RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^20, then n =
A.3
B.6
C.19
D.23
Answer: C.19
Explanation: 2^2n + 2^2n + 2^2n + 2^2n = 4^20
=> 4 x 2^2n = 4^20 = 2^40
=> 2^2 x 2^2n = 2^40
=> 2^(2n+2) = 2^40
=> 2n+2 = 40=> n =19
So. Answer will be C.
Question: When a certain number X is divided by 63, the remainder is 25. What is the remainder when X is divided by 8?
A.1
B.3
C.4
D.5
Answer: A.1
Explanation: When a certain number X is divided by 63, the remainder is 25. What is the remainder when X is divided by 8?
Putting a value say x = 255 we get remainder as 25 when divided by 63.
When 25 divided by 8 we get 1 as remainder.
A is the answer.
Question: John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?
A.1/16
B.2/16
C.3/16
D.7/16
Answer: B.2/16
Explanation: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2 & #3 & #4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T ----> P = (1/2)^4 = 1/16
T-H-H-H ----> P = (1/2)^4 = 1/16
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/16 + 1/16 = 2/16
Answer (B).
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336
A.2
B.4
C.6
D.8
Answer: B.4
Explanation: 264 is divisible by 3, 4 and 11
=> 264 is divisible by 132
396 is divisible by 3, 4 and 11
=> 396 is divisible by 132
462 is divisible by 3 and 11, but not divisible by 4
=> 462 is not divisible by 132
792 is divisible by 3, 4 and 11
=> 792 is divisible by 132
968 is divisible by 4 and 11, but not divisible by 3
=> 968 is not divisible by 132
2178 is divisible by 3 and 11, but not divisible by 4
=> 2178 is not divisible by 132
5184 is divisible by 3 and 4, but not divisible by 11
=> 5184 is not divisible by 132
6336 is divisible by 3, 4 and 11
=> 6336 is divisible by 132
Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is 4
B)
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
A.100000
B.100500
C.105000
D.Data inadequate
Answer: C.105000
Explanation: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 5000) From the question,
(x - 500) × 126⁄100 = 6⁄5x ⇒ x = 105000
Answer C
Question: A man has some hens and cows. If the number of heads be 44 and the number of feet equals 128, then the number of hens will be
A.22
B.24
C.26
D.20
Answer: B.24
Explanation: Explanation :
Let number of hens = h and number of cows = c
number of heads = 44
=> h + c = 44 ---(Equation 1)
number of feet = 128
=> 2h + 4c = 128
=> h + 2c = 64 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 64 - 44
=> c = 20
Substituting the value of c in Equation 1, we get
h + 22 = 44
=> h = 44 - 20 = 24
i.e., number of hens = 24
Answer : B
Question: 4, 7, 16, 43, 124, (...)
A.22
B.367
C.27
D.32
Answer: B.367
Explanation: Explanation :
4
4 × 3 - 5 = 7
7 × 3 - 5 = 16
16 × 3 - 5 = 43
43 × 3 - 5 = 124
124 × 3 - 5 = 367
Answer : Option B
Question: The average of 11 results is 20. The average of first 5 of them is 15 and that of last 5 is 22 . Find the 6th result?
A.35
B.50
C.100
D.120
Answer: A.35
Explanation: 6th result = sum of 11 results - sum of 10 results
= 11*20-5*15-5*22
= 220-75-110
= 35
Answer is A
Question: The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 30%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
A.20%
B.24%
C.30%
D.32%
Answer: C.30%
Explanation: take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 30% then output equals 143
To restore new holidy demand output to original 100.
final -initial/final*100
=43/143*100=30% approxiamately.
option C is correct.
Question: Three taps A, B and C can fill a tank in 24, 30 and 40 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in :
A.8 hours
B.10 hours
C.14 hours
D.16 hours
Answer: C.14 hours
Explanation: (A+B)'s 1 hour's work = (1/24 + 1/30) = 9/120 = 3/40.
(A+C)'s 1 hour's work = (1/24 + 1/40) = 8/120 = 2/30.
Part filled in 2 hours = (3/40 + 2/30) = 17/120.
Part filled in 12 hours = (6 * 17/120) = 17/20.
Remaining part = (1 - 17/20) = 3/20.
now, it is the time of A and B and 3/20 part is filled by A and B in 1 hour, then, 3/40 part will filled in 2 hours.
.'. total time taken to fill the tank = (12 + 2) = 14 hours Answer : C
Question: If a and b are positive integers such that a/b = 4.37, which of the following must be a divisor of a?
A.19
B.13
C.12
D.7
Answer: A.19
Explanation: 1) A and B are positive INTEGERS
2) A/B = 4.37
A = 437
B = 100
437/100 = 4.37
These values are the smallest values as 437 is neither divisible by 5 or 2, the factors of 100.
