A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are…
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-I: 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?
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
The Question cannot be answered even by using both the Statements together
Solution
Statement I alone: among distinct primes whose sum is prime and less than 23, only (3, 5, 11) gives a prime sum 19 - unique, so sufficient. Statement II alone: with one number 5, both (5,7,11) summing to 23 and (5,11,13) summing to 29 are prime - not unique, so not sufficient. Hence the question can be answered using one statement (I) alone but not the other.