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# If a^2 + 7a < 0, then which one of the following could be the value of

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Joined: 02 Jan 2017
Posts: 315
If a^2 + 7a < 0, then which one of the following could be the value of [#permalink]

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08 Mar 2017, 04:11
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If a^2 + 7a < 0, then which one of the following could be the value of a?

(A) –3

(B) 0

(C) 1

(D) 2

(E) 3
[Reveal] Spoiler: OA
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Re: If a^2 + 7a < 0, then which one of the following could be the value of [#permalink]

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08 Mar 2017, 07:34
vikasp99 wrote:
If a^2 + 7a < 0, then which one of the following could be the value of a?

(A) –3

(B) 0

(C) 1

(D) 2

(E) 3

$$a^2 + 7a < 0$$

$$= a ( a + 7 ) < 0$$

So, $$a < 0$$ and $$a < -7$$

Among the given options and considering the form $$a < -7$$ , only option (A) –3 is true...
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Re: If a^2 + 7a < 0, then which one of the following could be the value of [#permalink]

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10 Mar 2017, 09:33
vikasp99 wrote:
If a^2 + 7a < 0, then which one of the following could be the value of a?

(A) –3

(B) 0

(C) 1

(D) 2

(E) 3

We can substitute our answer choices for a:

A) -3

Is (-3)^2 + 7(-3) < 0 ?

Is 9 - 21 < 0 ?

Alternate Solution:

The expression a^2 + 7a can only be negative if 7a is negative (because the square of every real number is nonnegative). If 7a is negative, a must be negative, and there is only one answer choice that is negative, which is -3.

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Re: If a^2 + 7a < 0, then which one of the following could be the value of   [#permalink] 10 Mar 2017, 09:33
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