RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product
(n − 1)(n − 2)...3.2.1 is not divisible by n is
A.5
B.7
C.13
D.14
Answer: B.7
Explanation: Explanation :
(n-1)! is always divisible by n unless and untill n is a prime number
e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number
Therefore, find all prime numbers in the range of 12 to 40 i.e
13, 17, 19, 23, 29, 31 and 37
Hence, the number of positive integers n is 7.
Answer : B
Question: The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?
A.48 years
B.52 years
C.56 years
D.Cannot be determined
Answer: A.48 years
Explanation: Let the present ages of P and Q be 5x and 7x years respectively.
Then, 7x - (5x + 6) = 2
2x = 8 => x = 4
Required sum = 5x + 7x = 12x = 48 years.
ANSWER:A
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 60%?
A.150%
B.160%
C.156%
D.158%
Answer: C.156%
Explanation: The question is very easy. My logic is the following:
A surface = 6*a^2
After 60% increase A surface = 6* ((1.6a)^2) = 6*2.56*a^2
The increase in the surface area = (6*2.56*a^2 - 6*a^2)/6*a^2 = (6*a^2(2.56-1))/(6*a^2) = 2.56-1=1.56 = 156%
Answer :C
Question: Usha took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If she paid Rs. 375 as interest at the end of the loan period, what was the rate of interest?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: Let rate = R% and time = R years.
Then, (1500 * R * R) / 100 = 375
15R2 = 375
R2 = 25 => R = 5
Answer:B
Question: If q is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of q ?
A. 10
B. 12
C. 14
D. 16
Answer: C. 14
Explanation: Answer is C.
numbers in format of 3^k in the series from 1 to 30 inclusive q are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Question: What is the greatest prime factor of 3^6 - 1 ?
A.2
B.3
C.7
D.13
Answer: D.13
Explanation: 3^6-1 = (3^3)^2 -1 = (27^2)-1
Dividing (27^2)-1 by 13 will give us a reminder of 0 ( Hint: (2*13+1)^2-1/13 = (Reminder 1)-1=0
Hence the greatest prime factor must be 13.
ANSWER:D
Question: What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/6
A.2/5
B.3/5
C.1/6
D.1/7
Answer: C.1/6
Explanation: Explanation:
2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/6 = .833
So biggest is 5/6 and smallest is 2/3
Their difference is 5/6 - 2/3 = 1/6
Option C
Question: A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy?
A.100 m, 15
B.100 m, 16
C.120 m, 15
D.120 m, 16
Answer: D.120 m, 16
Explanation: Explanation :
Let ,the length of the side of the property be 'x' and 'y' be the number of posts bought.
When the space between polls is 8 m, the number of poles is (x/8)+1.
=>(x/8)+1 =y. --------------(i)
When space between poles is 6m, the number of poles is (x/6)+1 and 5 more are required.
=(x/6)+1 =y+5 --------------(ii)
On solving both of the equations, we get :-
x=120 and y=16.
Answer : D
Question: A, B and C have Rs.600 between them, A and C together have Rs.250 and B and C Rs.450. How much does C have?
A.70
B.90
C.120
D.100
Answer: D.100
Explanation: A+B+C = 600
A+C = 250
B+C = 450
--------------
A+B+2C = 700
A+B+C = 600
----------------
C = 100
ANSWER:D
Question: P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is R's share?
A.108
B.120
C.134
D.144
Answer: A.108
Explanation: Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
R's share = 378 * (6/21) = 108. Answer : Option A
Question: If x is an integer and 2.134 × 10^x is less than 220,000, what is the greatest possible value for x?
A.7
B.6
C.5
D.4
Answer: C.5
Explanation: x is an integer and 2.134 × 10x is less than 220,000, what is the greatest possible value for x?
for 2.134 × 10x is less than 220,000 to remain true, the greatest number is 213,400, which makes x=5
C. 5
Question: A circle in the coordinate plane passes through points (-3, -2) and (-1, 4). What is the smallest possible area of that circle?
A.13π
B.26π
C.10π
D.52π
Answer: C.10π
Explanation: The distance between the two points is sqrt(40).
radius = sqrt(40)/2
Area= pi*(sqrt(40)/2)^2
C.10π
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
A.40 m
B.60 m
C.70 m
D.80 m
Answer: B.60 m
Explanation: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was
A.344
B.218
C.200
D.388
Answer: C.200
Explanation: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200
Answer: C) Rs 200
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
A.22 sec
B.77 sec
C.76 sec
D.20 sec
Answer: D.20 sec
Explanation: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer:D
Question: The mean of set A does not exceed mean of any subset of set A. Which of the following must be true about set A?
I. Set A contains only one element
II. All elements in set A are equal
III. The median of set A equals the mean of set A
A.of the three qualities is necessary
B.II only
C.III only
D.II and III only
Answer: D.II and III only
Explanation: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. A = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Question: Given two sets X = {1,1,4,4,3,3} and Y = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
A.1/2
B.1/6
C.1/5
D.1/7
Answer: A.1/2
Explanation: One way to look at it:
The number from set X can be ANYTHING.
The number selected from set Y will determine whether the sum is odd or even.
For example, if a 4 is selected from set X, we need a 0 from set Y to get an even sum.
If a 3 is selected from set X, we need a 1 from set Y to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set X ANDselect the number from set Y that makes the sum even)
= P(select ANY number from set X)xP(select the number from set Y that makes the sum even)
= 1x1/2
= 1/2
= A
Question: If m+n gives remainder as 8 and m-n gives remainder as 6 when both are divide by 12, what is the remainder when m*n is divided by 6?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: let
m+n=12a+8
m-n=12b+6
m*n=(6*(a+b)+7)(6*(a-b)+1))
7%6=2
ans = 1
ANSWER:A
Question: Mary works in a restaurant a maximum of 80 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
A.600
B.720
C.760
D.620
Answer: C.760
Explanation: Mary receives $8(20)=$160 for the first 20 hours.
For the 60 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(60)=$600.
The total amount is $160+$600 = $760
Answer C 360.
Question: Rick deposited $850 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
A.5
B.25
C.50
D.55
Answer: D.55
Explanation: 5x+15y=850 --1
x+y=60 ---2
multiply eq 2 with 5 and subtract from eq 1
5x+15y=850
5x+5y=300
10y= 550
y=55 and x = 5
therefore $15 bills = 15
ANSWER:D
Question: If q is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
A.1
B.2
C.3
D.6
Answer: C.3
Explanation: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey q=4n, if it really wanted to convey so.
From other questions that I have seen, proper wordings could be:
If q is three times as large as n
OR simply,
If q is three times n=C
Question: A cricket bat is sold for $850, making a profit of $225. The profit percentage would be
A.24%
B.25%
C.30%
D.36%
Answer: D.36%
Explanation: 225/(850 - 225) = 225/625 = 9/25 bit more than 33%.
Answer: D
Question: What is the 8th term in this sequence?
2,3,5,16,27,43,76
A.127
B.125
C.178
D.124
Answer: B.125
Explanation: 2+3 =5 +0 =5
5+3 =10+6 =16
16+5 =21+6 =27
27+16=43+0 =43
43+27=70+6 =76
76+43=119+6 =125
so 8th term is 125
ANSWER:B
Question: Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is
A.37
B.29
C.27
D.48
Answer: D.48
Explanation: Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 60 or x = (60 * 4) / 5 = 48.
Answer: D
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
A.3
B.4
C.6
D.8
Answer: A.3
Explanation: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do,. 3
A
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
A.23%
B.10%
C.32%
D.98%
Answer: B.10%
Explanation: 2420 --- 242
100 --- ? => 10%
Answer: B
Question: If 'a' and 'b' are non-zero numbers such that their sum is six times the product, what is the value of 1/a + 1/b?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: a+b = 6ab
1/a + 1/b = (b + a)/(ab) = 6.
The answer is B.
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 270, then the least and greatest integer on the card would be
A.3 and 15
B.3 and 20
C.4 and 13
D.4 and 16
Answer: D.4 and 16
Explanation: Given: 15<x(x+1)<270.
Now, it's better to test the answer choices here rather than to solve:
If x=4 then x(x+1)=20>15 --> so, the least value is 4. Test for the largest value: if x=16 then
x(x+1)=16*17=272>270
Answer: D.
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed two times, what is the probability that the coin turns up tails on at least one of the tosses?
A.1/4
B.3/4
C.3/8
D.5/8
Answer: B.3/4
Explanation: P(2 heads)= 1/2*1/2=1/4.
P(at least one tail)=1-1/4=3/4.
The answer is B.
Question: How many times thekeys of a writter have to bepressed in order to write first 400 counting no's?
A.900
B.980
C.1000
D.1092
Answer: D.1092
Explanation: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
D
Question: Lakshmi went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 20%. then what was the cost of the tax free items?
A.Rs. 197
B.Rs. 190
C.Rs. 187
D.Rs. 167
Answer: A.Rs. 197
Explanation: Solution
Let the amount of taxable purchases be Rs.x.
Then, 20% of x	= 50/100
x ‹=› (50/100×100/20)
= 2.50
Cost of tax free items	= Rs.[200 - (2.50 + 0.50)]
= Rs. 197
Answer A
Question: A manufacturer sells a pair of watches to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for $30.09, there by earning a profit of 25%. The cost price for the manufacturer is:
A.16
B.17
C.18
D.19
Answer: B.17
Explanation: B
17
Let the cost price for the manufacturer be $x.
