Which of the following statements is true?

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2 is the smallest prime number.

If a number is a prime it must be odd.

The sum of two prime numbers is always a prime number.

If two numbers are co-primes, at least one of them must be a prime number.

answer is A.

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Detailed Solution

Consider option(1):
The pair of numbers whose highest common divisor is 1 are called co-primes and they need not be prime.
We know that 2 is the smallest prime number.
Therefore, option (1) is true.
Consider option(2):
Also, 2 is a prime number which is even.
So, if a number is a prime it may not be odd.
Therefore, option (2) is not true.
Consider option (3):
The sum of two prime numbers may not be a prime number.
Example: Let’s take two prime numbers 3 and 5.
The sum of numbers 3 and 5 is 8, which is not a prime number.
Therefore, option (3) is not true.
Consider option (4):
If two numbers are co-primes, then none of them may be a prime number.
Example: 27 and 64 are co-primes but both are not prime numbers.
Therefore, option (4) is not true.
Hence, option (1) is correct.

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