RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x?
A.30
B.31
C.32
D.32
Answer: B.31
Explanation: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 33
x = 31
Correct Option: B
Question: A fair coin is tossed 3 times. What is the probability of getting at least 2 tails?
A.3/4
B.3/2
C.1/2
D.3/4
Answer: C.1/2
Explanation: Let's find the probability of 2 tails , 3 tails
P(TTT)=((1/2)^3=1/8.
P(HTT)=(3!/2!)*(1/2)^3=3/8
Total Probablity = 1/8 + 3/8
=1/2
Answer(C)
Question: If M:N is 3:9 and N:P is 9:12 then M:P is equal to
A.1:5
B.1:4
C.1:6
D.1:8
Answer: B.1:4
Explanation: The two ratios given are having the same number 9 for N in both the ratios.
Hence- M:N = 3:9 N:P = 9:12
=> M:P = 3:12 = > 1:4
Answer B
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
A.10%
B.50%
C.25%
D.52%
Answer: C.25%
Explanation: Explanation:
cost price = (225 + 15) = 240 sell price = 300
gain = (60/240)*100 = 25%. Answer: C
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
A.987 ways
B.346 ways
C.600 ways
D.157 ways
Answer: C.600 ways
Explanation: The number of ways of selecting three men, two women and three children is:
= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 15 * 10
= 600 ways.
Answer: C
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
A.2000
B.6657
C.2776
D.2679
Answer: A.2000
Explanation: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Question: What is the prime factors’ number of 28?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 28 = 2^2*7^1
prime factors’ number will be 2+1 = 3.
Hence, answer is B.
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
A.1
B.6
C.7
D.8
Answer: C.7
Explanation: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer: C
Question: When the number 209y913 is exactly divisible by 11, then the smallest whole number that can replace y?
A.0
B.1
C.2
D.5
Answer: A.0
Explanation: The given number =209y913
Sum of the odd places =3+9+9+2=23
Sum of the even places = 1+y+0
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(1+y) = divisible by 11
22 � y = divisible by 11.
Y must be 0, to make given number divisible by 11.
A
Question: If the number 98348*0 is exactly divisible by 72, then the minimum value of * is?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: 72=8*9
divisibility 0f 8 last 3place should be divisible by 8
lly divisibility of 9 sum of digit should be divisible by 9
840 divisible by 8 nd 36 divisible by 9
ANSWER:D
Question: In a certain series, each term is m greater than the previous term. If the 14th term is 600 and the 11th term is 540, what is the first term?
A.40
B.80
C.140
D.200
Answer: C.140
Explanation: a + 13m = 660 (14th term)
a + 10m = 540 (11th term)
You get a = 140 and m = 40
Answer: C
Question: A man can row a boat at 30 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 70 km upstream?
A.35/9
B.35/10
C.35/11
D.35/12
Answer: C.35/11
Explanation: Speed upstream = 30-8=22 kmph.
Time required to cover 60 km downstream = d/s = 70/22 = 35/11 hours. Answer:C
Question: The decimal 0.1 is how many times greater than the decimal (0.001)^4?
A.10^8
B.10^9
C.10^10
D.10^11
Answer: D.10^11
Explanation: 0.1 = 10^-1
(0.001)^4 = (10^-3)^4 = 10^-12
10^11 * 10^-12 = 10^-1
The answer is D.
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
A.23
B.19
C.42
D.20
Answer: C.42
Explanation: Let the total number of workers be x. Then,
8000x = (18000 * 7) + 6000(x - 7)
= 2000x = 84000
= x = 42.
ANSWER:C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:?
A.56 km/hr
B.50 km/hr
C.59 km/hr
D.34 km/hr
Answer: B.50 km/hr
Explanation: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.3.9
B.4.2
C.5.3
D.1.5
Answer: D.1.5
Explanation: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Question: Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number?
A.3
B.5
C.6
D.7
Answer: A.3
Explanation: Let the number be x.
Then, x + 17 = 60
x
x2 + 17x - 60 = 0
(x + 20)(x - 3) = 0
x = 3
Option A
Question: At a supermarket, a variety of cookies was priced at 75 cents per 100 grams. Subsequently, the price was revised to 40 cents for 30 grams of the same cookies. By approximately what percent did the ratio of price to weight increase from the initial price of 75 cents per pound?
A.65
B.78
C.44
D.18
Answer: B.78
Explanation: Initial price/weight ratio = 75 / 100 = 225/300
Revised price/weight ratio = 40 / 30 = 400/300
Answer: B
Question: In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?
