Question

What is the value of \(x\)?
(1) \(x^2 − 5x + 4 = 0\)
(2) \(x\) is not prime.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
• D. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In data sufficiency, check if the second statement actually rules out any of the options from the first before concluding sufficiency.

Answer 1

The Correct Option is D

From (1): \(x^2 - 5x + 4 = 0 \Rightarrow (x - 1)(x - 4) = 0\), so \(x = 1\) or \(x = 4\). Not unique ⇒ insufficient. From (2): \(x\) is not prime ⇒ many possible values ⇒ insufficient. Together: Both \(1\) and \(4\) are non-prime numbers, so statement (2) does not eliminate either value from statement (1). Hence \(x\) is still not uniquely determined. \(\boxed{\text{D}}\) is correct.