Last visit was: 23 May 2024, 12:43 It is currently 23 May 2024, 12:43
Toolkit
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.

# If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 28 Jul 2010
Posts: 50
Own Kudos [?]: 156 [100]
Given Kudos: 11
Location: India
Concentration: Finance, Social Entrepreneurship
GMAT 1: 640 Q48 V30
WE:Project Management (Venture Capital)
Math Expert
Joined: 02 Sep 2009
Posts: 93435
Own Kudos [?]: 626117 [35]
Given Kudos: 81940
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11693 [5]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
General Discussion
Intern
Joined: 19 Aug 2012
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 0
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
If x^2+y^2=29, what is the value of (x-y)^2?
(1) xy=10
(2) x=5

The OA says the answer is A whereas I think statement 2 is also sufficient as given below.
x=5 hence y^2=29-25=4-->y=+2 or -2. Hence (x-y)^2= (5-2)^2 or (5+2)^2

Is it because of two answer choices, Statement 2 is insufficient?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4462
Own Kudos [?]: 28671 [0]
Given Kudos: 130
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
mtripathy wrote:
If x^2+y^2=29, what is the value of (x-y)^2?
(1) xy=10
(2) x=5

The OA says the answer is A whereas I think statement 2 is also sufficient as given below.
x=5 hence y^2=29-25=4-->y=+2 or -2. Hence (x-y)^2= (5-2)^2 or (5+2)^2

Is it because of two answer choices, Statement 2 is insufficient?

Precisely! When the question is asking for the value of something, then "sufficient" means you can determine a unique individual unambiguous value. There is absolutely only one place on the entire infinity of the number line where that value could be --- that's what "sufficient" means. If you can narrow things down to two values, it's not sufficient. Does that make sense?

Mike
Intern
Joined: 01 Aug 2014
Posts: 40
Own Kudos [?]: 97 [0]
Given Kudos: 34
GMAT 1: 710 Q44 V42
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
If x^2 + y^2=29, and according to stmt II x=5, then why can we not derive from that that y=2 and xy=10?
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11693 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
2
Kudos
Hi Anonamy,

If you plug X=5 into X^2 + Y^2=29, then what does that tell you about the value of Y. Be sure to be THOROUGH here. Is Y positive or negative? How would that impact the answer to the given question? Without too much work, you should be able to PROVE that there is more than one answer to the given question when X=5.

GMAT assassins aren't born, they're made,
Rich
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4940
Own Kudos [?]: 7680 [0]
Given Kudos: 216
Location: India
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
Top Contributor
Since we want the value of $$(x-y)^2$$, let’s first expand it and write it as $$(x-y)^2 = x^2 + y^2 + 2xy$$.

We see that the question gives us $$x^2 + y^2$$ = 29; so if we are to find the value of $$(x-y)^2$$, then we need the value of xy.

Statement I alone is sufficient since it gives us the value of xy directly. Note that this is a DS question and you are not expected to plug in the value of xy and $$x^2 + y^2$$ into the equation and find out the final value of $$(x-y)^2$$.

Statement I alone is sufficient to say that we can find the value of $$(x-y)^2$$. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, x = 5. Now, using this in the equation given as part of the question,$$x^2 + y^2$$ = 29, we can say $$y^2$$ = 4 or y = 2 or -2.

If x = 5 and y = 2, $$(x-y)^2$$ = 9; if x = 5 and y = -2, $$(x-y)^2$$ = 49.

Can we answer the question with a definitive answer? We cannot. Statement II alone is insufficient to find a unique answer to the question. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!
Aravind B T
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18899
Own Kudos [?]: 22304 [0]
Given Kudos: 285
Location: United States (CA)
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
Jayanth2689 wrote:
If x^2 + y^2 = 29, what is the value of (x - y)^2 ?

(1) xy = 10
(2) x = 5

Solution:

We need to determine the value of (x - y)^2 given that x^2 + y^2 = 29. Notice that (x - y)^2 = x^2 + y^2 - 2xy. Since x^2 + y^2 = 29, then (x - y)^2 = 29 - 2xy. Therefore, if we know the value of xy, then we know the value of (x - y)^2.

Statement One Alone:

Since we know xy = 10, we see that (x - y)^2 = 29 - 2xy = 29 - 2(10) = 9. Statement one alone is sufficient.

Statement Two Alone:

Let’s substitute x = 5 in x^2 + y^2 = 29:

5^2 + y^2 = 29

25 + y^2 = 29

y^2 = 4

y = 2 or -2

If y = 2, then (x - y)^2 = (5 - 2)^2 = 3^2 = 9. If y = -2, then (x - y)^2 = (5 - (-2))^2 = 7^2 = 49. We see that we have two possible values for (x - y)^2. Statement two alone is not sufficient.

Non-Human User
Joined: 09 Sep 2013
Posts: 33151
Own Kudos [?]: 829 [0]
Given Kudos: 0
Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
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: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
Moderator:
Math Expert
93435 posts