NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 06:40 It is currently 25 Apr 2024, 06:40
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the solution (x, y) of the following system of equations?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16597 [12]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
What is the solution (x, y) of the following system of equations? [#permalink] New post   28 Nov 2019, 01:24
1
Kudos
11
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

69% (02:34) correct 31% (02:38) wrong based on 134 sessions
Hide Show timer Statistics
[GMAT math practice question]

What is the solution (\(x, y\)) of the following system of equations?

\(\frac{7}{x+y} + \frac{3}{x-y} = 1\) and \(\frac{1}{x+y} - \frac{2}{x-y} = 5\)

A. (\(\frac{3}{4}, \frac{1}{4}\))

B. (\(\frac{3}{5}, \frac{1}{4}\))

C. (\(\frac{1}{4}, \frac{3}{4}\))

D. (\(\frac{3}{5}, \frac{1}{5}\))

E. (\(\frac{3}{4}, \frac{1}{5}\))
ShowHide Answer
Official Answer
C
User avatar
D
GMATGuruNY
Tutor
Joined: 04 Aug 2010
Posts: 1315
Own Kudos [?]: 3136 [2]
Given Kudos: 9
Schools:Dartmouth College
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   28 Nov 2019, 03:49
2
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

What is the solution (\(x, y\)) of the following system of equations?

\(\frac{7}{x+y} + \frac{3}{x-y} = 1\) and \(\frac{1}{x+y} - \frac{2}{x-y} = 5\)

A. (\(\frac{3}{4}, \frac{1}{4}\))

B. (\(\frac{3}{5}, \frac{1}{4}\))

C. (\(\frac{1}{4}, \frac{3}{4}\))

D. (\(\frac{3}{5}, \frac{1}{5}\))

E. (\(\frac{3}{4}, \frac{1}{5}\))


ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES.

The correct answer must satisfy the following equation:
\(\frac{7}{x+y} + \frac{3}{x-y} = 1\)
In every answer choice, \(x+y≤1\), with the result that \(\frac{7}{x+y}≥7\).
Implication:
For left side of the equation to sum to 1, \(\frac{3}{x-y}\) must be NEGATIVE.
\(\frac{3}{x-y}\) will be negative only if \(x<y\).
The correct answer must be C:
\(\frac{1}{4} < \frac{3}{4}\)

Show Spoiler
C
avatar
B
devavrat
Manager
Manager
Joined: 19 Feb 2019
Posts: 99
Own Kudos [?]: 28 [0]
Given Kudos: 58
Location: India
Concentration: Marketing, Statistics
Schools: Rotman '22 (D) Krannert '22 (D) Cass '21 (WL)
GMAT 1: 650 Q46 V34
GPA: 3
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   28 Nov 2019, 10:08
Quote:
In every answer choice, x+y≤1x+y≤1, with the result that 7x+y≥77x+y≥7.


Hi can you pls explain this in detail. I did not understand how you reached x+y <= 1
User avatar
D
GMATGuruNY
Tutor
Joined: 04 Aug 2010
Posts: 1315
Own Kudos [?]: 3136 [1]
Given Kudos: 9
Schools:Dartmouth College
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   28 Nov 2019, 13:05
1
Kudos
Expert Reply
devavrat wrote:
Quote:
In every answer choice, x+y≤1x+y≤1, with the result that 7x+y≥77x+y≥7.


Hi can you pls explain this in detail. I did not understand how you reached x+y <= 1


The answer choices represent options for (x, y).

Every option yields a sum for x and y that is less than or equal to 1:
A --> \(\frac{3}{4} + \frac{1}{4} = 1\)
B --> \(\frac{3}{5} + \frac{1}{4} = \frac{17}{20}\)
C --> \(\frac{1}{4} + \frac{3}{4}\) = 1
D --> \(\frac{3}{5} + \frac{1}{5} = \frac{4}{5}\)
E --> \(\frac{3}{4} + \frac{1}{5} = \frac{19}{20}\)
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16597 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   01 Dec 2019, 21:07
2
Kudos
Expert Reply
=>

Assume \(A = \frac{1}{(x+y)}\) and \(B = \frac{1}{(x-y)}.\)

Then we have \(7A + 3B = 1\) and \(A – 2B = 5\) or \(A = 2B + 5.\)

Substituting the second equation into the first gives us \(7(2B+5)+ 3B = 1, 17B + 35 = 1, 17B = -34\), and \(B = -2.\)

Substituting \(B = -2\) into \(A = 2B + 5\) gives us \(A = 2(-2) + 5, A = 1.\)

Then \(x + y = \frac{1}{A} = \frac{1}{1} = 1\) and \(x – y = \frac{1}{B} = \frac{1}{(-2)} = \frac{-1}{2}.\)

Adding \(x + y = 1\) and \(x - y = \frac{-1}{2}\) gives us \(x + y + x - 7 = 1 - \frac{1}{2}\).

We have \(2x = \frac{1}{2}\) or \(x = \frac{1}{4}.\)

Then we have \(y = 1 – x = \frac{3}{4}.\)

Therefore, the answer is C.
Answer: C
User avatar
D
QuantMadeEasy
Senior Manager
Senior Manager
Joined: 28 Feb 2014
Posts: 471
Own Kudos [?]: 559 [1]
Given Kudos: 74
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE:Engineering (Education)
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   01 Dec 2019, 22:33
1
Bookmarks
MathRevolution wrote:
[GMAT math practice question]

What is the solution (\(x, y\)) of the following system of equations?

\(\frac{7}{x+y} + \frac{3}{x-y} = 1\) and \(\frac{1}{x+y} - \frac{2}{x-y} = 5\)

A. (\(\frac{3}{4}, \frac{1}{4}\))

B. (\(\frac{3}{5}, \frac{1}{4}\))

C. (\(\frac{1}{4}, \frac{3}{4}\))

D. (\(\frac{3}{5}, \frac{1}{5}\))

E. (\(\frac{3}{4}, \frac{1}{5}\))

1/(x+y) = a, 1/(x-y) = b
7a + 3b = a
a - 2b = 5
Solving for a and b
a = 1, b = -2

x + y = 1
x - y = 1/2

x = 1/4
y = 3/4

C is correct.
User avatar
B
Ahmed9955
Manager
Manager
Joined: 18 Feb 2019
Posts: 87
Own Kudos [?]: 21 [0]
Given Kudos: 327
Location: India
Schools: Booth '24 Fuqua '24 ISB '23 NTU NUS Ross '24 Rotman '24 Yale '24
GMAT 1: 570 Q46 V21
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   03 Dec 2019, 04:31
Consider x+y=u & x-y =v
Solve for => 7/u +3/v = 1 ....Eq1
1/v -2/u = 5. .....Eq2
Solve for u & v
Then solve for x & y.
Correct ans C

Posted from my mobile device
User avatar
B
nisthagupta28
Intern
Intern
Joined: 28 Mar 2019
Posts: 47
Own Kudos [?]: 16 [0]
Given Kudos: 217
Location: India
GMAT 1: 660 Q44 V40
GMAT 2: 650 Q45 V37
Send PM
What is the solution (x, y) of the following system of equations? [#permalink] New post   13 Jun 2021, 22:28
Adding x+y=1
x+y=1
and x−y=−12
x−y=−1/2
gives us x+y+x−7=1−12
x+y+x−7=1−1/2.

Can someone explain this step?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32673
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: What is the solution (x, y) of the following system of equations? [#permalink] New post   04 May 2023, 03:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: What is the solution (x, y) of the following system of equations? [#permalink]
04 May 2023, 03:42
Moderators:
Bunuel
Math Expert
92912 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions