Question

Two different prime numbers X and Y, both are greater than 2, then which of the following must be true?

• A. X-Y=23
• B. X+Y is not equal to 87
• C. Both 1 and 2
• D. None of the above

Answer 1

The Correct Option is B

To determine why X+Y is not equal to 87 must be true when X and Y are two different prime numbers greater than 2, we first recognize the properties of such primes: 

1. Since X and Y are greater than 2, they must be odd numbers. This is because the only even prime number is 2.
2. The sum of any two odd numbers is an even number. Therefore, X + Y is even.
3. 87 is an odd number.

Since X + Y must be an even number and 87 is odd, it follows that X + Y cannot equal 87.

This analysis shows that the statement "X+Y is not equal to 87" is always true for any two different prime numbers X and Y, both greater than 2. This verifies that the correct answer is the second option.