# Q. Consider the following statements in respect of the sum S=x+y+z, where x, y and z are distinct prime numbers each less than 10:

1. The unit digit of S can be 0.

2. The unit digit of S can be 9.

3. The unit digit of S can be 5.

Which of the statements given above are correct?

a) 1 and 2 only

b) 2 and 3 only

c) 1 and 3 only

d) 1, 2 and 3

Correct answer: c) 1 and 3 only

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

## S=x+y+z

Let’s approach this step-by-step:

1. First, let’s list out the prime numbers less than 10:

2, 3, 5, 7

2. Now, we need to consider all possible combinations of three distinct primes from this list:

2 + 3 + 5 = 10

2 + 3 + 7 = 12

2 + 5 + 7 = 14

3 + 5 + 7 = 15

3. Let’s examine each statement:

Statement 1: The unit digit of S can be 0.

This is true, as we can see from the sum 2 + 3 + 5 = 10.

Statement 2: The unit digit of S can be 9.

This is false. None of the sums have a unit digit of 9.

Statement 3: The unit digit of S can be 5.

This is true, as we can see from the sum 3 + 5 + 7 = 15.

4. Therefore, statements 1 and 3 are correct, while statement 2 is incorrect.

The correct answer is c) 1 and 3 only.