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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] New post 30 Jan 2016, 09:21
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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) \(a^2b + ab^2\)



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Question: 15
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Difficulty: medium


B and C
[Reveal] Spoiler: OA

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Re: If a<b<0 which of the following numbers must be positive? [#permalink] New post 30 Jan 2016, 09:25
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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] New post 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] New post 15 Sep 2019, 05:40
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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

Answer: B and C

Cheers,
Brent
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Re: If a<b<0 which of the following numbers must be positive? [#permalink] New post 16 Sep 2019, 08:22
Quick question: If I only pick one choice from 2 correct answers, is the answer marked wrong?
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Re: If a<b<0 which of the following numbers must be positive? [#permalink] New post 16 Sep 2019, 08:40
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kloppismydad wrote:
Quick question: If I only pick one choice from 2 correct answers, is the answer marked wrong?


Yes, definitely.

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