RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If 7 cats can kill 7 rats in 7 minutes, how long will it take 100 cats to kill 100 rats?
A.5 minutes
B.6 minutes
C.7 minutes
D.8 minutes
Answer: C.7 minutes
Explanation: It will take 7 minutes for 100 cats to kill 100 rats.
1 cat can kill 1 rat in 7 minutes, so 100 cats can kill 100 rats in 7 minutes
Answer C
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
A.4%
B.4.04%
C.4.15%
D.4.34%
Answer: B.4.04%
Explanation: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Question: A train covers a distance of 12 km in 10 min. If it takes 11 sec to pass a telegraph post, then the length of the train is?
A.177 m
B.189 m
C.220 m
D.178 m
Answer: C.220 m
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 11
= 220 m.
Answer: C
Question: A cricketer scored 152 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
A.46.2%
B.54.54 %
C.60.52%
D.70%
Answer: C.60.52%
Explanation: Explanation :
Number of runs made by running = 152 - (12 x 4 + 2 x 6)
= 152 - (60)
= 92
Now, we need to calculate 92 is what percent of 152.
=> 92/152 * 100 = 60.52 %
Answer : C
Question: Michael is interested in dividing all of his boxed food equally among the shelves in his pantry. Unfortunately, the boxes don't divide evenly. It turns out that Michael will need to add three more shelves to the pantry and throw away four boxes of food. Which of the following can describe the initial number of boxes of food and the initial number of pantry shelves (in the order boxes of food; shelves)?
A.71; 4.
B.28; 6.
C.65; 7.
D.53; 4.
Answer: D.53; 4.
Explanation: Option D.) Initially 53 boxes of food then reduced to 49 boxes of food; and Initially 4 pantry shelves then increased to 7 pantry shelves.
49 / 7 = 7 boxes of food per pantry shelf.
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 44 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is :
A.39.6
B.43
C.40
D.38
Answer: A.39.6
Explanation: Solution: Average speed = 2XY / X+Y
= 2*44*36 / 44+36
= 39.6
Answer : A
Question: If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
6 = 36
Then 24 = ?
Hint: Its a logic Riddle not a mathematical riddle
A.1
B.2
C.4
D.6
Answer: C.4
Explanation: C
24
As stated
4=24 => 24=4
Answer is C
Question: What amount does Kiran get if he invests Rs.7680 at 8% p.a. compound interest for two years, compounding done annually?
A.8957
B.8978
C.7890
D.3408
Answer: A.8957
Explanation: A= P{1 + R/100}n
=> 7680{1 + 8/100}2
= Rs.8957
Answer: A
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 294, what is the least possible value of n?
A.8
B.10
C.12
D.14
Answer: D.14
Explanation: 294 = 2*3*7*7, so n must be at least 14.
The answer is D.
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 20p, in terms of p?
A.p
B.2p
C.5p
D.10p
Answer: D.10p
Explanation: y = 30p = 2*3*5*p
20p = 2^2*5*p
The greatest common factor of 30p and 20p is the product of all the common prime factors, using the lower power of repeated factors. The greatest common factor is 2*5*p = 10p
The answer is D.
Question: If A`s salary is 20% less then B`s salary , by how much percent is B`s salary more than A`s ?
A.15%
B.41%
C.37%
D.25%
Answer: D.25%
Explanation: Required percentage = [(20*100)/(100-20)]%=25%.
Answer is D.
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
A.76
B.28
C.23
D.98
Answer: C.23
Explanation: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer:C
Question: 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container M?
A.A:45
B.B:25
C.C:37.5
D.D:36
Answer: C.C:37.5
Explanation: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.
1st Replacement
After the first replacement you have 37.5-15=22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.
The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.
Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.
Final Replacement
The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.
Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. Choice C is correct.
Question: A train 150 m long crosses a platform 130 m long in 20 sec; find the speed of the train?
A.50
B.60
C.55
D.45
Answer: A.50
Explanation: D = 150 + 130 = 280
T = 20
S = 280/20 * 18/5 = 50 kmph.
Answer: A
Question: If 5 - 5/X = 4 + 4/X, then X =
A.1
B.9
C.-1
D.5/4
Answer: B.9
Explanation: We're given the equation 5 - 5/X = 4 + 4/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
5X - 5X/X = 4X + 4X/X
We can then eliminate that denominator, which gives us....
5X - 5 = 4X + 4
9 = X
B
Question: A dice is rolled twice. What is the probability of getting sum 9?
A.1/9
B.1/8
C.1/7
D.1/5
Answer: A.1/9
Explanation: Explanation:
Possible event = 6*6 = 36
Favourable outcomes= {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Thus probability; favourable/total
= 4/36
=> 1/9
ANSWER: A
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
A.20%
B.25%
C.33.33%
D.40%
Answer: A.20%
Explanation: 100 * (b + f) - 100 * b = (25/100) * 100 * b
b = 4 * f
Percentage of f = (f / (b + f)) * 100 = (f/5f) * 100 = 20%
ANSWER:A
Question: What number is obtained by adding the units digits of 734^98 and 347^81?
A.10
B.11
C.12
D.13
Answer: D.13
Explanation: The units digit of 734^98 is 6 because 4 raised to the power of an even integer ends in 6.
The units digit of 347^81 is 7 because powers of 7 end in 7, 9, 3 or 1 cyclically. Since 81 is in the form 4n+1, the units digit is 7.
Then 6+7 = 13.
The answer is D.
Question: If c is 25% of a and 50% of b, what percent of a is b?
A. 2.5%
B. 50%
C. 25%
D. 35%
Answer: B. 50%
Explanation: Answer = B
25a/100 = 50b/100
b = 25a/50 = 50a/100 =50%
Question: A is twice as fast as B. If B alone can do a piece of work in 10 days, in what time can A and B together complete the work?
A.10/3
B.8
C.9
D.7/3
Answer: A.10/3
Explanation: A can do the work in10/2 i.e., 5 days.
A and B's one day's work = 1/5+ 1/10 = (2 + 1)/10 = 10/3
So A and B together can do the work in 10/3 days.
Answer: A
Question: If a carpenter completes 3/8th of his work in 6 days, then how many more days will he require completing his remaining work?
A.10
B.99
C.77
D.66
Answer: A.10
Explanation: Explanation:
As 3/8th of the work is completed, the work remaining is 5/8th of the total.
(3/8):6::(5/8):x
x = 6*(5/8)/(3/8)
x = 10
ANSWER: A
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $141 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
A.5
B.7
C.9
D.11
Answer: C.9
Explanation: $141 = 27*$5 + 2*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 27, 24, 21, 18, 15,...,3 for a total of 9 combinations.
The answer is C.
Question: Evaluate:59- 12*3*2 =?
A.42
B.51
C.62
D.72
Answer: B.51
Explanation: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
59 - 12*3*2 = 59- 8 = 51
correct answer B
Question: Meg and Bob are among the 3 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
A.24
B.30
C.3
D.90
Answer: C.3
Explanation: Total # of ways the race can be finished is 3!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 3!/2=3.
Answer: C.
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the smallest sector?
A.1/72
B.1/36
C.1/18
D.1/12
Answer: B.1/36
Explanation: Largest angle = 80
Let, Difference between any two angles in A.P. = d
i.e. Sum of all angles will be
80 + (80-d) + (80-2d) + (80-3d) + (80-4d) + (80-5d) + (80-6d) + (80-7d) = 640 - 28d
But sum of all central angles in a circle = 360
i.e. 640 - 28d = 360
i.e. d = 280/28 = 10
Smallest Sector = (80-7d) = 80-7*10 = 10
Smallest sector as Fraction of entire circle = 10/360 = 1/36
Answer: option B
Question: If the equation x^2−6x=-k has at least one solution, which of the following must be true?
