Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Oct 2016, 01:56

### 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

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 28 Jul 2010
Posts: 62
Location: India
Concentration: Finance, Social Entrepreneurship
GMAT 1: 640 Q48 V30
WE: Project Management (Venture Capital)
Followers: 0

Kudos [?]: 6 [0], given: 11

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

### Show Tags

19 Sep 2010, 06:48
00:00

Difficulty:

25% (medium)

Question Stats:

66% (01:39) correct 34% (00:54) wrong based on 297 sessions

### HideShow timer Statistics

If x^2 + y^2 = 29, what is the value of (x-y)^2

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

[Reveal] Spoiler:
simple problem..just have to bring an equation for xy here..A is sufficient..as xy value is given..but i feel B is also sufficient..as i can solve the value for y with the value of x.. i.e x2 + y2 = 29 - 2xy

I feel it should be D? or am i assuming sumthing rong here?
[Reveal] Spoiler: OA
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 104

Kudos [?]: 900 [0], given: 25

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

19 Sep 2010, 07:56
If $$x^2+y^2=29$$, and even if you know $$x=5$$, it is not sufficient to solve for $$y$$, since the first equation is quadratic and you will get two answers for $$y$$, namely $$\sqrt{24}$$ and $$-\sqrt{24}$$. So its impossible to know the sign of y, and hence the sign of xy. This is why (2) is not sufficient
_________________
Manager
Joined: 23 Sep 2009
Posts: 151
Followers: 1

Kudos [?]: 90 [0], given: 37

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

19 Sep 2010, 16:36
Jayanth2689 wrote:
if x2 + y2 = 29, what is the value of (x+y)2

1. xy = 10
2. x = 5

simple problem..just have to bring an equation for xy here..A is sufficient..as xy value is given..but i feel B is also sufficient..as i can solve the value for y with the value of x.. i.e x2 + y2 = 29 - 2xy

I feel it should be D? or am i assuming sumthing rong here?

Option A is enough.
Option B: you definitely need to know the value of y otherwise ur equation will be like (X+Y)^2=29+10y. You cant proceed forward without knowing the value of Y.
Hence the ans: A
_________________

Thanks,
VP

Intern
Joined: 14 Oct 2010
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

17 Oct 2010, 05:47
Given X^2 + Y^2 = 29, from a) XY = 10
Therefore (x & y) can be (5 & 2) or (-5 & -2)
Therefore We cannot come to conclusion from a) right
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 104

Kudos [?]: 900 [0], given: 25

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

18 Oct 2010, 00:29
praba1130 wrote:
Given X^2 + Y^2 = 29, from a) XY = 10
Therefore (x & y) can be (5 & 2) or (-5 & -2)
Therefore We cannot come to conclusion from a) right

$$x^2+y^2=29$$
$$xy=10$$
$$x^2+y^2+2xy=49$$
$$(x+y)^2=49$$

Hence, it is sufficient
_________________
Manager
Joined: 25 Aug 2010
Posts: 98
Followers: 1

Kudos [?]: 4 [0], given: 1

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

20 Oct 2010, 10:24
Jayanth2689 wrote:
if x2 + y2 = 29, what is the value of (x+y)2

1. xy = 10
2. x = 5

simple problem..just have to bring an equation for xy here..A is sufficient..as xy value is given..but i feel B is also sufficient..as i can solve the value for y with the value of x.. i.e x2 + y2 = 29 - 2xy

I feel it should be D? or am i assuming sumthing rong here?

1 Alone sufficient....

(x+y)^2 = x^2 + y^2 + 2xy ----> 29 + xy

but from 1 , xy = 10 ...so i can get the value of (x+y)^2

from 2 it is not sufficient very clearly...
so ans is : 1
Current Student
Joined: 15 Jul 2010
Posts: 257
GMAT 1: 750 Q49 V42
Followers: 9

Kudos [?]: 164 [0], given: 65

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

20 Oct 2010, 13:59
A.

1) X^2+Y^2=29 and 2XY=20 sufficient

2) 25+y^2=29 Y=+2 or -2 thus giving two answers. insufficient
_________________

Consider KUDOS if my post was helpful.

My Debrief: http://gmatclub.com/forum/750-q49v42-105591.html#p825487

Intern
Joined: 18 Aug 2010
Posts: 2
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

28 Nov 2010, 13:10
1
This post was
BOOKMARKED
If x^2 + y^2 = 29, what is the value of (x-y)^2

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

Hi guys, I'd like some help here. The answer is A. I see why (1) is sufficient, but I don't get why (2) is not. We can just simply plug x = 5 into the equation, find y, and then solve for (x-y)^2

Thanks
Manager
Joined: 13 Jul 2010
Posts: 169
Followers: 1

Kudos [?]: 65 [1] , given: 7

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

28 Nov 2010, 13:25
1
KUDOS
Stmt 1 works because you know the sign of both of x and y is the same either both negative or both positive - this affects the result of (x-y)^2 as -5-(2) =-7 or -5-(-2)=-3. With stmt 2 you don't know the sign of 2 hence can't arrive at one answer.

Hope it helps.
Math Expert
Joined: 02 Sep 2009
Posts: 35285
Followers: 6637

Kudos [?]: 85613 [2] , given: 10240

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

28 Nov 2010, 13:25
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
krit wrote:
If x^2 + y^2 = 29, what is the value of (x-y)^2

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

Hi guys, I'd like some help here. The answer is A. I see why (1) is sufficient, but I don't get why (2) is not. We can just simply plug x = 5 into the equation, find y, and then solve for (x-y)^2

Thanks

Given: $$x^2+y^2=29$$.
Question: $$(x-y)^2=x^2-2xy+y^2=(x^2+y^2)-2xy=29-2xy=?$$ So, basically we should find the value of $$xy$$

(1) xy = 10. Directly gives us the value we needed. Sufficient.

