a=x+y and b=x-y. If a^2=b^2, what is the value of y? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 14:25

### 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 June
Open Detailed Calendar

# a=x+y and b=x-y. If a^2=b^2, what is the value of y?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 12 Dec 2012
Posts: 162
Location: Poland
Followers: 5

Kudos [?]: 175 [4] , given: 67

a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

18 Jan 2013, 15:08
4
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

48% (02:24) correct 52% (08:17) wrong based on 204 sessions

### HideShow timer Statistics

$$a=x+y$$ and $$b=x-y$$. If $$a^2=b^2$$, what is the value of y?

(1) $$\sqrt{x}+\sqrt{y}>0$$

(2) $$\sqrt{x}-\sqrt{y}>0$$

M Advanced Quant, Chapter 9 (Workout Sets), Problem 73.
[Reveal] Spoiler: OA

_________________

If I answered your question with this post, use the motivating power of kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7066

Kudos [?]: 92910 [3] , given: 10528

Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

18 Jan 2013, 15:18
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
$$a=x+y$$ and $$b=x-y$$. If $$a^2=b^2$$, what is the value of y?

Given that $$(x+y)^2=(x-y)^2$$ --> $$x^2+2xy+y^2=x^2-2xy+y^2$$ --> $$4xy=0$$ --> either $$x=0$$ or $$y=0$$.

(1) $$\sqrt{x}+\sqrt{y}>0$$. It's possible that $$x=0$$ and $$y$$ is any positive number, as well as, it's possible that $$y=0$$ and $$x$$ is any positive number. Not sufficient.

(2) $$\sqrt{x}-\sqrt{y}>0$$. $$x$$ cannot be 0, since in this case we'd have that $$\sqrt{y}<0$$ (which is wrong, since square root of a number is greater than or equal to 0), thus must be true that $$y=0$$. Sufficient.

Hope it's clear.
_________________
Intern
Joined: 29 May 2013
Posts: 11
Concentration: Operations, Strategy
Schools: ISB '15
Followers: 2

Kudos [?]: 6 [1] , given: 76

Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

23 Jun 2013, 13:19
1
KUDOS
Hello Bunuel

But square root of 4 is +/-2 correct? And -2 < 0
Can u please explain why u said square root of integer cannot b less than 0?

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7066

Kudos [?]: 92910 [0], given: 10528

a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

23 Jun 2013, 13:33
Shashank1149 wrote:
Hello Bunuel

But square root of 4 is +/-2 correct? And -2 < 0
Can u please explain why u said square root of integer cannot b less than 0?

Posted from GMAT ToolKit

Square root function cannot give negative result --> $$\sqrt{some \ expression}\geq{0}$$, for example $$\sqrt{x^2}\geq{0}$$ --> $$\sqrt{4}=2$$ (not +2 and -2). In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5, because both 5^2 and (-5)^2 equal to 25.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13414
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

09 Jun 2015, 01:52
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8264
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 379

Kudos [?]: 2453 [0], given: 163

Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

09 Jun 2015, 18:42
Hi All,

This DS question is rooted in Classic Quadratics and Radical rules. There's a heavy "logic" component to this prompt, and you'll have to do a certain amount of math to get to the solution...

We're given a number of facts to work with:
1) A = X+Y
2) B = X-Y
3) A^2 = B^2

We're asked for the value of Y.

Before dealing with the two Facts, I'm going to take a moment to simplify the information in the prompt.

A^2 = (X+Y)^2 = X^2 + 2XY + Y^2
B^2 = (X-Y)^2 = X^2 - 2XY + Y^2

A^2 = B^2.....so......

X^2 + 2XY + Y^2 = X^2 - 2XY + Y^2

If we cancel out the terms, we're left with...
2XY = -2XY

There are only 3 ways for this equation to exist....
X = 0 OR Y = 0 OR BOTH = 0

This is an important restriction that will impact the answer to this question.

