RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 20 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week?
A.4
B.3
C.2
D.5
Answer: C.2
Explanation: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 20 T-C=10 -> T= 15. C=5.
Mo drinks 3 cups of tea a day then number of days that are not rainy = 15/3 = 5
So number of rainy days = 7-5 = 2
C is the answer.
Question: A company, Chauncy Co., has an annual travel budget of $55,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on non transportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
A.Expenses will not go over the budget.
B.$500
C.$4,225
D.$5,725
Answer: D.$5,725
Explanation: Annual travel budget of $55,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 55000-60725 = 5725
Answer: Option D
Question: A train moves with a speed of 108 kmph. Its speed in metres per second is
A.10.8
B.18
C.30
D.38.8
Answer: C.30
Explanation: Solution
Speed	= 108 Kmph
= (108 x 5/18)m/sec
= 30 m/sec.
Answer C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire?
A.2 meters
B.4 meters
C.5 meters
D.3 meters
Answer: B.4 meters
Explanation: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 96,000 m : C is the circumference
C = 4 meters
correct answer B
Question: In how many years, Rs. 150 will produce the same interest at 6% as Rs. 500 produce in 2 years at 4½% ?
A.4 years
B.5 years
C.8 years
D.9 years
Answer: B.5 years
Explanation: Explanation :
Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.500 at 4½ % for 2 years
150×6×n/100=500×9/2×2/100
150×6×n=500×9/2×2
150×6×n=500×9
n=5 years
Answer : Option B
Question: Along a yard 414 metres long, 24 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
A.18
B.19
C.10
D.11
Answer: A.18
Explanation: Explanation:
24 trees have 23 gaps between them,
Required distance (414/23) = 18
Option A
Question: If 7 and 11 are prime numbers, which of the following CANNOT be the sum of a and b?
A.18
B.36
C.19
D.54
Answer: C.19
Explanation: ANS = C
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 240 m in length?
A.18.9 sec
B.88.9 sec
C.22.9 sec
D.21.00 sec
Answer: D.21.00 sec
Explanation: D = 110 + 240 = 350 m
S = 60 * 5/18 = 50/3
T = 350 * 3/50 = 21.00 sec
Answer: D
Question: An investor deposited $5,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
A.$5050
B.$5101
C.$5202
D.$5303
Answer: C.$5202
Explanation: The amount in the account after 6 months is 1.02*1.02($5,000) = $5202
The answer is C.
Question: The number of years of service of the eight employees in a production department are 15, 10, 9, 17, 6, 8, 14 and 16. What is the range in the number of years of service of the eight employees?
A.10
B.11
C.12
D.13
Answer: B.11
Explanation: = 17-6
= 11
Answer B
Question: How many litres of pure acid are there in 8 litres of a 20% solution
A.1.5
B.1.6
C.1.7
D.1.8
Answer: B.1.6
Explanation: Explanation:
Question of this type looks a bit typical, but it is too simple, as below...
It will be 8 * 20/100 = 1.6
Answer: Option B
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 20% of all the students at Morse have cars, how many students are in the three lower grades?
A.600
B.900
C.1200
D.1350
Answer: B.900
Explanation: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.2(x+300)
0.1x = 900
x = 900
The answer is B.
Question: A garrison of 2000 men has provisions for 60 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
A.1500
B.1893
C.1979
D.1900
Answer: A.1500
Explanation: 2000 ---- 60
2000 ---- 45
x ----- 20
x*20 = 2000*45
x = 4500
2000
-------
1500
Answer: A
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent Q of her bushes have only yellow roses?
