GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 03:46

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the solution (x, y) of the following system of equations?  [#permalink]

### Show Tags

28 Nov 2019, 01:24
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:07) correct 41% (02:48) wrong based on 29 sessions

### HideShow 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. ($$\frac{3}{4}, \frac{1}{5}$$)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 04 Aug 2010 Posts: 496 Schools: Dartmouth College Re: What is the solution (x, y) of the following system of equations? [#permalink] ### Show Tags 28 Nov 2019, 03:49 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: $$\frac{1}{4} < \frac{3}{4}$$ _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Manager Joined: 19 Feb 2019 Posts: 95 Concentration: Marketing, Statistics Re: What is the solution (x, y) of the following system of equations? [#permalink] ### Show Tags 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 Senior Manager Joined: 04 Aug 2010 Posts: 496 Schools: Dartmouth College Re: What is the solution (x, y) of the following system of equations? [#permalink] ### Show Tags 28 Nov 2019, 13:05 1 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 --> $$\frac{3}{4} + \frac{1}{5} = \frac{19}{20}$$ _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8235 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the solution (x, y) of the following system of equations? [#permalink] ### Show Tags 01 Dec 2019, 21:07 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 28 Feb 2014
Posts: 202
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: What is the solution (x, y) of the following system of equations?  [#permalink]

### Show Tags

01 Dec 2019, 22:33
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.
Intern
Joined: 18 Feb 2019
Posts: 10
Re: What is the solution (x, y) of the following system of equations?  [#permalink]

### Show Tags

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
Re: What is the solution (x, y) of the following system of equations?   [#permalink] 03 Dec 2019, 04:31
Display posts from previous: Sort by