Is the real number p negative? (1) p^2 > 0 (2) p^3 < 0 — GMAT

Is the real number $p$ negative?

(1) $p^2 > 0$
(2) $p^3 < 0$

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.

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

Statement (1) tells us that

p^2 > 0

, which means

p

can be any real number except 0. Since

p

could be positive (e.g.,

p = 5

) or negative (e.g.,

p = -5

), Statement (1) alone cannot answer whether

p

is negative.

Statement (2) tells us that

p^3 < 0

. Because taking an odd power of a real number preserves its sign,

p^3 < 0

implies

p

must be negative. This provides a definitive 'Yes' answer to the question stem, making Statement (2) sufficient alone.

Evaluate Statement (1):

p^2 > 0

p

can be any non-zero real number (e.g.,

p = 2

p = -2

Squaring any non-zero real number yields a positive value. Thus,

p

could be positive or negative, so Statement (1) is not sufficient.

Evaluate Statement (2):

p^3 < 0

p

must be negative.

An odd exponent preserves the sign of the base. If

p^3 < 0

, then

p

must be negative. This provides a definitive 'Yes' answer to whether

p

is negative, so Statement (2) is sufficient.

Properties of real numbers under even and odd exponents

Estimated Time:1m 0s

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