A Question is given followed by two Statements I and II Consider the Question and the Statements nbs...........

Math and Mental Ability Number System

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A Question is given followed by two Statements I and II. Consider the Question and the Statements.

There are three distinct prime numbers whose sum is a prime number.

Question: What are those three numbers ?

Statement-1: Their sum is less than 23.

Statement-II: One of the numbers is 5.

Which one of the following is correct in respect of the above Question and the Statements ?

This questions was previously asked in

UPSC CSAT, Previous year (2024)

View All CSAT Previous Year Papers

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

(b) The Question can be answered by using either Statement alone

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

(d) The Question cannot be answered even by using both the Statements together

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Explanation:

- Statement I: The three distinct prime numbers have a sum less than 23. This alone is insufficient to identify the specific numbers, as multiple combinations can satisfy this condition.

- Statement II: One of the numbers is 5. By itself, this does not define the other two numbers uniquely as several combinations with 5 could result in a prime sum.

- Combining Statements: The combination of having one number as 5 and the sum being less than 23 helps in narrowing down possible combinations. Specifically, the sums of 3, 5, and 7 result in 15, which is a prime number.

- Option 1 (a): Incorrect. Neither statement alone sufficiently defines the three numbers.

- Option 2 (b): Incorrect. Neither statement alone is sufficient.

- Option 3 (c): Correct. Both statements together allow us to identify 3, 5, and 7 as the numbers.

- Option 4 (d): Incorrect. Together, the statements are sufficient.