What is the 5th number? Statements: 1) 1st and 2nd numbers are 1 and 2…

In Data Sufficiency, a statement (or combination of statements) is sufficient only if it forces a single, definite value of the quantity asked. A set of given numbers merely following a visible trend is not the same as an explicitly stated rule — unless a formula, recurrence, or definition is actually given, any value consistent with the known numbers remains a valid possibility.

1. Statement (1) alone fixes only the 1st and 2nd numbers as 1 and 2. It says nothing about the 3rd, 4th, or 5th numbers, so it alone cannot determine the 5th number.

2. Statement (2) alone fixes only the 3rd and 4th numbers as 3 and 4. It says nothing about the 1st, 2nd, or 5th numbers, so it alone cannot determine the 5th number either.

3. Combining both statements fixes the 1st through 4th numbers as 1, 2, 3, 4 — but neither statement states any rule (such as "the nth number equals n") connecting the terms. The trend visible in 1, 2, 3, 4 is only an observation, not a stated definition, so more than one continuation for the 5th number remains consistent with both statements.

Cross-check: if the 5th number were truly forced, every rule consistent with 1, 2, 3, 4 would have to agree on it. But a rule such as "nth number = n" (giving 5) and an equally consistent but different assignment for the 5th term both satisfy statements (1) and (2) without contradiction, yet disagree on the answer. Since neither statement rules out this ambiguity, the two statements — even put together — are not sufficient.

Hence, both statements even put together are not sufficient to determine the 5th number.