If x and y are real numbers, is x > y? (1) y - x = |x + 3| + 1 (2) x + y = 10 — GMAT

If $x$ and $y$ are real numbers, is $x > y$ ?

(1) $y - x = |x + 3| + 1$
(2) $x + y = 10$

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Answer
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
EACH statement ALONE is sufficient.
E
Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

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

The option stating that Statement (1) alone is sufficient while Statement (2) alone is not is correct. Statement (1) demonstrates that

y - x = |x + 3| + 1 \ge 1

, which proves

y > x

. Consequently, the answer to 'Is

x > y

?' is a guaranteed, definitive 'No'. In GMAT Yes/No Data Sufficiency questions, any statement that yields a conclusive 'No' is sufficient. Statement (2) allows multiple relative orderings of

x

and

y

, making it insufficient.

Step-by-Step Solution

Analyze the question stem

The target is a Yes/No question: 'Is

x > y

?' Any statement that yields a definitive 'Yes' OR a definitive 'No' is sufficient.

Data Sufficiency Yes/No decision logic requires evaluating whether a statement yields a single consistent truth value.

Evaluate Statement (1):

y - x = |x + 3| + 1

Since absolute value is always non-negative (

|x + 3| \ge 0

), we have

y - x \ge 0 + 1 = 1 > 0

. Thus,

y - x > 0 \implies y > x

Because

y > x

is always true under Statement (1), the answer to 'Is

x > y

?' is a definitive 'No'.

Conclude sufficiency for Statement (1)

A definitive 'No' is SUFFICIENT. Statement (1) alone is sufficient.

In GMAT Data Sufficiency, a consistent negative answer resolves the question completely.

Evaluate Statement (2):

x + y = 10

x = 6

and

y = 4

, then

x > y

is 'Yes'. If

x = 4

and

y = 6

, then

x > y

is 'No'.

Since both 'Yes' and 'No' are possible, Statement (2) alone is NOT sufficient.

Key Concept

Definitive Yes/No Decision Logic in Data Sufficiency

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