Two Statements S1 and S2 are given below followed by a Question: S1: n is a prime number. S2: n leaves a…
Two Statements S1 and S2 are given below followed by a Question:
S1: n is a prime number.
S2: n leaves a remainder of 1 when divided by 4.
Question: If n is a unique natural number between 10 and 20, then what is n?
Which one of the following is correct in respect of the above Statements and the Question?
S1 alone is sufficient to answer the Question.
S2 alone is sufficient to answer the Question.
S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
S1 and S2 together are not sufficient to answer the Question.
Solution
Primes between 10 and 20: 11, 13, 17, 19 — not unique, so S1 alone not sufficient. Numbers between 10 and 20 leaving remainder 1 on division by 4: 13, 17 — not unique, so S2 alone not sufficient. Together: numbers that are prime AND leave remainder 1 mod 4: 13 and 17 — still two values, not unique. Hence S1 and S2 together are not sufficient.