What is the value of ‘x’? Statement 1: x2 + x – 6 = 0 Statement 2: x ≥ 0

Concept

In Data Sufficiency questions, a statement (or a combination of statements) is sufficient only when it pins down exactly one value that answers the question — if it allows more than one possible value, or no determinate value at all, it is insufficient.

Application

1. Statement 1 alone: solve x2 + x – 6 = 0 by splitting the middle term: x2 + 3x – 2x – 6 = 0, so x(x + 3) – 2(x + 3) = 0, giving (x + 3)(x – 2) = 0, so x = –3 or x = 2 — two possible values, so statement 1 alone is not sufficient.

2. Statement 2 alone: x ≥ 0 only says x is non-negative; it allows infinitely many values, so statement 2 alone is not sufficient either.

3. Combining both: the two candidate values from statement 1 are –3 and 2. Statement 2's condition x ≥ 0 eliminates –3 (since it is negative), leaving exactly one value, x = 2.

Cross-check

Substituting x = 2 back into statement 1: 22 + 2 – 6 = 4 + 2 – 6 = 0, which holds; and 2 ≥ 0 satisfies statement 2 as well, confirming the combined value is consistent with both statements.

Since neither statement alone determines a unique value but both together do, the two statements together are sufficient (and neither is sufficient alone).