A. 0.06N+3200
B. 0.1N+7200
C. 0.4N+7200
D. 0.12N+8000
Answer: D. 0.12N+8000
Explanation: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 20% votes so, 0.2*0.6*N plus 8,000 votes from independents: total=0.2*0.6*N+8,000=0.12*N+8,000.
Answer: D.
Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
A.145
B.253
C.253
D.352
Answer: B.253
Explanation: EXPLANATION
Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred’s digits is smaller than the unit’s digit.
Hence, required number = 253.
Answer B
Question: If each of 3 digit code is formed of integers from 1 to 40, inclusively, and each of the digits are different, how many possible codes are there?
A.54230
B.59365
C.59280
D.25789
Answer: C.59280
Explanation: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 40 possibilities
Second digit can have 39 possibilities
Third digit can have 38 possibilities
Total number of possible codes = 40*39*38 = 59280
Answer: C
Question: Find the odd man out. 121, 144, 169, 196, 225, 256, 288, 324, 361
A.121
B.169
C.225
D.288
Answer: D.288
Explanation: Explanation :
Each of the given numbers except 288 is a perfect square
Answer : Option D
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 12?
A.1/48
B.234/8
C.1/24
D.5/8
Answer: B.234/8
Explanation: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 12 = Integer, therefore we have 48 / 96 numbers divisible by 8
O E O / 12= Not Integer
We cannot forget multiples of 12 from 1 to 96
We have 8 numbers that are multiple of 12
Therefore, 48/96 + 8/96 = 23/48
answer : B
Question: The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.
A.4:25
B.4:15
C.3:25
D.3:15
Answer: A.4:25
Explanation: Explanation:
Let the diagonals of the squares be 2x and 5x.
Then ratio of their areas will be
Area of square=1/2∗Diagonal2
1/2∗2x2:1/2∗5x2
4x2:25x2=4:25
Option A
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 20 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
A. $198
B. $216
C. $192
D. $230
Answer: C. $192
Explanation: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 20
Emlpoyee paid = .8 * 240 = 192 $
Answer C
Question: Robert ate 9 chocolates, Nickel ate 2 chocolates. How many more chocolates did Robert ate than nickel?
A.A)4
B.B)7
C.C)9
D.D)5
Answer: B.B)7
Explanation: 9-2=7. Answer is B
Question: 244,180,131,95, ?
A.42
B.43
C.44
D.70
Answer: D.70
Explanation: 244 - 180 = 64 = 8^2
180 - 131 = 49 = 7^2
131 - 95 = 36 = 6^2
so we can write
95 - x = 25 = 5^2 , where x is the next number
x = 95 - 25 = 70
so the next number will be 70
ANSWER:D
Question: Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
A.47.5
B.47.9
C.47.6
D.47.2
Answer: A.47.5
Explanation: Explanation:
At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.
Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°
Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5°
Answer: A) 47.5 degrees
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
A.2882
B.778
C.268
D.3000
Answer: D.3000
Explanation: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000.Answer: D
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A.9400
B.9600
C.9800
D.9000
Answer: B.9600
Explanation: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
answer :B
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
A. 15 B. 18
A.22
B.18
C.99
D.77
Answer: B.18
Explanation: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Question: If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?
A.32.25%
B.40%
C.37.50%
D.36.75%
Answer: A.32.25%
Explanation: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
The area of new rectangle would be 115*115=13,225, which is 32.25% greater than the old area.
Answer: A.
Question: All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?
A.143
B.200
C.157
D.122
Answer: A.143
Explanation: DETAILED SOLUTION
If a number written in base 6 ends with a zero, it should be a multiple of 6. In other words, the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7. There are 33 multiples of 6 less than 201. There are 28 multiples of 7 less than 201. There are 4 multiples of 6 & 7 (or multiple of 42) from 1 to 200.
So, total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57. Number of numbers with non-zero units digit = 200 - 57 = 143.
Correct Answer : A
Question: If |10−2y|=|3y+5|, which of the following could be a value of y?
A.-15
B.9/5
C.-1
D.5
Answer: A.-15
Explanation: 10 - 2y = 3y + 5 or 10 - 2y = -3y - 5
5y = 5 or -y = 15
y = 1 or x = -15
Answer: A
Question: Find three rational numbers between 3 and 5.
A.6/2
B.7/2, 8/2
C.8/2
D.7/2, 9/2
Answer: D.7/2, 9/2
Explanation: Sol. 1st rational number = (3 + 5)/2 = 8/2 = 4
2nd rational number (i.e., between 3 and 4)
= (3 + 4)/2 = 7/2
3rd rational number (i.e., between 4 and 5)
= (4 + 5)/2 = 9/2
Answer D
Question: 10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range T of the 10 numbers?
