Inequalities problem set

[theachiever]

If TG>0 and G is negative which of the following must be positive?

A.T+G
B.2T+G
C.T-G
D.G-T
E.-G-T

[GMATGuruNY]

If TG>0 and G is negative which of the following must be positive?

A.T+G
B.2T+G
C.T-G
D.G-T
E.-G-T

Show that the answer choices DON'T have to be positive.
Let G=-1 and T=-1.

A: T+G = -1+(-1) = -2. Eliminate A.
B: 2T+G = 2(-1) + (-1) = -3. Eliminate B.
C: T-G = -1-(-1) = 0. Eliminate C.
D: G-T = -1-(-1) = 0. Eliminate D.

The correct answer is E.

E: -G-T = -(negative)-(negative) = positive + positive = positive.

[Brent@GMATPrepNow]

If TG>0 and G is negative which of the following must be positive?

A.T+G
B.2T+G
C.T-G
D.G-T
E.-G-T

Step 1: If G is negative, and (T)(G) is positive, then we can be certain that T is also negative.

Step 2: Determine which of the following must be positive?

A) T+G = negative + negative = negative. Since T+G need not be positive, eliminate it.

B) 2T+G = 2(negative) + negative = negative + negative = negative. Eliminate it.

C) T-G = negative - negative. This could be positive, but it need not be. For example, (-2) - (-1) = -1. Since T-G isn't always positive, eliminate it.

D) G-T = negative - negative = This could be positive, but it need not be. For example, (-2) - (-1) = -1. Since G-T isn't always positive, eliminate it.

By the process of elimination, E must be the correct answer. Take it and move onto the next question.

Cheers,
Brent