Then, 125% of 120% of 118% of x = 30.09.
125/100 * 120/100 * 118/100 * x = 3009/100
177/100 x = 3009/100 => x = 17
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 9 minutes 42 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
A.3%
B.5%
C.8%
D.9%
Answer: D.9%
Explanation: Bob's time = 640 secs.
His sis' time = 582 secs.
Percent increase needed = (640-582/640) * 100 = 58/640 * 100 = 9%. Ans (D).
Question: If a man can cover 32 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.118 km
B.162 km
C.1767 km
D.432 km
Answer: D.432 km
Explanation: 32 m/s = 32 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 32 * 18/5 * 15/4 km = 432 km.
Answer: D
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.11 1/8 min
B.11 1/4 min
C.11 8/4 min
D.11 1/9 min
Answer: B.11 1/4 min
Explanation: 3/12 + x/15
= 1
x= 11 1/4
Answer:B
Question: Jerry went to a shop and bought things worth Rs. 20, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.14
B.14.7
C.21.3
D.21.5
Answer: B.14.7
Explanation: Total cost of the items he purchased = Rs.20
Given that out of this Rs.20, 30 % is given as tax
=> Total tax incurred = 30 % = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (20−30/100−x)6/100 = 30/100
⇒ 6(20 −0.3 −x) = 30
⇒ (20 − 0.3 − x) = 5
⇒ x = 20 − 0.3 − 5 = 14.7
B)
Question: {330, 380, 350, n}
Which of the following could be the median of the 4 integers listed above?
I. 340
II. 350
III. 375
A.I only
B.II only
C.I and II only
D.II and III only
Answer: C.I and II only
Explanation: If 340 is the median, (n+350) / 2 = 340. Then n = 330. Thus 340 can be the median.
If 350 is the median, (n+350) / 2 = 350. Then n = 350. Thus 350 can be the median.
If 375 is the median, (n+350) / 2 = 375. Then n = 400. But 400 > 380, which would then be the second largest member of the set, thus 375 can not be the median.
The answer is C.
Question: A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 2, and the fifth digit is 4 times the sixth. How many different credit card numbers are possible?
A.12
B.18
C.24
D.36
Answer: C.24
Explanation: The first two digits are fixed.
The third digit can be 7, 8, or 9 so there are 3 choices.
The fourth digit can be 2, 4, 6, or 8 so there are 4 choices.
The fifth digit depends entirely on the sixth digit.
The sixth digit can be 1 or 2 so there are 2 choices.
The number of possibilities is 3*4*2 = 24
The answer is C.
Question: Two pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.1/8
B.1/4
C.1/2
D.1/4
Answer: C.1/2
Explanation: 3/12 + x/14
= 1
x= 10 1/2
Answer: C
Question: A walks at 30 kmph and 30 hours after his start, B cycles after him at 40 kmph. How far from the start does B catch up with A?
A.1200km
B.1500km
C.2000km
D.2500km
Answer: D.2500km
Explanation: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.
x/30 - x/40 = 30
x = 3600 km
Answer is 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.3 1/5 Km
B.3 1/7 Km
C.4 1/5 Km
D.4 1/7 Km
Answer: A.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
Option 'A'
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture?
A.1/2
B.1/3
C.1/4
D.1/6
Answer: D.1/6
Explanation: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration C would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Question: A channel provider give 2/3 part is movie channel and sport channel is 2 times grater than news channel.news channel is five more than entertainment channel.if entertainment channel is 10.then calculate total no. of channel.
A.165
B.130
C.225
D.286
Answer: A.165
Explanation: let total no. of channel is x.
movie channel=2x/3
entertainment channel=10
news channel=15
sports channel=30
so,2x/3+10+15+30=x,x-2x/3=55,x=55*3=165
answer A
Question: During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 45% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
A.714,240
B.2,261,760
C.2,052,413
D.3,690,240
Answer: C.2,052,413
Explanation: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 45% greater than the number sold during the first quarter = (1 + 45/100)x = 1.45 x
1.45 x = 2,976,000
=> x = 2,052,413
So, answer will be C
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
A.80%
B.105%
C.88%
D.124.2%
Answer: C.88%
Explanation: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,11 = 11/100
x= 80*11/100
x= 8.8
8.8/10 = 0.88 = 88%, Answer C
Question: Jane covered a distance of 360 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
A.2 hours 30 minutes
B.4 hours
C.2 hours
D.1 hour 45 minutes
Answer: B.4 hours
Explanation: Answer
Let Jane travel 'x' at 60 miles per hour.