(2) x = 5. Now even if we substitute the value of $$x$$ in $$x^2+y^2=29$$ we'll get two values for $$y$$: 2 and -2, hence two values for $$(x-y)^2$$: 9 and 49. Not sufficient.

Hope it's clear.
_________________
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 20 [0], given: 2

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

28 Nov 2010, 13:26
Yes you are right you CAN just plug x into the equation. BUT, you are forgetting that y can be POSITIVE or NEGATIVE.

For example: 2^2 = 4 ; -2^2 = 4 If you plug X = 5 into the equation that you are asked to find the value for, (x-y)^2 Then you will see, when you have 2 different values for Y you will get 2 different answers --> (5-2)^2 = 9 OR (5- (-2))^2 = 49

Therefore, with B, you have two possible answers and it is INSUFFICIENT
Intern
Joined: 18 Aug 2010
Posts: 2
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

28 Nov 2010, 13:30
wow...okay. It's clear now. I completely forgot the -2. Thank you all
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 20 [0], given: 2

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

04 Dec 2010, 18:21
If $$x^2 + y^2 = 29$$, what is the value of $$(x - y)^2$$ ?

1) xy = 10
2) x = 5

I am unsure about my approach. It led me to the wrong answer but I do not know where it is flawed. Looking at this problem I was able to see that according to this equation, $$x^2 + y^2 = 29$$, X or Y could either be +/-5 or +/-2.

Depending on which, we would have different answers to $$(x - y)^2$$

Statement 1) Fits into the equation for 5, 2 or -5, -2
Statement 2) If x = 5 then y MUST be 2

I chose D

There is a much different explanation in the book relating to factoring out $$(x - y)^2$$ --> $$x^2 -2xy + y^2$$ and then plugging in 29 to $$x^2 + y^2$$ as given in the problem.

Any thoughts?
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 442

Kudos [?]: 1924 [0], given: 210

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

04 Dec 2010, 18:28
jscott319 wrote:
If $$x^2 + y^2 = 29$$, what is the value of $$(x - y)^2$$ ?

1) xy = 10
2) x = 5

I am unsure about my approach. It led me to the wrong answer but I do not know where it is flawed. Looking at this problem I was able to see that according to this equation, $$x^2 + y^2 = 29$$, X or Y could either be +/-5 or +/-2.

Depending on which, we would have different answers to $$(x - y)^2$$

Statement 1) Fits into the equation for 5, 2 or -5, -2
Statement 2) If x = 5 then y MUST be 2

I chose D

There is a much different explanation in the book relating to factoring out $$(x - y)^2$$ --> $$x^2 -2xy + y^2$$ and then plugging in 29 to $$x^2 + y^2$$ as given in the problem.

Any thoughts?

I thought of the explanation that's given in the book too.

Quote:
If x = 5 then y MUST be 2
- Why so? Why can't it be -2? $$(5)^2 + (-2)^2 = 29$$ as well.
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 20 [0], given: 2

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

04 Dec 2010, 18:45
Hmm good point , ha. What could lead me out of this train of thought and into thinking more in line with what led you to the solution your way?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6966
Location: Pune, India
Followers: 2027

Kudos [?]: 12746 [1] , given: 221

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

04 Dec 2010, 19:04
1
KUDOS
Expert's post
jscott319 wrote:
Looking at this problem I was able to see that according to this equation, $$x^2 + y^2 = 29$$, X or Y could either be +/-5 or +/-2.

Another thing, you can't assume that the equation will have only integral values.
x = 3 and y = root(20) also satisfies this equation as do many other values.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 442

Kudos [?]: 1924 [0], given: 210

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

04 Dec 2010, 19:19
1
This post was
BOOKMARKED
VeritasPrepKarishma wrote:
jscott319 wrote:
Looking at this problem I was able to see that according to this equation, $$x^2 + y^2 = 29$$, X or Y could either be +/-5 or +/-2.

Another thing, you can't assume that the equation will have only integral values.
x = 3 and y = root(20) also satisfies this equation as do many other values.

Good point Karishma!

Quote:
Hmm good point , ha. What could lead me out of this train of thought and into thinking more in line with what led you to the solution your way?

Haha, I'm an engineer and I went to a retardedly hard high school. It's kind of second nature now. But I think when you get a question like this, think about common mistakes. As I mentioned, assuming that positive and positive, and negative and negative go together is not right. Also, you cannot assume only integral values. So just think of all possible combinations. I'd actually advise you to get the GMAT Club tests and go through as many as you can, while noting down the stuff that you get wrong, especially if its stuff like this will help you keep track of stuff.
Intern
Joined: 19 Aug 2012
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

23 Dec 2012, 17:46
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: 3526
Followers: 1191

Kudos [?]: 5315 [0], given: 58

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

23 Dec 2012, 20:00
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
_________________

Mike McGarry
Magoosh Test Prep

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12217
Followers: 542

Kudos [?]: 151 [0], given: 0

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

11 Jul 2014, 14:38
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   [#permalink] 11 Jul 2014, 14:38

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
12 If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy? 18 31 Jul 2014, 07:03
What is the value of x^2 + y^2 ? (1) x^2+ y^2 = 2xy + 1 (2) 4 05 Jun 2011, 09:16
4 What is the value of x^2-y^2? (1) x+y=0 (2) x-y=2 3 02 Jan 2011, 14:08
6 If (x+y)^2 = (x+y^2)^2, what is the value of y? 1) x = y^2 5 25 Jul 2010, 13:03
What is the value of x^2 + y^2? 1) x^2 + y^2 = 2xy + 1 2) 6 24 Jul 2010, 08:50
Display posts from previous: Sort by