If a and b are negative integers, which of the . . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Jan 16, 2018 9:21 am

If a and b are negative integers, which of the following statements must be true?

I. (-a)^b is positive.
II. (-a)^(-b) is positive.
III. a^(-b) is positive.

A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III

The OA is the option C.

How can I verify which options are true? Experts, can you help me here? Please.

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Source: Beat The GMAT — Problem Solving | Tue Jan 16, 2018 9:21 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Tue Jan 16, 2018 10:14 am

Hello Vincen.

Let's take a look at your question.

If we choose a = -2 and b = -3, we will have

I. (-a)^b = (2)^(-3) = 1/(2^3) --> Positive
II. (-a)^(-b) = 2^3 --> Positive
III. a^(-b) = -2^3 --> Negative

Then, the correct answer is the option C.

I hope this answer can help you to understand.

I'm available if you'd like a follow-up.

Regards.

GMAT Prep From The Economist
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:43 am

Vincen wrote:If a and b are negative integers, which of the following statements must be true?

I. (-a)^b is positive.
II. (-a)^(-b) is positive.
III. a^(-b) is positive.

A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III

We can say a = -2, and b = -1.

I. (-a)^b = (-(-2))^-1 = 2^-1 = 1/2

Thus, (-a)^b is positive.

II.(-a)^(-b) = (-(-2))^(-(-1)) = 2^1 = 2

Thus, (-a)^(-b) is positive.

III. a^(-b) = -2^-(-1) = -2^1 = -2

Thus, a^(-b) IS NOT positive.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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