A.25
B.27
C.30
D.52
Answer: D.52
Explanation: Positions: 1 2 3 4 5 6 7 8 9 10
Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b
y - x = 25
Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.
b - a = 30 --> b = 30 + a
In order to increase the range, we have to maximize the value of 'b'.
'b' can be maximized by taking the max value of 'a'.
From the assumed values, maximum value of 'a' can be 22.
Therefore, b = 30 + 22 = 52
Range T= 52 - 0 = 52
Answer: D
Question: The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If y12 = 110, what is the value of y ?
A.11
B.12
C.13
D.15
Answer: A.11
Explanation: ab = (a - 1)(b - 1)
y12 = (y-1)(12-1) =110 --> y-1=10 --> y=11
Answer: A
Question: A swimming pool can be filled by pipe A in 3 hours and by pipe B in 6 hours, each pump working on its own. At 9 am pump A is started. At what time will the swimming pool be filled if pump B is started at 10 am?
A.11:20
B.11:30
C.11:40
D.11:50
Answer: A.11:20
Explanation: the rates of the two pumps are
pump A: 1 / 3 , pump B: 1 / 6
Working together, If pump A works for t hours then pump B works t - 1 hours since it started 1 hour late. Hence
t * (1 / 3) + (t - 1) * (1 / 6) = 1
Solve for t
t = 7 / 3 hours = 2.3 hours = 2 hours 20 minutes.
The swimming pool will be filled at
9 + 2:20 = 11:20
Answer A
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails, on the second toss the coin lands on heads, and then lands on tails on the last toss?
A.1/8
B.1/3
C.1/4
D.1/2
Answer: A.1/8
Explanation: P(THT) = 1/2*1/2*1/2=1/8
The answer is A.
Question: Jaya ranks 5th in a class of 53. What is her rank from the bottom in the class?
A.49th
B.48th
C.47th
D.50th
Answer: A.49th
Explanation: There are 4 students above her.
When takan from bottom there are 4 students below her rank .
So her rank wud be 53-4 i.e. 49th.
ANSWER:A
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.49%
B.30%
C.40%
D.44%
Answer: C.40%
Explanation: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP
= Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer: C
Question: A train of 45 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
A.6
B.3
C.4.2
D.9
Answer: C.4.2
Explanation: D = 45 * 60 + 1500 = 4200 m
T = 4200/60 * 18/5 = 252 sec = 4.2 mins
Answer:C
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 42, find the ages of Toby and Debby?
A.6 and 14
B.5 and 9
C.8 and 10
D.5 and 10
Answer: B.5 and 9
Explanation: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 42
x = 9
The ages of Toby and Debby are 5 and 9.
Answer : B
Question: In what ratio should a variety of Rice costing Rs. 10 per kg be mixed with another variety of Rice costing Rs. 13.25 per kg to obtain a mixture costing Rs. 10.75 per kg?
A.2 :1
B.1 :2
C.5 :1
D.4 :1
Answer: A.2 :1
Explanation: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (13.25 - 10.75) / (10.75 - 10) = 6/3=2/1
ANSWER:A
Question: How many different ways can you select a pilot and a co pilot if you have 30 people to choose from?
A. 870
B. 920
C. 1398
D. 4950
Answer: A. 870
Explanation: You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (30C2) x 2 = 870.
Ans A
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
A.100 m
B.200 m
C.300 m
D.400 m
Answer: B.200 m
Explanation: perimeter of rectangle=2(l+b)
2(l + 100) = 600
=> l = 200 m
ANSWER:B
Question: Find the simple interest on $2000 for 3 years at 10% per annum?
A.$250
B.$300
C.$500
D.$600
Answer: D.$600
Explanation: SI = PTR/100
= 2000*3*10/100 = $600
Answer is D
Question: If n is the product of the integers from 1 to 11, inclusive, how many different prime factors greater than 1 does n have?
A.Four
B.Five
C.Six
D.Seven
Answer: B.Five
Explanation: n = 1*2*3*4*5*6*7*8*9*10*11
The prime factors of n are 2, 3, 5, 7, and 11.
There are 5 prime factors.
The answer is B.
Question: A train covers a certain distance at a speed of 250kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
A.400km/hr
B.500km/hr
C.600km/hr
D.700km/hr
Answer: B.500km/hr
Explanation: Explanation:
Distance = 250×4 = 1000km
Required speed = (1000/2) = 500km/hr
Answer: Option B
Question: Which of the following is a prime number
A.9
B.2
C.4
D.8
Answer: B.2
Explanation: Explanation:
A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.
