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

 It is currently 22 Feb 2019, 14:44

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If x and y are both positive and √x^2 + y^2 = 3x−y, then x/y =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53066
If x and y are both positive and √x^2 + y^2 = 3x−y, then x/y =  [#permalink]

### Show Tags

17 Oct 2018, 01:26
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:42) correct 18% (01:55) wrong based on 50 sessions

### HideShow timer Statistics

If x and y are both positive and $$\sqrt{x^2 + y^2} = 3x−y$$, then x/y =

A. 0
B. 1/4
C. 1/2
D. 3/4
E. 3/2

_________________
CEO
Joined: 11 Sep 2015
Posts: 3447
Re: If x and y are both positive and √x^2 + y^2 = 3x−y, then x/y =  [#permalink]

### Show Tags

17 Oct 2018, 05:38
Top Contributor
Bunuel wrote:
If x and y are both positive and $$\sqrt{x^2 + y^2} = 3x−y$$, then x/y =

A. 0
B. 1/4
C. 1/2
D. 3/4
E. 3/2

GIVEN: $$\sqrt{x^2 + y^2} = 3x−y$$
Square both sides to get: $$x^2 + y^2 = (3x-y)^2$$
aka: $$x^2 + y^2 = (3x-y)(3x-y)$$
Expand: $$x^2 + y^2 = 9x^2 - 6xy + y^2$$
Simplify: $$x^2 = 9x^2 - 6xy$$
Simplify more: $$0 = 8x^2 - 6xy$$
Add 6xy to both sides: $$6xy = 8x^2$$
Divide both sides by x: $$6y = 8x$$
Divide both sides by y: $$6 = \frac{8x}{y}$$
Divide both sides by 8: $$6/8 = \frac{x}{y}$$
Simplify: $$3/4 = \frac{x}{y}$$

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Senior Manager
Joined: 18 Jun 2018
Posts: 263
Re: If x and y are both positive and √x^2 + y^2 = 3x−y, then x/y =  [#permalink]

### Show Tags

17 Oct 2018, 05:43
Bunuel wrote:
If x and y are both positive and $$\sqrt{x^2 + y^2} = 3x−y$$, then x/y =

A. 0
B. 1/4
C. 1/2
D. 3/4
E. 3/2

OA: D

$$\sqrt{x^2 + y^2} = 3x−y$$

Squaring both sides, we get

$$x^2 + y^2 = (3x-y)^2$$
$$x^2 + y^2 =9x^2+y^2-6xy$$
$$8x^2-6xy=0$$
$$2x(4x-3y)=0$$

As$$x\neq{0},\quad 4x-3y$$ should be equal to Zero.
$$4x-3y=0$$
$$4x=3y$$
$$\frac{x}{y}=\frac{3}{4}$$
Math Expert
Joined: 02 Aug 2009
Posts: 7334
If x and y are both positive and √x^2 + y^2 = 3x−y, then x/y =  [#permalink]

### Show Tags

17 Oct 2018, 05:46
Bunuel wrote:
If x and y are both positive and $$\sqrt{x^2 + y^2} = 3x−y$$, then x/y =

A. 0
B. 1/4
C. 1/2
D. 3/4
E. 3/2

Two ways..

1) Square both sides.. Since all terms are in X and y, squaring should help
$$\sqrt{x^2 + y^2} = 3x−y........x^2+y^2=9x^2+y^2-6xy......8x^2=6xy..........\frac{x^2}{xy}=\frac{x}{y}$$=$$\frac{3}{4}$$

2) substitute x/y=a.....x=ay
$$\sqrt{(ay)^2 + y^2} = 3ay−y$$.......$$\sqrt{a^2 + 1} = 3a-1$$......$$a^2+1=9a^2+1-6a.....8a^2-6a=0......a(8a-6)=0$$
But a is not 0, so 8a-6=0...a=6/8=3/4

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

If x and y are both positive and √x^2 + y^2 = 3x−y, then x/y =   [#permalink] 17 Oct 2018, 05:46
Display posts from previous: Sort by