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## Is a negative?

tagged by: Brent@GMATPrepNow

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#### Is a negative?

Sun Dec 03, 2017 2:57 am
Is a negative?

(1) (1 + a)^3 is negative.
(2) 1 - a is positive.

Can some experts know how to identify the best option?

OA A

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Sun Dec 03, 2017 11:12 am
lheiannie07 wrote:
Is a negative?

(1) (1 + a)^3 is negative.
(2) 1 - a is positive.
Target question: Is a < 0?

Statement 1: (1 + a)^3 is negative
KEY CONCEPT: Odd powers preserve the sign of the base
So, POSITIVE^(odd number) = some POSITIVE number
and NEGATIVE^(odd number) = some NEGATIVE number

So, if (1 + a)^3 is NEGATIVE , then we can be certain that (1 + a) is NEGATIVE (since 3 is an odd power)
That is 1+a < 0
Since it is also true that a < a + 1 (for all values of a), we can COMBINE the inequalities to get: a < 1+a < 0
So, as we can see, it is definitely the case that a < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1 - a is positive.
There are several values of a that satisfy statement 2. Here are two:
Case a: a = 0.3. Notice that 1 - 0.3 = 0.7, which is positive. In this case, a > 0
Case b: a = -2 Notice that 1 - (-2) = 3, which is positive. In this case, a < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEO
https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/video/982

Cheers,
Brent

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Sun Dec 03, 2017 11:00 am
Hi lheiannie07,

Start off by identifying the question type:
Yes or no

We are given no information about a in the prompt, so it could be ANY number.

Let's check fact 1:

$$\left(1+a\right)^3\ is\ negative,\ so\ \left(1+a\right)^3\ <\ 0$$

As a rule, we know that if a cubed number is negative, its cubic root must also be negative, therefore:

$$\left(1+a\right)\ <\ 0$$

Subtracting 1 from both sides of the inequality yields:
$$a<-1$$

Therefore, a is always negative. Fact 1 is sufficient so we can slash answer choices B,C, and E

Now, to check fact 2:

$$\left(1-a\right)\ is\ positive,\ hence\ 1-a>0$$

Add an "a" to each side of the inequality and we will get:

$$1>a$$

Since the prompt doesn't give us any information regarding a, it could be anything, including decimals and zeros. As such, fact 2 is insufficient since it includes non-negative numbers (zero and positive decimals).

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