BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is a negative?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Fri Nov 10, 2017 9:33 pm
Thanked: 7 times
Followed by:1 members

TTT

by OWN » 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).

Answer choice A.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Is a negative?

by Brent@GMATPrepNow » 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

Answer: A

RELATED VIDEO
https://www.gmatprepnow.com/module/gmat ... /video/982

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1