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# If a(a − 5)(a + 2) = 0, is a negative? (1) a(a − 7) ≠ 0 (2) a^2 − 2a −

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Math Expert
Joined: 02 Sep 2009
Posts: 50714
If a(a − 5)(a + 2) = 0, is a negative? (1) a(a − 7) ≠ 0 (2) a^2 − 2a −  [#permalink]

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30 Oct 2018, 03:45
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Difficulty:

45% (medium)

Question Stats:

57% (00:50) correct 43% (01:56) wrong based on 37 sessions

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If a(a − 5)(a + 2) = 0, is a negative?

(1) a(a − 7) ≠ 0

(2) a^2 − 2a − 15 ≠ 0

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Joined: 18 Jul 2018
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Re: If a(a − 5)(a + 2) = 0, is a negative? (1) a(a − 7) ≠ 0 (2) a^2 − 2a −  [#permalink]

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30 Oct 2018, 04:13
1
From the question a = 0, a = 5 or a = -2.

From statement 1:

$$a\neq{0}$$ and $$a\neq{7}$$.
a can be either 5 or -2. Positive or negative.
Insufficient.

From statement 2:

$$a^2-2a-15 \neq{0}$$

$$(a-5)(a+3) \neq{0}$$
$$a\neq{5}$$ or $$a\neq{-3}$$

a can be either 0 or -2.
Since 0 is unsigned.
Insufficient.

Combining both gives a = -2.
a is negative.
Sufficient.

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Re: If a(a − 5)(a + 2) = 0, is a negative? (1) a(a − 7) ≠ 0 (2) a^2 − 2a − &nbs [#permalink] 30 Oct 2018, 04:13
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