A.20
B.30
C.50
D.70
Answer: B.30
Explanation: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, 0.8T+x=T
x=0.2T
so,Q= 1.5x=0.3T
30% flowers are yellow flowers
OA B
Question: During the months May through October, Teddy the bear septuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
A.49m - 1300
B.49m - 1200
C.7m - 1300
D.7m - 1200
Answer: A.49m - 1300
Explanation: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 7m - 300
April' 75 = 7m - 400
Oct' 75 = 49m - 1200
April'76 = 49m - 1300
Hence answer will be (A) 49m - 1300
Question: A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/2 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
A.2.5%
B.20%
C.28.3%
D.45.2%
Answer: B.20%
Explanation: Fiction Novels = 5,508
Transferred to another location = 6,120
Transferred fiction novels = 3,060
Non Transferred Fiction Novels = 2,448
Percent of the remaining collection was fiction novels = 2,448/(18360 - 6120 ) * 100 => 20%
Hence answer will be (B)
Question: Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 35-ounce cans or 25-ounce cans of chili paste. If the restaurant must order 20 more of the smaller cans than the larger cans to fulfill its weekly needs, then how manysmallercans are required to fulfill its weekly needs?
A.60
B.70
C.80
D.100
Answer: B.70
Explanation: let x be the number of 35 ounce cans. Therefore (x+20) is the number of 25 ounce cans.
Total volume is same, therefore
35x=25(x+20)
10x=500
x=50
Therefore, number of 15 ounce cans=50+20=70
Ans - B
Question: Evaluate 30!/28!
A.720
B.600
C.870
D.910
Answer: C.870
Explanation: we have 30!/28! = 30*29*28!/28! = 30*29 = 870
Answer is C
Question: Last year the price per share of Stock Y increased by s percent and the earnings per share of Stock Y increased by t percent, where s is greater than t. By what percent did the ratio of price per share to earnings per share increase, in terms of s and t?
A.[100(s – t)] / (100 + s + t) %
B.[100(s – t)] / (100 + s) %
C.100*(s-t)/(100+t) %
D.(s – t) %
Answer: C.100*(s-t)/(100+t) %
Explanation: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+s/100) and the new earning is: E*(1 + t/100)
The new P/E is: (1+s/100)P/(1+t/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+s/100)/(1+t/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(s-t)/(100+t) % Answer : C
Question: The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?
A.0.2
B.0.25
C.0.3
D.0.35
Answer: D.0.35
Explanation: Blood group -	frequency
A - 50
B - 65
O - 70
AB - 15
Let P(E) be the event of getting O blood group
P(E) = Frequency for O blood group / Total frequencies in the above table
= 70 / (65+50+70+15)
= 70 / 200
= 0.35
My answer is (D)
Question: How much time will 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
A.7 years
B.4 years
C.5 years
D.3 years
Answer: B.4 years
Explanation: Time = (100 * 81) / (450 * 4.5) = 4 years.Answer:B
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE.
A.110
B.112
C.114
D.116
Answer: C.114
Explanation: Total no' of arrangements 5P5 = 5! = 120
no' of arrangements start with AE = 1 × 6 = 6
no' of arrangements which do not start with AE = 120 - 6 = 114.
C
Question: What is the present worth of Rs. 198 due in 2 years at 5% simple interest per annum?
A.128
B.277
C.180
D.888
Answer: C.180
Explanation: Let the present worth be Rs. x. Then,
S.I. = (198 - x)
(x * 5 * 2) / 100 = (198 - x)
10x = 19800 - 100x
110x = 19800 => x = 180.
Answer: C
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 20 Gallons of water and 40 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
A.300
B.75
C.100
D.150
Answer: A.300
Explanation: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 40 gallons salt is added and 20 gallons of water is added.
So salt now becomes -> (0.2x + 40) and water --> (0.6x+20)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+40) = (0.6x+20)/2 => 0.4x+80 =0.6x+20 =>0.2x =60
Solving, x = 300
Answer : A
Question: Two partners (Pella and Leon) invested Rs.7000 and Rs.18000, respectively in a business. Pella runs the business while Leon is a sleeping partner in the business. Pella receives 6% of the profit for managing the business the rest is divided in proportion of their capitals. Out of a total profit of Rs.8500, how much did Pella receive?
A.3004.84
B.3019.84
C.2747.2
D.3059.84
Answer: C.2747.2
Explanation: ratio of their investments Rs.7000:18000=7:18
6% of the profit for managing the business =6/100*8500=510
remaining profit=8500-510=7990
share profit in ratio of investment 7990/25 =319.6
Pella's ratio share=7*319.6=2237.2
total money Ben collects=2237.2+510=2747.2
Answer: C
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 20,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
A.1 million
B.1.25 million
C.10 million
D.12.7 million
Answer: D.12.7 million
Explanation: If you type that into the calculator, it results in 12.8 mil
[D], 12.7 mil, is the correct answer... see 2 posts above for quick approx method
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
A.9
B.8!
C.5
D.7
Answer: B.8!
Explanation: Total number of letters = 8
Using these letters the number of 8 letters words formed is 8P8
= 8!.
Answer:B
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
A.87
B.78
C.25
D.17
Answer: C.25
Explanation: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100
= (100 * 30)/40 = 25 * 3
= 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer:C
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
A.100 m
B.190 m
C.115 m
D.110 m
Answer: A.100 m
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 6 = 100 m
Answer: A
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59___?
A.35
B.36
C.37
D.71
Answer: D.71
Explanation: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 59 + 12 = 71.
correct answer D)71
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
A.16%
B.16.66%
C.16.69%
D.16.98%
Answer: B.16.66%
Explanation: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
A.15 m, 12 m
B.15 m, 11 m
C.15 m, 20 m
D.15 m, 10 m
Answer: D.15 m, 10 m
Explanation: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
D
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
A.88 Kmph
B.89 Kmph
C.72 Kmph
D.16 Kmph
Answer: C.72 Kmph
Explanation: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Question: Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
A.30%
B.100/3%
C.35%
D.44%
Answer: D.44%
Explanation: Some articles were bought at 6 articles for Rs. 5
and sold at 5 articles for Rs. 6.
6 articles are sold for Rs 6*6/5= Rs 36/5
profit on Rs 5 = 36/5 -5 = Rs. 11/5
% profit = 100*(11/5)/5 = 100*11/25 = 44%
ANSWER:D
Question: (17)4.25 x (17)? = 178
A.2.29
B.2.75
C.4.25
D.3.75
Answer: D.3.75
Explanation: Solution
let (17)4.25 * (17)x = 178. then, (17)4.25 + x = (17)8.
∴ 4.25 + x = 8 ⇔ x = (8 - 4.25) ⇔ x = 3.75
Answer D
Question: A number x is multiplied by 3, and this product is then divided by 7. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ?
A.25/9
B.3/7
C.5/3
D.3/5
Answer: B.3/7
Explanation: sqrt(3x/7) to be perfect square x has to 3/7
Ans: B
Question: If m=m6−−√m=m6 , which of the following could be the value of m?
A.1/6
B.6
C.36
D.63
Answer: D.63
Explanation: Volume of a sphere = 4/3*pi.R^3
Surface area of a sphere = 4*pi.R^2
given V = 2SA
4/3*pi.R^3 =2* 4*pi.R^2
=> R =6
Option D
Question: Four children — A, B, C, and D — are going to sit in four chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?
A.6
B.12
C.18
D.24
Answer: B.12
Explanation: The number of ways to seat 4 people is 4! = 24.
Child C will sit to the left of Child D in exactly half of these arrangements.
The total number of possible arrangements is 24/2 = 12
The answer is B.
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 210, what is the least possible value of n?
A.7
B.9
C.11
D.13
Answer: A.7
Explanation: 210 = 2*3*5*7, so n must be at least 7.
The answer is A.
Question: If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
A.483
B.720
C.885
D.645
Answer: B.720
Explanation: Let x be the number of days in the initial plan. Therefore, the whole field is 120⋅x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
120x=85(x+2)+40
35x=210
x=6
So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720 hectares.
correct answer is B)720
Question: In one hour,a boat goes 8 km along the stream and 2 km against the stream.The speed of the boat in still water (in km/hr) is :
A.3
B.5
C.8
D.9
Answer: B.5
Explanation: Solution
Speed in still water =1/2(8+2)kmph.= 5 kmph. Answer B
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999 ?
A.Rs.45,000
B.Rs.60,000
C.Rs.70,000
D.Rs.75,000
Answer: B.Rs.60,000
Explanation: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(18000x2/6) = Rs. 60,000. Answer B
Question: A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
A.10
B.15
C.21
D.36
Answer: A.10
Explanation: Since the order in which we select the socks does not matter, we can use combinations.
We can select 2 socks from 5 socks in 5C2 ways.
5C2 = 10
Answer : A
Question: Find the area of circle whose radius is 7m?
A.209
B.154
C.278
D.265
Answer: B.154
Explanation: 22/7 * 7 * 7 = 154
Answer: B
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 100 and n is not prime, what is the greatest possible value of f(n)?
A.99
B.95
C.91
D.87
Answer: B.95
Explanation: A) 99 = 11*3*3 ( 99 is not product of distinct primes. 3 is repeated). so can't be the answer.
B)95 = 5*19
C)91 = 7*13
D) 87 is prime, so cannot be the answer
E) 78 = 13*2*3
largest possible n is B.
Answer is B.
Question: how many positive integers less than 9999 are such that the product of their digits is 210.
A.24
B.58
C.26
D.34
Answer: A.24
Explanation: The prime factorization of 210 is 2*3*5*7. So one way to make the right kind of number is to use those four digits, in any of the 4! = 24 orders you can put them in.
Notice though that we can also get 210 as a product by multiplying 5, 6 and 7. So we can make some 3-digit numbers with the right product: 3! = 6 of them to be exact.
But we can also get the right product using the digit 1 along with the digits 5, 6, and 7. Again we can arrange those digits in 4! = 24 orders.
A
Question: The contents of a certain box consist of 24 apples and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be apples?
A. 24
B. 26
C. 30
D. 46
Answer: B. 26
Explanation: apples = (apples + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
A.34
B.28
C.12
D.17
Answer: B.28
Explanation: Explanation:
Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
ANSWER IS B
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.Rs.3948
B.Rs.3929
C.Rs.3927
D.Rs.3900
Answer: D.Rs.3900
Explanation: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Question: For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 7 of whom are females, by how much does the index for the females exceed the index for the males in the group?
A. 0.05
B. 0.0625
C. 0.2
D. 0.3
Answer: D. 0.3
Explanation: Index for females = (20-7)/20 = 13/20 = 0.65
Index for males = (20-13/20 = 7/20 = 0.35
Index for females exceeds males by 0.65 - 0.35 = 0.3
Answer: D
Question: In an increasing sequence of 3 consecutive integers, the sum of the first 2 integers is 561. What is last integer in the sequence?
A. 281
B. 282
C. 275
D. 270
Answer: B. 282
Explanation: Solution:
In solving this problem we must first remember that when we have 3 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
We are given that the sum of the first 2 integers is 560. This means that:
x + x+1 = 561
2x + 1 = 561
2x = 560
x = 280
the last integer can be expressed and simplified as:
x+2 = 280+2
= 282
Answer: B
Question: A person borrows Rs. 9000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
A.100 rs
B.150 rs
C.160 rs
D.180 rs
Answer: D.180 rs
Explanation: Gain in 2 years =
[(9000*6*2)/100]-[(9000*4*2)/100]
1080-720=360
Gain in 1 year =(360/2)=180 rs
ANSWER:D
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 276. What is their H.C.F.?
A.18
B.23
C.28
D.32
Answer: B.23
Explanation: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 276
x = 23
HCF of 2x, 3x and 4x = x = 23
The answer is B.
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
A.1/6
B.1/7
C.1/8
D.1/11
Answer: A.1/6
Explanation: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
A
Question: If the number of 741,61n, where n represents the ones digit, is a multiple of 3, then the value of n could be which of the following?
A.7
B.6
C.5
D.4
Answer: C.5
Explanation: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.
i.e 7+4+1+6+1+n= multiple of 3
or, 19 + n = multiple of 3.
If n=5, 19 + n =24,which is a multiple of 3.
Hence answer is C.
Question: If a-b= 8 and a^2+b^2=164, find the value of ab
A.10
B.12
C.50
D.18
Answer: C.50
Explanation: 2ab = (a^2 + b^2) - (a - b)^2
= 164 - 64 = 100
=> ab = 50
ANSWER: C
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
A.1/2
B.2/3
C.3/5
D.4/7
Answer: A.1/2
Explanation: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)