If x is a real number, is |x - 3| 0 Which of the following describes the sufficiency of the statements?

If x is a real number, is |x - 3| < 5? (1) 1 < x < 6 (2) x > 0 Which of the following desc… — GMAT

If $x$ is a real number, is $|x - 3| < 5$ ?

(1) $1 < x < 6$
(2) $x > 0$

Which of the following describes the sufficiency of the statements?

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

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

The correct choice is the option stating that Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Rephrasing

|x - 3| < 5

yields

-2 < x < 8

. Statement (1) restricts

x

(1, 6)

, which is completely inside

(-2, 8)

, guaranteeing a 'Yes' answer. Statement (2) allows values like

x = 2

('Yes') and

x = 10

('No'), so it is not sufficient.

Rephrase the target inequality from the stem.

The absolute value inequality

|x - 3| < 5

is equivalent to

-5 < x - 3 < 5

. Adding 3 to all parts gives

-2 < x < 8

. The question asks: 'Is

x

strictly between

-2

and

8

Simplifying the stem into a clear range for

x

makes evaluating sufficiency straightforward.

Evaluate Statement (1):

1 < x < 6

Every number in the interval

(1, 6)

is strictly between

-2

and

8

. Thus, the answer to 'Is

-2 < x < 8

?' is a definitive 'Yes'. Statement (1) alone is sufficient.

Since the entire set of allowed values under statement (1) is a subset of

(-2, 8)

, statement (1) provides a conclusive answer.

Evaluate Statement (2):

x > 0

x = 2

, then

-2 < 2 < 8

is True (Yes). However, if

x = 10

, then

-2 < 10 < 8

is False (No). Because both 'Yes' and 'No' are possible, Statement (2) alone is not sufficient.

A statement is insufficient if it permits values that produce conflicting answers to the target question.

Absolute Value Inequalities and Range Containment in Data Sufficiency