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Is a positive?

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Is a positive?

by Gmat_mission » Mon Jun 18, 2018 2:14 am

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Is a positive?

(1) a - a = 0
(2) a + a = 2a

[spoiler]OA=E[/spoiler].

The first equation says that a is negative. Am I wrong? Please, someone clarifies this to me. <i class="em em-neutral_face"></i>
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by Vincen » Mon Jun 18, 2018 3:01 am

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Hello Gmat_mission.

Let's take a look at your question.

We need to answer is a is positive or not.

First Statement
(1) a - a = 0
This statement doesn't tell us anything about a, because $$a-a=0\ \ \ \Rightarrow\ \ 0=0.$$ Then, we don't know anything about a. Not Sufficient.

Second Statement
(2) a + a = 2a
This statement doesn't tell us anything about a, because $$a+a=2a\ \ \ \Rightarrow\ \ 2a=2a\ \Rightarrow\ \ 0=0.$$ Then, we don't know anything about a. Not Sufficient.

First Statement+ Second Statement
(1) a - a = 0
(2) a + a = 2a
Again, none of the statements give us information about a. Not Sufficient.

Therefore, the correct answer is the option E.

I hope it is clear enough.
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by Brent@GMATPrepNow » Mon Jun 18, 2018 4:35 am

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Gmat_mission wrote:Is a positive?

(1) a - a = 0
(2) a + a = 2a
Target question: Is a positive?

Jump straight to....

Statements 1 and 2 combined
There are infinitely many values of a that satisfy BOTH statements. Here are two:
Case a: a = 1 (this satisfies BOTH statements). In this case, the answer to the target question is YES, a IS positive
Case b: a = -1 (this satisfies BOTH statements). In this case, the answer to the target question is NO, a is NOT positive
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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by Brent@GMATPrepNow » Mon Jun 18, 2018 4:37 am

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Gmat_mission wrote: The first equation says that a is negative. Am I wrong?
All values (positive or negative) of a will satisfy the equation a - a = 0

For example, if a = 3, then we get: 3 - 3 = 0 (works!)
Conversely, if a = -3, then we get: -3 - (-3) = 0 (works!)
And, if a = 0, then we get: 0 - 0 = 0 (works!)

Cheers,
Brent
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