The value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 437, we have to 'factor-down' 437. This gives us (19)(23). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Answer: A
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 12% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
A.22%
B.23%
C.24%
D.25%
Answer: D.25%
Explanation: Since 12% of the customers who sample the candy are not caught, then 88% of the customers who sample the candy are caught:
{% of customers who sample candy}*0.88 = 0.22;
{% of customers who sample candy} = 0.25.
Answer: D.
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 200. Find the total worth of the stock?
A.20029
B.20000
C.10000
D.20027
Answer: C.10000
Explanation: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 200 => x = 10000
Answer: C
Question: A is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?
A.Grandfather
B.Daughter
C.Grandmother
D.Granddaughter
Answer: D.Granddaughter
Explanation: A is the sister of B and B is the daughter of C.
So, A is the daughter of C. Also, D is the father of C.
So, A is the granddaughter of D.
Answer: D
Question: In the diagram shown, the number of rectangles of all
sizes is
A.11
B.15
C.7
D.13
Answer: A.11
Explanation: We systematically count rectangles by searching for groups of rectangles that are of similar size.
The largest rectangles in the diagram are all roughly the same size and overlap in pairs.
There are 3 of these; each is shaded black and shown below
Rectangle 2 (shown above) consists of 4 small rectangles.
We shade these rectangles black and label them 4; 5; 6; 7, as shown below
Together, Rectangle 4 and Rectangle 5 (shown above) create Rectangle 8, shown below.
Similarly, Rectangle 6 and Rectangle 7 together create Rectangle 9, shown below.
Finally, Rectangle 4 and Rectangle 6 (shown above) together create Rectangle 10, shown below.
Similarly, Rectangle 5 and Rectangle 7 together create Rectangle 11, shown below.
There are no other rectangles that can be formed.
In total, there are 11 rectangles in the given diagram.
correct answer A
Question: If one-third of one fourth of a number is 15, then three-tenth of that number is:
A.35
B.25
C.45
D.54
Answer: D.54
Explanation: Let the number be x. Then,
1/3 of 1/4 of x = 15
x = 15 * 12 = 180
So, required number = (3/10 * 180) = 54.
ANSWER:D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.2.9 sec
C.1.3 sec
D.2.9 sec
Answer: A.2.5 sec
Explanation: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer:A
Question: If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?
A.30%
B.40%
C.50%
D.70%
Answer: C.50%
Explanation: (Explanation:Friends, we know we will need gain amount to get gain percent, right.
So lets get gain first.
Let the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12
Gain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%
C
Question: Today is Monday. After 29 days, it will be :
A.Tuesday
B.Saturday
C.Monday
D.Sunday
Answer: A.Tuesday
Explanation: Each day of the week is repeated after 7 days.
So, after 28 days, it will be Monday
After 29 days, it will be Tuesday
Answer is A
Question: Pipe A can fill a tank in 4 hours, pipe B in 12 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled ?
A.2.8 hours
B.2 hours
C.3.5 hours
D.3 hours
Answer: A.2.8 hours
Explanation: Explanation:
Part filled by A in 1 hour = 1/4
Part filled by B in 1 hour = 1/12
Part filled by C in 1 hour = 1/40
Part filled by (A+B+C) in 1 hour =
1/4+1/12+1/40=43/120
So all pipes will fill the tank in 2.8 hours.
Option A
Question: Two letters from the word FARTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Two letters from the word FARTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
A.1/500
B.1/28
C.27/28
D.124/125
Answer: C.27/28
Explanation: There are 6 consonants and 2 vowels in FARTHING.
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So, Answer is 1 - 1/28 = 27/28 ------> C.
Question: A cube of edge 15cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
A.6cm
B.8.25cm
C.11.25cm
D.15.12cm
Answer: C.11.25cm
Explanation: Increase in volume = volume of the cube = 15*15*15 cm^3
Rise in water level = volume / area = 15*15*15/20*15 = 11.25cm
Answer is C
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
A.226
B.992
C.665
D.771
Answer: B.992
Explanation: (800*3*3)/100 = 72
920 + 72 = 992
Answer: B
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 6 m, the volume of the box (in m3) is:
A.4830
B.5184
C.6420
D.8960
Answer: B.5184
Explanation: Clearly, l = (48 - 12)m = 36 m,
b = (36 -12)m = 24 m,
h = 8 m.
Volume of the box = (36 x 24 x 12) m3 = 5184 m3. Answer: Option B
Question: Two people are playing with a pair of dice. Instead of numbers, the dice have different colors on their sides. The first person
wins if the same color appears on both the dice and the second person wins if the colors are different. The odds of their winning
are equal. If the first dice has 5 red sides and 1 blue side, find the colour(s) on the second one.
