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?
Answer & explanation
Answer: (d) S1 and S2 together are not sufficient to answer the Question.
Between 10 and 20 the primes are 11, 13, 17 and 19; of these, 13 and 17 both leave remainder 1 on division by 4. Even together the statements leave two possible values of n, so they are not sufficient.
- S1: n = 11, 13, 17 or 19.
- S2: n = 13 or 17 (the numbers between 10 and 20 that are 1 more than a multiple of 4).
- Together: 13 and 17 both satisfy S1 and S2, so n is still not fixed.
Remember · In number data sufficiency, list every value that fits; if more than one survives, the data are insufficient.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·