Fact 1: √X + √Y > 0

Since radicals are either POSITIVE or ZERO, either X or Y could = 0 (but not both).
IF....X=1, Y=0 the answer to the question is 0
IF....X=0, Y=1 the answer to the question is 1
Fact 1 is INSUFFICIENT

Fact 2: √X − √Y > 0

Here, the DIFFERENCE is > 0, so the only way for that difference to be POSITIVE, given ALL of the restrictions we've already discussed, is for the X to be POSITIVE and the Y to be 0. Here, the answer to the question is ALWAYS 0.
Fact 2 is SUFFICIENT.

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Director Joined: 26 Mar 2013 Posts: 652 Followers: 3 Kudos [?]: 131 [0], given: 94 Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink] ### Show Tags 10 Jun 2015, 05:34 EMPOWERgmatRichC wrote: Hi All, This DS question is rooted in Classic Quadratics and Radical rules. There's a heavy "logic" component to this prompt, and you'll have to do a certain amount of math to get to the solution... We're given a number of facts to work with: 1) A = X+Y 2) B = X-Y 3) A^2 = B^2 We're asked for the value of Y. Before dealing with the two Facts, I'm going to take a moment to simplify the information in the prompt. A^2 = (X+Y)^2 = X^2 + 2XY + Y^2 B^2 = (X-Y)^2 = X^2 - 2XY + Y^2 A^2 = B^2.....so...... X^2 + 2XY + Y^2 = X^2 - 2XY + Y^2 If we cancel out the terms, we're left with... 2XY = -2XY There are only 3 ways for this equation to exist.... X = 0 OR Y = 0 OR BOTH = 0 This is an important restriction that will impact the answer to this question. Fact 1: √X + √Y > 0 Since radicals are either POSITIVE or ZERO, either X or Y could = 0 (but not both). IF....X=1, Y=0 the answer to the question is 0 IF....X=0, Y=1 the answer to the question is 1 Fact 1 is INSUFFICIENT Fact 2: √X − √Y > 0 Here, the DIFFERENCE is > 0, so the only way for that difference to be POSITIVE, given ALL of the restrictions we've already discussed, is for the X to be POSITIVE and the Y to be 0. Here, the answer to the question is ALWAYS 0. Fact 2 is SUFFICIENT. Final Answer: [Reveal] Spoiler: B GMAT assassins aren't born, they're made, Rich Hi Rich, Nice explanation and powerful 'TESt It' methodology. I reached the same result: X = 0 OR Y = 0 OR BOTH = 0 but I was afraid that I'm mistaken because of zeros in the result so I applied 'Testing it' in the equation but it got so complicated with many variables and situations. However, I want to ask about Fact 2. If I choose X=0 & Y= 9 for easy roots example. So The result will be the following: √X − √Y > 0 then Fact 2: √0 − √9 > 0------> .... √9 will be either 3 or -3. If it is 3, then 0-3>0 so not satisfying the condition but if Y=-3, then 0- (-3)= 3>0 so it is OK with condition. Therefore, Y will always any positive number. So Fact 2 should be insufficient as there many values for Y. What is wrong in the above? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8264 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 379 Kudos [?]: 2453 [2] , given: 163 Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink] ### Show Tags 10 Jun 2015, 18:26 2 This post received KUDOS Expert's post Hi Mo2men, There are a couple of issues here: First, √9 has just ONE solution: +3 The equation X^2 = 9 has TWO solutions: +3 and -3.... but we have to work with what we were given and we were given RADICALS, so there is no negative option. Second, knowing that the radical has just one solution, X = 0 is NOT an option in Fact 2, since we need the result of the calculation to be > 0. By extension, Y MUST = 0. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13414
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]

### Show Tags

10 Oct 2016, 20:42
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.
_________________
Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y?   [#permalink] 10 Oct 2016, 20:42
Similar topics Replies Last post
Similar
Topics:
What is the value of a^2b^2? (A) 2a + b = 12 (B) 3a + 3b = 27 3 07 Jan 2017, 02:46
7 If bc ≠ 0, what is the value of (a^2 - b^2 - c^2)/bc? 6 05 Jun 2015, 05:23
3 If a^2=b^2=25, what is the value of a + b ? 3 29 Jul 2014, 05:49
What is the value of a^2 - b^2? 5 02 May 2013, 09:11
27 a = x + y and b = x - y. If a^2 = b^2, what is the value of 10 12 Jun 2012, 22:35
Display posts from previous: Sort by