A.12
B.2
C.3
D.4
Answer: C.3
Explanation: Let no of red sides in second dice = x
No of blue sides = 6-x
Now since their odds are equal
(5/6)X(x/6)+(1/6)X((6-x)/6)=(5/6)X((6-x)/6)+(1/6)X(x/6)
=>x=3
So No. of red and blue faces on second dice will be equal i.e. 3
ANSWER:C
Question: When the integer k is divided by 7, the remainder is 4. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 3
II. 6k + 2
III. 8k + 4
A.I only
B.II only
C.III only
D.I and II only
Answer: D.I and II only
Explanation: k = 7j + 4
4k + 3 = 28j + 16 + 3 = 28j + 14 + 5
6k + 2 = 42j + 24 + 2 = 42j + 21 + 5
8k + 4 = 56j + 32 + 4 = 56j + 35 + 1
The answer is D.
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?
A.3
B.6
C.9
D.18
Answer: B.6
Explanation: The trains will travel the perimeter of the circle which is 12π miles. The relative speed of the trains is 2π miles per hour. Time taken to meet = 12π/2π = 6 hours
ANSWER:B
Question: What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent?
A.11500
B.12660
C.15220
D.11760
Answer: D.11760
Explanation: (84000*4*7/2)/100 = i
i = 11760
Answer: D
Question: Chauncy, an English bulldog, received 1,618 votes in the Mr. Bulldog USA competition, giving him approximately 20 percent of the vote. Approximately what percent of the remaining votes would he have needed to receive in order to win 30 percent of the total votes?
A.10%
B.12.5%
C.15%
D.17.5%
Answer: A.10%
Explanation: Let X be total number of votes.
Given 1618 = 20/100(X) => X = 8090.
Now 30%(8090) = 2427.
Difference now is 2427-1618 = 809
809 is 10% of 8090. Then he needed 10% more votes to win 30% of total votes.
Answer: option A is correct answer..
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A.?
A.16
B.12
C.15
D.20
Answer: B.12
Explanation: (A+B)-(B-C)=12
A-C=12
Answer is B
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
A.7 years
B.9 years
C.4 years
D.6 years
Answer: D.6 years
Explanation: Explanation:
100 ---- 300 --- 3
900 --- 3
----
6 years
Answer: Option D
Question: By selling a bat for Rs.630/- a man loses 10% what is that bat cost price
A.s.600/-
B.s.630/-
C.s.700/-
D.s.780/-
Answer: C.s.700/-
Explanation: 90 % ------> 630 (90 * 7 = 630)
100 % ------>700 (100 * 7 = 700)
Cost price = Rs.700/-
C)
Question: in a soccer bet,we play 4 teams.first team odd 1.28,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
A.219.5
B.223.0
C.235.01
D.266.74
Answer: B.223.0
Explanation: in the case we won the bet,we have:
1.28* 5.23* 3.25* 2.0*5.00=219.50
we will win 223
so correct answer is B
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
A.4!
B.8!
C.9!
D.10!
Answer: B.8!
Explanation: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
A.8 hours 15 mins
B.8 hours
C.9 hours
D.7 hours
Answer: A.8 hours 15 mins
Explanation: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4
= 8 ¼ hours = 8 hour 15 minutes
Answer is A.
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 29 metre of cloth ?
A.175 seconds
B.195 seconds
C.155 seconds
D.227 seconds
Answer: D.227 seconds
Explanation: Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128 : 1 :: 29 : x => x = {\color{Blue} \frac{29\times 1}{0.128}}
=> x = 226.56
So time will be approx 227 seconds
Answer: D
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.4. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
A.0.49
B.0.6
C.0.448
D.0.5
Answer: C.0.448
Explanation: probability of adams approval = 0.7
baker approval =0.4
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.4*0.4+0.7*0.4*0.6+0.7*0.6*0.4
=0.112+0.168+0.168
=0.448
C
Question: The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.25 kmph
B.13 kmph
C.65 kmph
D.55 kmph
Answer: A.25 kmph
Explanation: Speed of the boat in still water
= (30+80)/2
= 55 kmph. Speed of the stream
= (80-30)/2
= 25 kmph.
Answer: A
Question: 2, 3, 6, 0, 10, -3, 14, (...)
A.-6
B.8
C.-2
D.4
Answer: A.-6
Explanation: There are two series
2, 6, 10, 14, ... (Adding 4)
3, 0, -3, ... (Subtracting 3)
Hence, next term is -3 - 3 = -6
Answer is A
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.10 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A.160
B.175
C.190
D.200
Answer: C.190
Explanation: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.10 + X x 3.20 = 432
X = 30.
Hence, total hours of work = (160 + 30) = 190.
answer :C
Question: Two friends plan to walk along an 18-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 25% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?
A.10
B.11
C.12
D.13
Answer: A.10
Explanation: If Q complete x kilometers, then P completes 1.25x kilometers.
x + 1.25x = 18
2.25x=18
x = 8
Then P will have have walked 1.25*8=10 km.
The answer is A.
Question: The average of four consecutive even numbers is 27. find the largest of these numbers?
A.25
B.30
C.41
D.23
Answer: B.30
Explanation: Sol: let the numbers be x,x+2,x+4 and x+6. then,
(x+(x+2)+(x+4)+(x+6))/4) = 27
(4x+12)/4 = 27
x+3=27; x=24.
Therefore the largest number=(x+6)=24+6=30.
Ans: B
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 20 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
A.80%
B.160%
C.120%
D.124.2%
Answer: B.160%
Explanation: 0,16R = x/100*0.1R
Answer B
Question: 2 dice are thrown simultaneously. Find the probability of getting a multiple of 2 on 1 dice and multiple of 3 on the second dice?
A.9/13
B.11/36
C.12/32
D.13/45
Answer: B.11/36
Explanation: 11/36
B
Question: John makes $60 a week from his job. He earns a raise and now makes $120 a week. What is the % increase?
A.16%
B.100%
C.17%
D.17.61%
Answer: B.100%
Explanation: Increase = (60/60)*100 = (6/6)*100 = 100%.
B
Question: A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
A.20
B.25
C.30
D.35
Answer: B.25
Explanation: Initially the person has played 25 games with probablity of winning as 40%
Thus, number of games won = 10
Later when the probability of winning changes to 80% and assuming x games were played by him:
Total number of win, 60% of all games =0.6(x+25)=10+0.8x=0.6(x+25)=10+0.8x
0.2x=50.2x=5
x=25 x=25
so, he has to play 25 games.
Alternatively, this could be solved by allegation method.
B = 25games ;ANSWER:B
Question: Can you tell Which of the following fractions is the largest?
A.5/6
B.11/14
C.12/15
D.17/21
Answer: A.5/6
Explanation: another way is by taking LCM of denominators(2*3*5*7)
(a) 175 (as lcm is 2*3*5*7 where 2*3 part is already in denominator just multiply 5*7 to numerator) ,similarly
(b) 165
(c)168
(d)170
(e)174
clearly (a) is largest..
Ans A
Question: The product of two positive integers is 323 and their difference is 2. What is the smaller number?
A.17
B.18
C.16
D.19
Answer: A.17
Explanation: Let's use trial and error to find the two numbers.
20*18 = 360 (too high)
19*17 = 323
The answer is A.
Question: A merchant marks his goods up by 20% and then offers a discount of 5% on the marked price. What % profit does the merchant make after the discount?
A.8%
B.6 %
C.21%
D.14%
Answer: D.14%
Explanation: Let the price be 100.
The price becomes 120 after a 20% markup.
Now a discount of 5% on 120.
Profit=114-100
14%
answer D
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A?
A.187888
B.276889
C.267777
D.504000
Answer: D.504000
Explanation: B's monthly income = 15000 * 112/100 = Rs. 16800
B's monthly income = 2 parts ----> Rs. 16800
A's monthly income = 5 parts = 5/2 * 16800 = Rs. 42000
A's annual income = Rs. 42000 * 12 = Rs.504000
Answer:D
Question: Bookman purchased 60 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 660, how many paperback copies were sold?
A.22
B.24
C.26
D.28
Answer: B.24
Explanation: The bookman had 10 hardback ad 60-10=50 paperback copies;
14 copies were sold, hence 60-14=46 copies were left. Let # of paperback copies left be p then 10p+20(46-p)=660 --> 10 p=260 --> p=26
# of paperback copies sold is 50-26=24
Answer: B
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 6 is rolled?
A.25/216
B.50/216
C.25/72
D.25/36
Answer: C.25/72
Explanation: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 6, there are three ways:
A 6 on the first roll and non 6 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 6 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Question: Company A imported 10,000 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 20 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?
A.420
B.840
C.800
D.1680
Answer: C.800
Explanation: Answer A.
We are told that 10% of all imported widgets are made of brass and of those, 20% are green and 40% are red. Since we know that there are only three colors, the remaining 40% must be blue. 40% blue of 20% brass widgets leads to 8% blue brass widgets out of the total 10,550 widgets.
10,000 /100 * 8 = 800.
Answer C.
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
A.1/9
B.1/7
C.1/5
D.1/1
Answer: B.1/7
Explanation: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:B