A.k > 9
B.k < −9
C.k = 9
D.k ≤ 9
Answer: D.k ≤ 9
Explanation: x^2−6x=-k
=> x^2−6x + k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 36 - 4*1*(-k) ≥0
=> 36 - 4k ≥0
=> k ≤9
Answer D
Question: Look at this series: 544, 509, 474, 439, 404 ... What number should come next?
A.206
B.408
C.369
D.507
Answer: C.369
Explanation: 369
This is a simple subtraction series. Each number is 35 less than the previous number.
C
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days?
A.65mtr.
B.52mtr
C.70mtr.
D.112mtr.
Answer: D.112mtr.
Explanation: 20 men is 6 days can build 112 metres
25 men in 3 days can build = 112*(40/20)x(3/6)
= 112 meters
Answer: D.
Question: Sherlock Homes and Dr. Watson have to travel from Rajeev Gandhi chowk to Indira
Gandhi International Airport via the metro. They have enough coins of 1, 5, 10 and 25
paise. Sherlock Homes agree to pay for Dr. Watson only if he tells all the possible
combinations of coins that can be used to pay for the ticket.
How many combinations are possible if the fare is 50 paise ?
A.52
B.49
C.45
D.44
Answer: B.49
Explanation: Let the number of 1, 5, 10 and 50 paise coins required are x, y, z and w respectively.
So when paid total amount is: x + 5y + 10z + 25w, which is equal to the fare paid.
So, x + 5y + 10z + 25w = 50
The number of non negative integral solution of this equation will be equal to the
number of ways the fare can be paid.
x + 5y + 10z + 25w = 50
In this equation w can be either 0, 1 or 2
Case 1: When w is 2
No other coins are required to pay
So there is only one way to pay: (0, 0, 0, 2)
Total no of ways : 1
Case 2: When w is 1
x + 5y + 10z = 25
In this case z can have only three values possible: 0, 1 or 2
Case I: When z is 0
x + 5y = 25
possible values are: (25, 0, 0, 1), (20, 1, 0, 1), (15, 2, 0, 1), (10, 3, 0, 1),
(5, 4, 0, 1), (0, 5, 0, 1)
Case II: When z is 1
x + 5y = 15
possible values are: (15, 0, 1, 1), (10, 1, 1, 1), (5, 2, 1, 1), (0, 3, 1, 1)
Case III: When z is 2
x + 5y = 5
possible values are: (5, 0, 2, 1), (0, 1, 2, 1)
Total no of ways : 12
Case 3: When w is 0
x + 5y + 10z = 50
In this case z can have only three values possible: 0, 1, 2, 3, 4 or 5
Case I: When z is 0
x + 5y = 50
possible values are: (50, 0, 0, 0), (45, 1, 0, 0), (40, 2, 0, 0), (35, 3, 0, 0),
(30, 4, 0, 0), (25, 5, 0, 0), (20, 6, 0, 0), (15, 7, 0, 0), (10, 8, 0, 0), (5, 9, 0, 0),
(0, 10, 0, 0)
Case II: When z is 1
x + 5y = 40
possible values are: (40, 0, 1, 0), (35, 1, 1, 0), (30, 2, 1, 0), (25, 3, 1, 0),
(20, 4, 1, 0), (15, 5, 1, 0), (10, 6, 1, 0), (5, 7, 1, 0), (0, 8, 1, 0)
Case III: When z is 2
x + 5y = 30
possible values are: (30, 0, 2, 0), (25, 1, 2, 0), (20, 2, 2, 0), (15, 3, 2, 0),
(10, 4, 2, 0), (5, 5, 2, 0), (0, 6, 2, 0)
Case IV: When z is 3
x + 5y = 20
possible values are: (20, 0, 3, 0), (15, 1, 3, 0), (10, 2, 3, 0), (5, 3, 3, 0), (0,
4, 3, 0)
Case V: When z is 4
x + 5y = 10
possible values are: (10, 0, 4, 0), (5, 1, 4, 0), (0, 2, 4, 0)
Case VI: When z is 5
1 2 3 4 5 6 7 8 9
x + 5y = 0
possible values are: (0, 0, 5, 0)
Total no of ways : 36
So total no of ways = 1 + 12 + 36 = 49
ANSWER:B
Question: Nirmal and Kapil started a business investing Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4600, what was Kapil’s share initially ?
A.Rs 2300
B.Rs 2400
C.Rs 2500
D.None of above
Answer: A.Rs 2300
Explanation: Explanation:
Nirmal:Kapil = 9000*12:(12000*6+6000*6) = 1:1
Kapils share = Rs. [4600 *(1/2)) = Rs. 2300
Option A
Question: There are t members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of t?
A.11
B.12
C.15
D.18
Answer: B.12
Explanation: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, t = m + 1(Michael) = 12
option B
Question: There are 7 cups placed on a table; 4 are juice cups and the other 3 are tea cups. If 2 cups are to be selected at random from the 7 cups, what is the probability that at least one of the juice cup will be selected?
A.6/7
B.2/7
C.3/7
D.4/7
Answer: A.6/7
Explanation: Total probability=7C2=21
4C2 +4C1*3C1=6+12=18
therefore the probability that at least one of the fashion magazines will be selected= 18/21=6/7
answer is A
Question: The positive integers a and b leave remainders of 4 and 7, respectively, when divided by 9. What is the remainder when a − 2b is divided by 9?
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: a=9x+4
so a could be 4, 13,22, 31,40,49,58,67,76,85
b=9y + 7
so b could be 7,16,25,34,43
Selecting any random number for a and b such that a-2b is positive number,
say a=22, b=7 => 2b=14
Hence a-2b = 8 Hence remainder when divided by 9 =8
say a=67, b=25 => 2b=50
Hence a-2b = 17 Hence remainder when divided by 9 is again 8
say a=49, b=7 => 2b=14
Hence a-2b = 35 Hence remainder when divided by 9 is again 8
Answer is 8.
ANSWER:D
Question: A certain sum becomes four times itself at simple interest in nine years. In how many years does it become ten times itself?
A.27 years.
B.25 years.
C.29 years.
D.17 years.
Answer: A.27 years.
Explanation: Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.
R = (100 * 3x)/(x * 9) = 100/3 %
If the sum becomes ten times itself, then interest is 9x.
The required time period = (100 * 9x)/(x * 100/3) = (100 * 9x * 3)/(x * 300) = 27 years.
ANSWER:A
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7400 less if they could find two more equal investors. How much is the total investment in the new business.
A.a)	$ 64,000
B.b)	$ 54,000
C.c)	$ 55,500
D.d)	$ 5,400
Answer: C.c)	$ 55,500
Explanation: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7400).
3x = 5(x-7400)
x= 5*7400/2 = 18500
3x = 55500 and the answer is C.
Question: A box contain the number of balls which is as much greater than 20 is less than 30. The number of balls is?
A.40
B.25
C.30
D.50
Answer: B.25
Explanation: Answer
Let the number be x.
Then, x - 20 = 30- x
â‡’ 2x = 30+ 20= 50
â‡’ 2x = 50
âˆ´ x = 25
Correct Option: B
Question: If x is even and y is odd, then x-y
A.Even whenever xy is odd
B.Odd
C.Odd whenever xy is even
D.Even
Answer: B.Odd
Explanation: x is even and y is odd, then x + y is
Let's take x=4 and y=7.
x+y=4+7=11.
x+y=11=odd.
Option: B
Question: The price of 2 saris and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A.Rs. 2200
B.Rs. 2300
C.Rs. 2400
D.Rs. 2480
Answer: C.Rs. 2400
Explanation: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
C
Question: The average of weight of three men A,B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg.more than that of D, replaces A, then the average weight of B,C,D and E becomes 79 kg. The weight of A is :
A.70 kg
B.72 kg
C.75 kg
D.80 kg
Answer: C.75 kg
Explanation: Explanation:
A+B+C = 3×84=252
A+B+C+D= (4×80)=320
D = (320-252)=68 and E = (68+3)=71
Now, B+C+D+E = (4×79)=316
B+C+D=(316-71)=245 kg
So, A = (320-245)=75 kg
Correct Option: C
Question: The floor of a rectangular room is 15 m long and 12 m wide. The room is surrounded by a verandah of width 2 m on all its sides. The area of the verandah is :
A.124 m2
B.120 m2
C.108 m2
D.58 m2
Answer: A.124 m2
Explanation: Area of the outer rectangle = 19 × 16 = 304 m2
Area of the inner rectangle = 15 × 12 = 180 m2
Required area = (304 – 180) = 124 m2
Answer A
Question: If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: Let 1 men's 1 day work = x and 1 boy's 1 day work = y.
Then, 6x + 8y = 1/10 and 26x + 48y = 1/2
Solving these two equations, we get:
x = 1/100 and y = 1/200
(15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4
15 men and 20 boys can do the work in 4 days.
Answer:A
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits S equal to 28?
A.14
B.24
C.28
D.48
Answer: D.48
Explanation: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So S=24+24=48.D
Question: Exactly three sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll?
A.0.184
B.0.16
C.0.18
D.0.147
Answer: D.0.147
Explanation: Total no. of sides = 10
Sides that are red =3
Probability that the die lands with red side up = 3/10
Therefore, Probability that the die does not land with red side up = 1 - 3/10 = 7/10
Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll
= (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face)
= (7/10) X (7/10) X (3/10)
= 128/1000
= 0.147
D
Question: The value of Underrot 32pi/4 + Underrot 25 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)
A.6
B.35
C.41
D.30
Answer: D.30
Explanation: Under root (32pi/4) ~ 25
Under root (25) = 5
Hence, 25+5 = 30 is the approx answer. D is the correct answer.
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
A.3.6
B.7.2
C.8.4
D.10
Answer: B.7.2
Explanation: Speed =(600/5*60)m/sec.
= 2 m/sec.
Converting m/sec to km/hr
=(2*18)/5	km/hr
=7.2 km/hr.
Answer:B
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
A.3 1/3%
B.8 1/3%
C.3 5/3%
D.5 1/3%
Answer: A.3 1/3%
Explanation: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Question: A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
A. 1/14
B. 1/7
C. 2/7
D. 5/7
Answer: D. 5/7
Explanation: Total ways to choose 4 employees from 8 employees = 8C3
Two women = 5C2
Two Men = 3C1
P = (5C2 * 3C1)/8C2 = 5/7 hence D.
Question: A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?
A.238
B.180
C.988
D.177
Answer: B.180
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 120)/25 = x/15 => x = 180 m.
Answer: B
Question: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d|
A.10
B.12
C.15
D.18
Answer: B.12
Explanation: This is the hard one, definitely a 700+ level question. We need numbers a, b, c, and d such that
6x^2 + x - 12 = (ax + b)(cx + d)
This means that ac = 6, bd = –12, and ad + bc = 1. The a & c pair could be (1, 6) or (2, 3), in some order. The absolute values of the b & d pair could be (1, 12) or (2, 6) or (3, 4), and of course, in each case, one of the two would have to be negative. After some trial and error, we find:
6x^2 + x - 12 = (2x + 3)(3x - 4)
Thus, we see:
|a| + |b| + |c| + |d| = 2 + 3 + 3 + 4 = 12
Answer = B
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
A.3/15
B.3/10
C.3/11
D.3/12
Answer: C.3/11
Explanation: The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.Answer: C
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 3 times the probability that both events A and B occur. What is the probability that event A occurs?
A.44/7
B.9/8
C.25/8
D.3/4
Answer: D.3/4
Explanation: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 3 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 3*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 3*2b*b
3b-2b^2 = 6b^2
3b = 8b^2
b = 3/8 = 3/8
So, a = 2b = 3/4
THE CORRECT ANSWER IS D.