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Does x + y = 5?

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Does x + y = 5?

by Gmat_mission » Sun May 13, 2018 10:27 am

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Does x + y = 5?

(1) 4x + y = 17
(2) x + 4y = 8

[spoiler]OA=C[/spoiler].

How can I show that the correct answer is the option C? Could someone give me a good explanation? Please. Thanks.
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Source: — Data Sufficiency |
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by Vincen » Sun May 13, 2018 11:11 am

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Gmat_mission wrote:Does x + y = 5?

(1) 4x + y = 17
(2) x + 4y = 8

[spoiler]OA=C[/spoiler].

How can I show that the correct answer is the option C? Could someone give me a good explanation? Please. Thanks.
Hello Gmat_mission.

Let's take a look at your question.

x + y = 5?

(1) 4x + y = 17

Since we have two variables and one equation, we can not conclude anything here. Hence, this statement IS NOT SUFFICIENT.

(2) x + 4y = 8

Again, we have two variables and one equation, we can not conclude anything. Hence, this statement IS NOT SUFFICIENT.

(1) 4x + y = 17 and (2) x + 4y = 8

Now, if we add both equations we will get: $$5x+5y=25$$ $$\Rightarrow\ \ \ x+y=5.\ $$ Since we could give an answer to the original question, then we conclude that both statements together are SUFFICIENT.

Therefore, the correct answer is the option C.
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