Data Sufficiency

Max@Math Revolution wrote:[GMAT math practice question]

Is x < 0?

1) x³ + 1 < 0
2) x³ + x + 1 < 0

Target question: Is x < 0?

Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE

An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE

Statement 1: x³ + 1 < 0
Subtract 1 from both sides to get: x³ < -1
If x³ is less than -1, then x³ is NEGATIVE
Since an odd power (like 3) preserves the sign of the base, we know that x is NEGATIVE
The answer to the target question is YES, it is true that x < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x³ + x + 1 < 0
Subtract 1 from both sides to get: x³ + x < -1
Let's see what happens when x is POSITIVE, and when x is NEGATIVE

If x is POSITIVE, we get: POSITIVE³ + POSITIVE < -1
Use the above rule to simplify: POSITIVE + POSITIVE < -1
This is IMPOSSIBLE, so it CANNOT be the case that x is positive

If x is NEGATIVE, we get: NEGATIVE³ + NEGATIVE< -1
Use the above rule to simplify: NEGATIVE + NEGATIVE < -1
PERFECT!
The answer to the target question is YES, it is true that x < 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent