Direction: The problem consists of a problem followed by two statements.…
2024
Direction: The problem consists of a problem followed by two statements. Decide whether the data in the statements are sufficient to answer the question. Select your answer according to whether:
A. Statement I ALONE is sufficient, but statement II alone is not sufficient.
B. Statement II ALONE is sufficient, but statement I alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
If x is a positive integer, is x a prime number?
I. x is even.
II. x < 4.
- A.
A
- B.
B
- C.
C
- D.
D
Show answer & explanation
Correct answer: C
Concept: In Data Sufficiency, a statement (or combination of statements) is sufficient only when it narrows the situation down to exactly one definite answer to the question asked — if more than one outcome remains possible, it is insufficient. A prime number is a positive integer greater than 1 with exactly two positive divisors, 1 and itself; note that 1 itself is not prime.
Applying it here:
Statement I alone: x is a positive even integer. Positive even integers are not uniformly prime or uniformly non-prime, so this alone leaves more than one possible outcome for the question — insufficient.
Statement II alone: x is a positive integer less than 4, so x is 1, 2, or 3. These three values do not all share the same primality status, so this alone also leaves more than one possible outcome — insufficient.
Statements I and II together: x must satisfy both conditions at once — positive, even, and less than 4. Checking 1, 2, and 3 for evenness leaves exactly one integer that fits both conditions.
That single remaining integer can be checked directly against the definition of a prime number, which settles the question with one definite answer.
Cross-check: No other integer among 1, 2, 3 is even, so the combination of both statements leaves no ambiguity — a stronger result than either statement produced alone.
Result: Since neither statement alone fixes a single outcome but both together do, the correct choice is that BOTH statements TOGETHER are sufficient, while NEITHER statement is sufficient ALONE.