If x is a real number, is x > 0? (1) |x| = 5 (2) x + 3 > 5 — GMAT

If $x$ is a real number, is $x > 0$ ?

(1) $|x| = 5$
(2) $x + 3 > 5$

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

Answer

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

The choice stating that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient, is correct because Statement (1) yields two possible values for

x

(

5

and

-5

), resulting in both 'Yes' and 'No' answers. In contrast, Statement (2) simplifies to

x > 2

, which guarantees that

x > 0

with a definitive 'Yes'.

Step-by-Step Solution

Rephrase the target question

The target asks whether

x

lies to the right of

0

on the real number line (a Yes/No question).

Establishing clear sufficiency criteria requires identifying what yields a definitive 'Yes' or definitive 'No'.

Evaluate Statement (1):

|x| = 5

x

can be

5

-5

. If

x = 5

, the answer is Yes (

5 > 0

). If

x = -5

, the answer is No (

-5 \ngtr 0

Since Statement (1) allows both a 'Yes' and a 'No' response, it is NOT sufficient.

Evaluate Statement (2):

x + 3 > 5

Subtracting

3

from both sides gives

x > 2

. Any number strictly greater than

2

is automatically greater than

0

Statement (2) provides a definitive 'Yes' answer to the question

x > 0

, so Statement (2) ALONE is sufficient.

Key Concept

Absolute Value Definition and Single-Variable Inequality Simplification in Data Sufficiency

Question

Answer

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Key Concept

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