So from above options 2 is that number
Answer: Option B
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 40 other employees of Company K, how many employees does Company K have?
A. 160
B. 180
C. 190
D. 200
Answer: A. 160
Explanation: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 40
so 25% of x = 40
x = 160
Therefore there a total of 160 employees in the company K
Correct answer - A
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
A.27
B.28
C.200
D.277
Answer: C.200
Explanation: d2/2 = (20 * 20)/2
= 200
Answer:C
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.17 1/6
B.17 1/3
C.17 1/7
D.17 1/2
Answer: C.17 1/7
Explanation: 1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer: C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
A.1/7
B.2/5
C.1/5
D.1/3
Answer: C.1/5
Explanation: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability
= 1/5
Answer:C
Question: The average salary of all the workers in a workshop is Rs. 10000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 8000. The total number of workers in the workshop is :
A.14
B.21
C.88
D.37
Answer: A.14
Explanation: Explanation:
Lot the total number of workers be v Then,
10000v = (12000 * 7) + 8000 (v - 7) <=> 2000v = 28000 <=> v = 14
Answer: A) 14
Question: What is the least possible product of 4 different integers, each of which has a value between –2 and 10, inclusive?
A.–5040
B.–3600
C.–720
D.–1440
Answer: D.–1440
Explanation: Maximize the total product with a -ve sign
so -2 * 10 * 9 * 8 = 720 * -2 = -1440
Answer is D.
Question: How many odd prime numbers are there less than 75?
A.20
B.1
C.2
D.16
Answer: A.20
Explanation: Odd prime number less than 75:3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73
There is 20 the odd prime number
Answer is A
Question: Suresh invested a sum of Rs. 15000 at 9 percent per annum Simple interest and Rs. 12000 at 8 percent per annum compound interest for a period of 2 years. What amount of interest did Suresh earn in 2 years?
A.4496.8
B.4596.8
C.4696.8
D.4796.8
Answer: C.4696.8
Explanation: S.I = PTR/100
S.I =15000*9*2/100
S.I= 2700
C.I =P(1+r/100)^n -P
C.I= 12000(1+8/100)^2-12000
C.I=1996.8
total amount in 2 years
as interest = S.I +C.I
= 2700+1996.8
=4696.8
ANSWER:C
Question: Anish borrowed 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was 9000. How much did he borrow?
A.32,000
B.33,000
C.30,000
D.35,000
Answer: B.33,000
Explanation: Let x be the other amount
\ 3x⁄10 + 3600 = 900 ⇒ x = 18000
\ total borrowed sum = 33000
Answer B
Question: Let A represent a set of four distinct prime numbers. If the sum of the numbers in A is even and x is a member of A, then what is the least possible value that x can be?
A.1
B.2
C.3
D.5
Answer: C.3
Explanation: We are told that A is a set of four distinct prime numbers, and the sum of the numbers in A is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of A must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Question: An eight-digit telephone number consists of exactly two zeroes. One of the digits is repeated thrice. Remaining three digits are all distinct. If the first three digits (from left to right) are 987, then find the probability of having only one 9, one 8 and one 7 in the telephone number.
A.1/18
B.1/20
C.1/10
D.5/47
Answer: C.1/10
Explanation: Explanation :
Case A: There is only one 9, one 8 and one 7 in the number.
Hence there has to be one digit from {1,2,3,4,5,6} repeated thrice.
Total number of ways in which such a number can exist is :
=>6C1×5!/(3!×2!).
=60.
Case B: One of the three digit {9,8,7} is repeated thrice.
Hence, there will be one digit from {1,2,3,4,5,6}.
Total number of ways in which such a number can exist:
=>3C1×6C1×5!/(3!×2!).
=>540
Total possible telephone numbers:
=60+540=600.
Hence the required Probability is 60/600 = 1/10.
Answer : C
Question: A room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
A.10
B.15
C.17
D.19
Answer: B.15
Explanation: Let us calculate both the length and width of the room in centimeters.
Length = 7 meters and 20 centimeters = 720 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 720 and 432 = 144
Thus, the number of square tiles required = (720 x 432 ) / (144 x 144) = 5 x 3 = 15
Answer: B
Question: The ratio of Rita's age to her mother's age is 3:8. The difference of their ages is 35 years. The ratio of their ages after 4 years will be:
A.7:12
B.5:12
C.38:43
D.42:47
Answer: B.5:12
Explanation: Rita age=3x
mother's age=8x
their difference = 8x-3x=35
x=7
therefore Rita's current age=21
mother's current age=56
4 years hence their ratio of ages will be 25:60
ans is 5:12
ANSWER:B