Question

Is integer \( x \) a prime number? Statement (I): \( 47 < x < 53 \)
Statement (II): \( x > 1 \)

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

Data sufficiency does not require the answer to be "Yes." If the provided information allows you to conclude "No" definitively, the statement is still considered sufficient.

Answer 1

The Correct Option is A

Concept: A prime number is an integer greater than 1 that has no divisors other than 1 and itself.

Step 1: Evaluate Statement (I). The integers satisfying \( 47 < x < 53 \) are: \[ x \in \{48, 49, 50, 51, 52\} \] Let's check each for primality:
• \( 48 = 2 \times 24 \) (Composite)
• \( 49 = 7 \times 7 \) (Composite)
• \( 50 = 2 \times 25 \) (Composite)
• \( 51 = 3 \times 17 \) (Composite)
• \( 52 = 2 \times 26 \) (Composite) Since none of these integers are prime, we can definitively answer "No, \( x \) is not a prime number." Because we can provide a definitive answer, Statement (I) is sufficient.

Step 2: Evaluate Statement (II). \( x > 1 \). This includes prime numbers (e.g., 2, 3, 5) and composite numbers (e.g., 4, 6, 8). It is insufficient. {(A) Statement (I) alone is sufficient.}