Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 17:35 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # M19-07 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56304

### Show Tags

1
6 00:00

Difficulty:   55% (hard)

Question Stats: 54% (01:01) correct 46% (01:01) wrong based on 241 sessions

### HideShow timer Statistics What is $$y$$ in terms of $$x$$?

(1) $$\frac{1}{\frac{x}{y} + \frac{y}{x}} = \frac{1}{2}$$

(2) $$\frac{x}{y} - \frac{y}{x} = 0$$

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56304

### Show Tags

Official Solution:

Let $$z$$ equal $$\frac{x}{y}$$.

Statement (1) by itself is sufficient. S1 gives that $$\frac{1}{z + \frac{1}{z}} = \frac{1}{2}$$ or $$z + \frac{1}{z} = 2$$ or $$z^2 + 1 = 2z$$ or $$(z - 1)^2 = 0$$ from where $$z = 1$$ and $$y = x$$.

Statement (2) by itself is insufficient. S2 gives that $$z - \frac{1}{z} = 0$$ or $$z = \frac{1}{z}$$ or $$z^2 = 1$$. This means that either $$y = x$$ or $$y = -x$$.

_________________
Intern  Joined: 27 Mar 2014
Posts: 9

### Show Tags

1
Hi Bunuel,

Can you provide some helpful tips/tricks of when we should know/recognize to use the "substitute for z" technique? It makes sense when you know to do this, but how do you recognize that this technique is a more efficient way of approaching the problem?
Current Student B
Joined: 26 Jan 2016
Posts: 100
Location: United States
GPA: 3.37

### Show Tags

1) Here you can make a quadratic

For statement one add the two fractions in the denominator together and you get 1/(x²+y²/xy)--> xy/x²+y²=1/2 cross multiple and get 2xy=x²+y² or 0=x²+y²-2XY

(x-y)²=0
x-y=0
x=y
suff

2. Here we get x/y=y/x or x²=y², if we square root both sides we dont know if x and y are each negative, each positive, or one is negative and one is positive insuff
Senior Manager  S
Joined: 08 Jun 2015
Posts: 421
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33

### Show Tags

+1 for option A.
_________________
" The few , the fearless "
Intern  B
Joined: 09 Dec 2014
Posts: 37

### Show Tags

1
Bunuel wrote:
What is $$y$$ in terms of $$x$$?

(1) $$\frac{1}{\frac{x}{y} + \frac{y}{x}} = \frac{1}{2}$$

(2) $$\frac{x}{y} - \frac{y}{x} = 0$$

Statement 1: $$\frac{1}{\frac{x}{y} + \frac{y}{x}} = \frac{1}{2}$$

==> $$\frac{1}{((x^2 + y^2)/xy)} = \frac{1}{2}$$

$$\frac{xy}{(x^2 + y^2)} = \frac{1}{2}$$

2xy = $$x^2 + y^2$$

$$x^2 + y^2$$ - 2xy=0 ==> $$(x-y)^2 = 0$$ ==> x-y = 0 ==> x=y
Sufficient.

Statement 2: $$\frac{x}{y} - \frac{y}{x} = 0$$

$$\frac{(x^2 - y^2)}{xy} = 0$$

Multiply both sides by xy

$$x^2 - y^2 = 0$$

$$x^2 = y^2$$ ==> y= +x OR y= -x
Insufficient.

_________________
Thanks,
Ramya
Intern  B
Joined: 02 Jan 2018
Posts: 4

### Show Tags

Hello Bunuel

I could be wrong here but
Option B can give you y = modulus (x), which IMO is expressing y in terms of x
Intern  B
Joined: 18 May 2018
Posts: 18
Location: India
Concentration: Marketing, Strategy
Schools: DeGroote'21 (A)
GMAT 1: 730 Q49 V40 ### Show Tags

1
For statement 2, Y can be expressed as a square root of $$x^2$$. Technically that is sufficient within the parameters of the question, no?
Intern  Joined: 07 Aug 2018
Posts: 2

### Show Tags

1
agree with others, why is X^2 = Y^2 not sufficient? is it not expressing X in terms of Y? Pls respond Bunuel why this is not the case. Thank you in advance for your help
Math Expert V
Joined: 02 Sep 2009
Posts: 56304

### Show Tags

notoriousmnz wrote:
agree with others, why is X^2 = Y^2 not sufficient? is it not expressing X in terms of Y? Pls respond Bunuel why this is not the case. Thank you in advance for your help

Thank you guys. This question is removed to tests' data base for revision.
_________________ Re: M19-07   [#permalink] 10 Nov 2018, 08:51
Display posts from previous: Sort by

# M19-07 post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel  