If 7x – y

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

If 7x – y

by BTGmoderatorDC » Sun Feb 04, 2018 1:34 am
If 7x - y = 23 and 7y - x = 31, then x + y =

(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

Can some experts show me the best solution?

OA E

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

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.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews