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.
