Eq1.
Given J-6 = (D-6)^2 --> Eq 2..
sub J-6 value in eq 2... 3D = D^2 - 12D + 36.
0 = D^2 - 15D + 36 => D = 12 or D = 3.
When D = 12 we get from eq 1... J+3 = 45 => J =42..
When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15...
In the above options only 42 exits..
IMO option D is correct answer..
Question: An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 8 minutes, what part of the cistern will be emptied?
A.1/2
B.1/3
C.1/4
D.2/5
Answer: B.1/3
Explanation: 8/16 * 2/3 = 1/3
The answer is B.
Question: What is the probability that a 4-person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains at least 1 woman?
A.11/102
B.77/204
C.77/102
D.91/102
Answer: D.91/102
Explanation: Total Members = 6+7+5 = 18
Total ways of making 4 person committee = 18C4 = 3060
Total Members without women = 6+5 = 11
Total ways of choosing e person committee without any women = (6+5)C4 = 330
favorable probability = 1- (330/3060) = 1- (11/102) = 91/102
Answer: option D
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
A.4 1/5 Km
B.4 1/7 Km
C.3 1/5 Km
D.3 1/7 Km
Answer: C.3 1/5 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
C)
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
A.45%
B.49%
C.57%
D.59%
Answer: C.57%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.400, find the number of 10 paise coins ?
A.914
B.714
C.718
D.724
Answer: B.714
Explanation: 50*3k + 20*4k + 10*5k = 40000
280k = 40000 => k = 142.85
50p coins = 3k = 3*142.85 = 428
20p coins = 4k = 4*142.85 = 571
10p coins = 5k = 5*142.85 = 714
ANSWER:B
Question: The decimal d is formed by writing in succession all the positive, even integers in increasing order after the decimal point; that is d = 0.246810121416...
What is the 100th digit of d to the right of decimal point?
A.6
B.1
C.0
D.2
Answer: D.2
Explanation: One-digit even numbers: There are (1)(10/2) = 4 even one-digit numbers.
0.2468
4 digits down, 96 remaining. The next 5 even numbers will be 10, 12, 14, 16, and 18, ... so it follows that: (2)(5) = 10 digits.
Two-digit numbers: 90 digits, which brings us to the number 98.
Three-digit numbers: we only need 6 more digits. The next even numbers are 100, and 102, thus 2 is the 100th digit.
Answer: D
Question: The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.255
B.267
C.255
D.277
Answer: C.255
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (120 + x)/30 = 25/2
=> x = 255 m. Answer:C
Question: Two motor cycles were sold for Rs 9,900 each, gaining 10% on one and losing 10% on the other. The gain or loss per cent in the whole transaction is
A.Neither loss nor gain
B.1% profit
C.100/99 % profit
D.1% loss
Answer: D.1% loss
Explanation: C.P. of the 1st Motor Cycle = (9900 x 100)/(100 + 10) = Rs 9000
C.P. Of the 2nd Motor Cycle = (9900 x 100)/(100 - 10) = Rs 11000
Total C.P = Rs 20,000
Total S.P = Rs 19,800
Therefore, Loss per cent = (200/20000) x 100 = 1
ANSWER:D
Question: A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?
A.$3,000
B.$3,150
C.$4,000
D.$4,150
Answer: A.$3,000
Explanation: Total salary = $150+ 15% (x) where x = all the sales she makes.
How much x should be for total to be 600
$150+15%(x) = $600
15%(x) = $450
x = $3000
Answer :A
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 30 days, then together ,all will finish the work in :
A.13 1/3 days
B.12 1/3 days
C.15 days
D.12 days
Answer: D.12 days
Explanation: C alone can finish the work in 30 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/30) = 1/12
All the three together will finish it in 1/12 = 12 days.
ANSWER:D
Question: Merry invested Rs. 8000 in a scheme for 3 years at compound interest rate 7% p.a. How much amount will Merry get on maturity of the fixed deposit?
A.s.8980
B.s.9800.34
C.s.9841
D.s.8900
Answer: B.s.9800.34
Explanation: Amount = [8000 * (1 + 7/100)3]
= 8000 * 107/100 * 107/100 * 107/100
= Rs.9800.34
Answer:B
Question: The number 4 is the smallest positive
integer that has exactly three factors:
1, 2, and 4. If k is the next-highest integer
that also has exactly three factors, what is
the sum of the three factors of k?
A.13
B.14
C.16
D.18
Answer: A.13
Explanation: The greatest of the five possible answers is 20, so k is less than 20. Use trial and error to
find the value of k:
Factors of 5: 1 5
Factors of 6: 1 2 3 6
Factors of 7: 1 7
Factors of 8: 1 2 4 8
Factors of 9: 1 3 9
Thus, k = 9, and the sum of the factors of k is 1 + 3 + 9 = 13.
correct answer A)13
Question: A 15 lt mixture contains water with 20% of alcohol.If 5 more lts of water added to the mixture what is the percentage of alcohol?
A.10%
B.15%
C.20%
D.25%
Answer: B.15%
Explanation: Initially the mixture contains 20% of 15=15*(20/100)=3 lts of alcohol
after mixing another 5 lts of water...
the total liquid is 20 lts..
so alcohol percentage=(3/20)*100=15%
ANSWER:B
Question: Two pipes can fill a tank in 12 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
A.5.5 Hours
B.7.5 Hours
C.8.5 Hours
D.9.5 Hours
Answer: C.8.5 Hours
Explanation: In 1 hour it fill 1/12 + 1/12 - 1/20 = 7/60
So fill tank fillup in 60/7 = 8.5 Hours
ANSWER:C
Question: A set of 17 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
A.32
B.37
C.40
D.45
Answer: D.45
Explanation: The correct answer is D.
A set of 17 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 15 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 27
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 27
The maximum value n15 can have is 27 + n1 (18) = 45
D
Question: P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 140 days, in how many days can R alone complete the remaining work?
A.50 days
B.102.7 days
C.100 days
D.150 days
Answer: B.102.7 days
Explanation: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 390 days
P works for 60 days--> 60/200 work done => 30%
Q works for 140 days--> 140/250 work done => 56%
260% work left ... R alone will take 26% * 395 = 102.7 days
Answer is (B)
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of b - a ?
A.-10
B.10
C.-19
D.20
Answer: A.-10
Explanation: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
B - A = 100 - 110 = -10
Ans :A
Question: The successive discounts 20% and 15% are equal to a single discount of?
A.22
B.27
C.32
D.997
Answer: C.32
Explanation: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.Answer: C
Question: Find the mean proportional between 25 & 36?
A.A)59
B.B)30
C.C)63
D.D)65
Answer: B.B)30
Explanation: Formula = √a×b
A = 25 and B = 36
√25×36 = 5 × 6 = 30
B
Question: What is the units digit of 222^(333)*333^(222)?
A.0
B.2
C.4
D.6
Answer: C.4
Explanation: Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 4.
Final Answer:
C
Question: The simple interest on Rs. 26 for 6 months at the rate of 7 paise per rupeeper month is
A.1.2
B.10.92
C.12.98
D.12.38
Answer: B.10.92
Explanation: Sol.
S.I. = Rs. [26 * 7/100 * 6] = Rs. 10.92
Answer B
Question: 1*2+ 2*2^2+ 3*2^3+ 4*2^4……………………+2012*2^2012
A.8100312
B.8100313
C.8100412
D.8200312
Answer: A.8100312
Explanation: take 2 outside as common
we get 2(1+2*1^2+3*1^3+.........2012*1^2012)
then 2(1+2+.....2012)
we get 8100312
ANSWER:A
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
A.338
B.187
C.120
D.882
Answer: C.120
Explanation: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C
Question: There are 20 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
A.10
B.30
C.190
D.60
Answer: C.190
Explanation: 20 players are there.
two players play one game with one another.
so 20C2=20*19/2
=190
SO OPTION C is correct
Question: In a sequence, each term is obtained by adding 7 to the preceding one. If the sum of the first 30 terms is equal to 705, what is the result of the addition of the first 40 terms?
A.2000
B.2250
C.2340
D.2400
Answer: C.2340
Explanation: a is first term and d = 7 since the preceding number is always greater than the previous one..
Now 30th term is a+29(7).
Sum of n terms is n/2(first term + last term)and here we have to get sum of 30 terms , we get 30/2 ( a + a+203) = 705 ( given sum of 30 terms is 705)
=> 15(2a+203) = 705
=> 2a+203 = 47
=> 2a=-156
=> a = -78
Now to get sum of first 40 terms , we need to get 40th term value i.e. -78+39(7) = 195.
Sum of first 40 terms = 40/2( -78 + 195) =2340 .
Hence option C is correct answer..
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
A. 0.22
B. 0.44
C. 0.55
D. 22
Answer: D. 22
Explanation: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents.
Answer: D.
Question: A cube of side two meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
A.2878
B.2778
C.1000
D.8000
Answer: D.8000
Explanation: Along one edge, the number of small cubes that can be cut
=200/10 = 20
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 20 * 20 * 20 = 8000
Answer: D
Question: If x is a whole number, then x²(x² - 1) is always divisible by
A.multiple of 12
B.24
C.12 - x
D.12
Answer: D.12
Explanation: Solution
Putting x = 12,we get 2²(2² - 1)	= 12.
So, x²(x² - 1) is always divisible by 12.
Answer D
Question: For how many positive integers is the number of positive divisors equal to the number itself ?
A.none
B.one
C.two
D.three
Answer: B.one
Explanation: The factors of 1: {1}. 1 factor. WORKS!
The factors of 2: {1,2}, 2 factors. WORKS!
The factors of 3: {1,3}, 2 factors. Doesn't work
The factors of 4: {1,2,4}, 3 factors. Doesn't work
As we can see, if an integer n has n factors, then the factors of n must be: {1, 2, 3,....., n)
So, we can quickly see that the only positive integers that meet this criterion are 1 and 2
Answer:B
Question: If the average (arithmetic mean) of x^2, 2x^2, and 3x^2 is 200, what is the value of x?
A.10
B.12
C.15
D.20
Answer: A.10
Explanation: AM of x^2, 2x^2 and 3x^2 = x^2 + 2x^2 + 3x^2 / 3 = 6x^2/3
Given that 2x^2 = 200
x^2 = 100
x = 10
Answer is A
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
A.5/5
B.5/9
C.5/21
D.5/98
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Question: Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in.
A.40 min
B.25 min
C.54 min
D.65 min
Answer: C.54 min
Explanation: Distance = Speed * time
3*20/3= 20km
New Speed = 18 kmph
Therefore time = 20/18 = 10/9= 54min
Answer : C.
Question: The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 5 guards.
To choose 2 out of 5, we will have 5C2 = 10 different pairs.
The answer is C.
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
A.3/7
B.4/9
C.4/7
D.5/11
Answer: C.4/7
Explanation: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
C)