# Number System Questions and Answers

This set of Aptitude Questions and Answers (MCQs) focuses on “Number System”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.

1. Which of the following is not a twin prime?
a) 3,5
b) 11,13
c) 17,19
d) 13,17

Explanation: Two prime numbers whose difference is 2 are called twin primes.
In the given options, 17 – 13 ≠ 2, hence it is not a twin prime.

2. Which of the following is a prime number?
a) 571
b) 517
c) 533
d) 559

Explanation: We know that, (24)2 > 571,517,533,559
Prime numbers less than 24 are 2, 3, 5, 7, 11, 13, 17, 19, 23.
517 is divisible by 11.
533 and 559 are divisible by 13.
Clearly, none of them divides 571. Hence, it is a prime number.

3. In which of the following case, the two numbers are co-prime?
a) Two consecutive even number
b) Two composite number
c) Two consecutive odd integers
d) Two consecutive odd numbers

Explanation: In two consecutive even number, there will be always a factor of 2.
Two composite number, may or may not be co-prime. Integers can take negative values, but prime numbers cannot be negative. Hence, two consecutive odd integers are not always co-prime. Two consecutive odd numbers are always co-prime, because they do not have any common factors except 1.

4. In which of the following case, the two numbers are co-prime?
a) Three consecutive natural numbers
b) Two prime and on composite number
c) Three consecutive natural numbers with first one being even
d) Three consecutive natural numbers with first one being odd

Explanation: Three consecutive natural numbers are always not co-prime. For example, in (2,3,4) there is a common factor between 2 and 4.
Two prime and one composite number are not always co-prime because sometimes the composite number may be multiple of prime number chosen.
Three consecutive natural numbers with first one being even are not co-prime because the first and third term being even, has a factor of 2 common in between them.
Three consecutive natural numbers with first one being odd are always co-prime because there is no common factors in between them.

5. How many prime numbers are less than 70?
a) 16
b) 19
c) 20
d) 18

Explanation: Prime numbers less than 70 are, 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67.
Hence, the number of prime numbers less than 70 is 19.

6. Which of the following is not a prime number?
a) 233
b) 251
c) 241
d) 259

Explanation: 162 > 233,251,241,237
Prime numbers less than 16 are 2,3,5,7,11,13
233, 251 and 241 are not divisible by any of the above numbers. Hence these are prime numbers.
But, 259 is divisible by 7. Hence, it is not a prime number.

7. Which is the smallest prime number?
a) 1
b) 2
c) 3
d) 4

Explanation: We know that 1 is neither prime nor composite. Hence the smallest prime number is 2.

8. Which is the smallest odd prime number?
a) 1
b) 5
c) 3
d) 7

Explanation: We know that 1 is neither prime nor composite. Hence the smallest odd prime number is 3.

9. Find the sum of all 2-digit prime numbers.
a) 1043
b) 1100
c) 1187
d) 1130

Explanation: 11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89+97 = 1043.

10. Consider the following statements.
I. To obtain prime numbers less than 256, we are to reject all the multiples of 2, 3, 5, 7, 11 and 13.
II. Every composite number less than 256 is divisible by a prime number less than 16.
Which of the statement(s)given above is/are correct?
a) Only I
b) Only II
c) Both I & II
d) Neither I nor II

Explanation: As 256 is the square of 16. So, as to obtain prime numbers less than 256, we reject all multiples of prime numbers less than 16 i.e., 2, 3, 5, 7, 11 and 13.
Similarly, every composite number less than 256 is divisible by a prime number less than 16 i.e., 2, 3, 5, 7, 11 and 13.
Hence, both the statements given are correct.

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