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

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Founder
Joined: 18 Apr 2015
Posts: 7014
Followers: 117

Kudos [?]: 1369 [0], given: 6372

If a<b<0 which of the following numbers must be positive? [#permalink]  30 Jan 2016, 09:21
Expert's post
00:00

Question Stats:

65% (00:55) correct 34% (00:41) wrong based on 44 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

_________________
Founder
Joined: 18 Apr 2015
Posts: 7014
Followers: 117

Kudos [?]: 1369 [0], given: 6372

Re: If a<b<0 which of the following numbers must be positive? [#permalink]  30 Jan 2016, 09:25
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
_________________
Intern
Joined: 10 Jun 2018
Posts: 32
Followers: 0

Kudos [?]: 16 [1] , given: 4

Re: If a<b<0 which of the following numbers must be positive? [#permalink]  04 Sep 2018, 20:01
1
KUDOS
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.
Re: If a<b<0 which of the following numbers must be positive?   [#permalink] 04 Sep 2018, 20:01
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