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# If ab > 0 and a < 0, which of the following is negative?

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Math Expert
Joined: 02 Sep 2009
Posts: 51035
If ab > 0 and a < 0, which of the following is negative?  [#permalink]

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06 Mar 2018, 20:42
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Difficulty:

15% (low)

Question Stats:

88% (00:29) correct 12% (00:30) wrong based on 35 sessions

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If ab > 0 and a < 0, which of the following is negative?

A) b

B) -b

C) -a

D) a/b

E) -(a + b)

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: If ab > 0 and a < 0, which of the following is negative?  [#permalink]

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06 Mar 2018, 20:42
Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
If ab > 0 and a < 0, which of the following is negative?  [#permalink]

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07 Mar 2018, 14:20
Bunuel wrote:
If ab > 0 and a < 0, which of the following is negative?

A) b

B) -b

C) -a

D) a/b

E) -(a + b)

Number theory
Given: $$ab > 0$$

Result? $$a$$ and $$b$$ have the same sign.
Either both are negative, or both are positive.
(-2)*(-3) = 6
(2)*(3) = 6

Given: $$a < 0$$

$$a$$
is negative.

The variables have the same sign.
$$b$$ must also be negative.

a < 0
Let a = -6
ab > 0
Let ab = 18
(-6)(b) = 18
b = -3

A) b
b = -3. Negative. Correct. Keep.

B) -b
-b = -(-3) = 3. Positive. Reject.

C) -a
a = -6. -a = -(-6) = 6. Positive. Reject.

D) a/b
-6/-3 = 2. Positive. Reject.
(if the product of two numbers is positive, the quotient of two numbers will be positive).

E) -(a + b)
-(-6 +(-3)) =
-(-6 - 3) =
-(-9) = 9. Positive. Reject.
If ab > 0 and a < 0, which of the following is negative? &nbs [#permalink] 07 Mar 2018, 14:20
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