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If a<b<0 which of the following numbers must be positive?

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If a<b<0 which of the following numbers must be positive? [#permalink]  30 Jan 2016, 09:21
Expert's post
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Question Stats:

69% (00:56) correct 30% (00:51) wrong based on 164 sessions
If $$a<b<0$$ which of the following numbers must be positive?

Indicate all such numbers.

A) $$a - b$$
B) $$a^2 - b^2$$
C) $$ab$$
D) $$a^2b$$
E) $$a^2b + ab^2$$

Practice Questions
Question: 15
Page: 469
Difficulty: medium

B and C
[Reveal] Spoiler: OA

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Founder
Joined: 18 Apr 2015
Posts: 13882
GRE 1: Q160 V160
Followers: 313

Kudos [?]: 3671 [1] , given: 12895

Re: If a<b<0 which of the following numbers must be positive? [#permalink]  30 Jan 2016, 09:25
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Expert's post
Solution

The values a = -3 and b = -2 satisfy the given inequality.

So, let's plug these values for a and b into the answer choices....

A) (-3) - (-2) = -1 NEGATIVE

B) (-3)² - (-2)² = 9 - 4 = 5 POSITIVE

C) (-3)(-2) = 6 POSITIVE

D) (-3)²(-2) = -18 NEGATIVE

E) (-3)²(-2) + (-3)(-2)² = (-18) + (-12) = -30 NEGATIVE

Substitute and you come up with the answers B and C
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Re: If a<b<0 which of the following numbers must be positive? [#permalink]  04 Sep 2018, 20:01
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B and C will be the answer
a^2 - b^2 will positive because a<b and both are negative numbers. Squaring them will make them positive and a will be bigger than b.
C is a answer cause negative * negative = positive.
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Re: If a<b<0 which of the following numbers must be positive? [#permalink]  15 Sep 2019, 05:40
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Expert's post
Carcass wrote:
If $$a<b<0$$ which of the following numbers must be positive?

Indicate all such numbers.

A) $$a - b$$
B) $$a^2 - b^2$$
C) $$ab$$
D) $$a^2b$$
E) $$a^2b + ab^2$$

A) $$a - b$$
Given: $$a<b$$
Subtract b from both sides: $$a-b<0$$
This tells us a-b is NEGATIVE

B) $$a^2 - b^2$$
$$a^2 - b^2=(a+b)(a-b)$$
Since a and b are both negative, we know that a+b = NEGATIVE
And, we already learned (above) that a-b is NEGATIVE
So, $$a^2 - b^2=(a+b)(a-b)$$ = (NEGATIVE)(NEGATIVE) = POSITIVE

C) $$ab$$
Since a and b are both negative, we know that ab = (NEGATIVE)(NEGATIVE) = POSITIVE

D) $$a^2b$$
Since a and b are both negative, we know that$$a^2b=(a)(a)(b)$$ = (NEGATIVE)(NEGATIVE)(NEGATIVE) = NEGATIVE

E) $$a^2b + ab^2$$
Factor to get: $$ab(a +b)$$
We already learned (above) that ab is POSITIVE, and that a-b is NEGATIVE
So, $$ab(a +b)$$ = (POSITIVE)(NEGATIVE) = NEGATIVE

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: If a<b<0 which of the following numbers must be positive? [#permalink]  16 Sep 2019, 08:22
Quick question: If I only pick one choice from 2 correct answers, is the answer marked wrong?
Founder
Joined: 18 Apr 2015
Posts: 13882
GRE 1: Q160 V160
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Kudos [?]: 3671 [0], given: 12895

Re: If a<b<0 which of the following numbers must be positive? [#permalink]  16 Sep 2019, 08:40
Expert's post
Quick question: If I only pick one choice from 2 correct answers, is the answer marked wrong?

Yes, definitely.

regards
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Re: If a<b<0 which of the following numbers must be positive? [#permalink]  16 Sep 2019, 08:53
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Expert's post
Quick question: If I only pick one choice from 2 correct answers, is the answer marked wrong?

I should add that getting 1 of 2 correct answers is no different from getting 0 of 2 correct answers.
That is, there are no partial marks on the GRE.
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Brent Hanneson – Creator of greenlighttestprep.com

Re: If a<b<0 which of the following numbers must be positive?   [#permalink] 16 Sep 2019, 08:53
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