If both a and b are nonzero integers, which of the following must be positive?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If both a and b are nonzero integers, which of the following must be positive?

by BTGmoderatorDC » Mon May 18, 2020 5:59 pm

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If both a and b are nonzero integers, which of the following must be positive?

I. a^2 + b^2
II. a^2 – b^2
III. (a – b)^2

A. I only
B. II only
C. III only
D. I and II
E. I, II, and III

OA A

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Mon May 18, 2020 5:59 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If both a and b are nonzero integers, which of the following must be positive?

by Scott@TargetTestPrep » Sun May 24, 2020 6:05 am

BTGmoderatorDC wrote: ↑
Mon May 18, 2020 5:59 pm
If both a and b are nonzero integers, which of the following must be positive?

I. a^2 + b^2
II. a^2 – b^2
III. (a – b)^2

A. I only
B. II only
C. III only
D. I and II
E. I, II, and III

OA A

Since both a and b are nonzero integers, a^2 and b^2 are both positive, and hence the sum a^2 + b^2 is also positive. Statement I is true. However, the difference a^2 - b^2 might not be positive. For example, if a = 1 and b = 2, then a^2 - b^2 = 1 - 4 = -3, which is not positive. Statement II is not true. Finally, if a = 1 and b = 1, then (a - b)^2 = (1 - 1)^2 = 0, which is not positive. Statement III is not true either.

Answer: A

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