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What is the value of x?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Jul 31, 2018 4:48 am

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BTGmoderatorDC wrote:What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39
We see that there are two variables x and y. To get the value of x, we must know the value of y. We see that each of the statements gives a linear equation. If the two linear equations are not the same, we can solve for x.

Upon simplifying each statement, you get the equation 2x - 5y - 6 = 0. In other words, we have only one equation. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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by deloitte247 » Wed Aug 01, 2018 2:20 am

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2x - 5y + 6 = Statement 1
2x - 5y = 12 - 6
2x - 5y = 6
$$\frac{2x}{2}=\ \frac{\left(6\ +\ 5y\right)}{2}$$
$$x\ =\ \frac{\left(6\ +\ 5y\right)}{2}$$
No sufficient information for the value of x and y. Hence statement 1 is not sufficient.

Statement 2 = 8x - (4x + 10y) + 27 = 39
8x - 4x - 10y = 12
$$\frac{4x}{2\ }\ -\ \frac{10y}{2\ }=\ \frac{12}{2}$$
2x - 5y = 6
It is the same thing with statement 1 and it is not sufficient because the information for x and y is not enough.
Combining statement 1 and 2 together.
Statement 1 = 2x - 5y = 6
$$Statement\ 2\ =\ \frac{4x}{2\ }-\ \frac{10y}{2}\ =\ \frac{12}{2}$$
= 2x - 5y = 6
The two statement are equivalent to each other and since each statement alone is not sufficient, both statement combined are also NOT SUFFICIENT.
Option E is correct.
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