What is the value of $x$?

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun Nov 24, 2019 1:11 pm

What is the value of $x$?

(1) $\dfrac{x}{7} + 5y = 109$
(2) $175y = 763(5 - x)$

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Data Sufficiency | Sun Nov 24, 2019 1:11 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Nov 25, 2019 3:31 am

M7MBA wrote:What is the value of $x$?

(1) $\dfrac{x}{7} + 5y = 109$
(2) $175y = 763(5 - x)$

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Let's take each statement one by one.

Needless to state that each statement alone is sufficient to answer the question. Let' take both statements together.

The linear equation $\dfrac{x}{7} + 5y = 109$ is manipulated to x = 763 - 35y and the linear equation $175y = 763(5 - x)$ is manipulated to 763x/5 = 763 - 35y. Since RHS of both the equations are equal, we have x = 763x/5. The only possible value for x is 0. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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