As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.
Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles.
Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles.
Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.
Therefore, total distance = 60x + 400 - 80x.
Total distance travelled = 340 miles.
Therefore, 360 = 60x + 400 - 80x
20x = 80 or x = 4 hours.
Choice B
Question: 225, or 15^2, is the first perfect square that begins with two 2s. What is the sum of the digits of the next perfect square to begin with two 2s?
A.9
B.12
C.13
D.14
Answer: C.13
Explanation: Because 16^2 = 256,y the next perfect square to begin with two 2s cannot be 3-digit.
Let's try 4-digit. 40^2 = 1,600 and 50^2 = 2,500. So, if there is a 4-digit perfect square to begin with two 2s it must be between 41^2 and 49^2. Test the middle number 45^2 = 2,025. Test larger number: 46^2 = 2,116. Test next number: 47^2 = 2,209. Bingo! The sum of the digits = 2 + 2 + 0 + 9 = 13.
Answer: C.
Question: The simple interest on Rs. 23 for 3 months at the rate of 5 paise per rupeeper month is
A.3.45
B.4.5
C.2.25
D.3.21
Answer: A.3.45
Explanation: Sol.
S.I. = Rs. [23 * 5/100 * 3] = Rs. 3.45
Answer A
Question: If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
A.88 kg
B.65 kg
C.72 kg
D.44 kg
Answer: C.72 kg
Explanation: (3 * 4)/48 = (9 * 2)/ x
x = 72 kg
Answer:C
Question: If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?
A.2:1
B.2:8
C.2:9
D.2:5
Answer: A.2:1
Explanation: Let 1 man's 1 day work = x and 1 boy's 1 day work = y.
Then, 12x + 16y = 1/5 and 13x + 24y = 1/4
Solving these two equations, we get:
x = 1/100 and y = 1/200
Required ratio = x:y = 1/100 : 1/200 = 2:1.
Answer: A
Question: What is the average (arithmetic mean) of the numbers 15, 16, 17, 17, 18, and 19?
A.14.2
B.16.5
C.17
D.17.5
Answer: C.17
Explanation: The average of 15,16,17,18,19 ( sequence numbers) is 17 & now average of 17 & 17(remaining digit from given list) is 17 . Hence answer is 17.
ANSWER:C
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most
A.200
B.215
C.220
D.230
Answer: B.215
Explanation: Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215
B
Question: Of the three-digit integers greater than 800, how many have distinct digits ?
A. 90
B. 82
C. 80
D. 45
Answer: B. 82
Explanation: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 800 to 999 = 299 (3-digit numbers greater than 800);
A. all digits are distinct = 2*9*8=144
Answer: B
Question: How many terms of the arithmetic series 24 21 18 15 g + + + + , be taken continuously so that their sum is – 351
A.26
B.21
C.9
D.10
Answer: A.26
Explanation: In the given arithmetic series, a= 24 = d =-3 .
Sn = – 351
n/2(48-3n+3)=-351
n=26 or -9
hence, 26 terms needed to get sum -351
Option A
Question: In a certain game of dice, the player’s score is determined as a sum of three throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If John plays this game against 22 other players, what is the probability of the minimum score that will guarantee John some monetary payoff?
A.41/50
B.1/216
C.1/221
D.1/84
Answer: B.1/216
Explanation: To guarantee that John will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and John will get nothing.
P(18)=1/6^3=1/216.
Answer: B.
Question: Data sufficiency question:
If solution (x) with alcohol (14%) and solution (y) with alcohol (20%) mixed together to form 24 liters of mixture.
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: Explanation:
Let a liters of first solution, and 'b' liters of second solution has been taken.
So using weighted average formula = n1×a1+n2×a2n1+n2n1×a1+n2×a2n1+n2 = n1×14+n2×20n1+n2=15n1×14+n2×20n1+n2=15
⇒n1=5n2⇒n1n2=51⇒n1=5n2⇒n1n2=51
As total volume was given as 24 liters, first solution = 16×24=416×24=4
So statement 1 is sufficient.
Answer:A
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
A.157
B.197
C.152
D.1518
Answer: D.1518
Explanation: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: D
Question: Some ladies can do a piece of work in 12 days. Two times the number of such ladies will do half of that
work in :
A.6 days
B.4 days
C.12 days
D.3 days
Answer: D.3 days
Explanation: Expl : Let x ladies can do the work in 12 days. More ladies, less days (Indirect)
Less work, less days (direct)
Ladies 2x : x Work 1 : ½
2x : x , 1 : ½ : : 12 : y
:. 2x * 1*y = x* ½ *12 or y = 3
Hence the required number of days = 3
Answer:D