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If 7x – y

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by GMATGuruNY » Sun Feb 04, 2018 3:06 am
lheiannie07 wrote:If 7x – y = 23 and 7y – x = 31, then x + y =

(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Adding together the two equations, we get:
(7x-y) + (7y-x) = 23 + 31
6x + 6y = 54
x+y = 9.

The correct answer is E.
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by EconomistGMATTutor » Sun Feb 04, 2018 10:24 am
If 7x - y = 23 and 7y - x = 31, then x + y =

(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Hi lheiannie07,
Let's take a look at your question.

$$7x-y=23\ ...\ \left(i\right)$$
$$7y-x=31\ ...\ \left(ii\right)$$

Adding Eq(i) and (ii),
$$7x-y+7y-x=23+31\ $$
$$6x+6y=54\ $$
$$6\left(x+y\right)=54\ $$
$$x+y=\frac{54}{6}=9$$

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.
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by Jeff@TargetTestPrep » Tue Feb 06, 2018 5:23 pm
lheiannie07 wrote:If 7x – y = 23 and 7y – x = 31, then x + y =

(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
If we add the two given equations, we will have:

6x + 6y = 54

Divide both sides by 6, we have:

x + y = 9

Answer: E

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