It is currently 23 Aug 2017, 10:35

### 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
Your Progress

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 √(xy) = xy, what is the value of x + y?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41058

Kudos [?]: 119439 [3] , given: 12020

If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

15 Oct 2014, 16:01
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:13) correct 36% (01:01) wrong based on 180 sessions

### HideShow timer Statistics

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0
[Reveal] Spoiler: OA

_________________

Kudos [?]: 119439 [3] , given: 12020

Intern
Joined: 18 Dec 2013
Posts: 39

Kudos [?]: 27 [1] , given: 98

Location: Canada
GPA: 2.84
WE: Project Management (Telecommunications)
If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

15 Oct 2014, 20:57
1
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

[Reveal] Spoiler:
Answer: C

Statement 1: $$X=-1/2$$.... substitute in main equation

Scenario A: $$Y = -2/1$$ is a reciprocal
$$\sqrt{xy}=xy$$
LHS =$$\sqrt{-1/2*-2/1}= \sqrt{1}= 1$$
RHS =$$-1/2*-2/1= -1*-1 = 1$$
Therefore, LHS = RHS

Scenario B: $$Y = 0$$
LHS =$$\sqrt{-1/2*-0}= \sqrt{0}= 0$$
RHS =$$-1/2*0= 0$$
Therefore again, LHS = RHS

Hence, we have two possible solutions, therefore Statement 1 is insufficient

Statement 2 : $$Y$$ is not equal to zero
But, X could be equal to zero or be the reciprocal of Y, therefore, statement 2 would fall under the same scenarios as statement 1

Hence, we have two possible solutions, therefore Statement 2 is insufficient

Both Statement 1 & 2 together confirms that $$X & Y$$ both are not equal to zero, therefore, they have to be reciprocals and since statement gives us the value of $$X=-1/2$$, we can also the value of $$Y=-2/1$$ (Reciprocal of X) and thereafter we can find the value of $$X + Y = -1/2 + -2/1 = -5/2$$

Hence, both together are sufficient, therefore C is the correct Answer!

Kudos [?]: 27 [1] , given: 98

Manager
Joined: 21 Jul 2014
Posts: 127

Kudos [?]: 158 [1] , given: 12

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

15 Oct 2014, 21:26
1
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

I did something similar to DMMK, except for one thing:
I know $$\sqrt{n}$$ = $$n$$ only when $$n$$ = 0 or $$n$$ = 1. For all other values of $$n$$, the two would not be equal. Knowing this made it much simpler to plug in the statements. I just had to determine if from the statement(s) provided, can I rule out xy = 0 or xy=1.

Stament 1:
Knowing that x = -1/2, y could equal 0 or -2, and still make the premise true. Either value of y would make x + y a different value. Therefore, it is insufficient.

Statement 2:
Knowing that y is not equal to 0, x could equal zero or the inverse of y, and still make the premise true. Either value of x would make x + y a different value. Therefore, it is insufficient.

Now to evaluate both statements together.

The reason we rejected statement 1 by itself was because y could equal one of two possible values. Statement 2 eliminates one of those options. Therefore y must equal -2. And therefore both statements together are sufficient to answer "what is the value of x+y."

Kudos [?]: 158 [1] , given: 12

Senior Manager
Joined: 13 Jun 2013
Posts: 279

Kudos [?]: 445 [1] , given: 13

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

15 Oct 2014, 22:12
1
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

let xy=k, thus
k^(1/2) =k;
squaring both sides we have
k=k^2
k(k-1)=0
k=0 or 1
i.e. xy=0 or xy=1

st.1

for x=-1/2
both y=0 and y=-2 satisfy the possible value of xy i.e. 0 or 1
hence not sufficient

st.2

y is not equal to zero. clearly not sufficient.
as nothing is said about x, therefore x can take any value it can be zero, fraction, integer etc.

combining st.1 and st.2

we know that y cannot be equal to zero. thus y=-2 and x=-1/2
and x+y= -2-(1/2)=-5/2

hence sufficient.

Kudos [?]: 445 [1] , given: 13

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17173

Kudos [?]: 263 [0], given: 0

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

15 Nov 2015, 12:31
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.
_________________

Kudos [?]: 263 [0], given: 0

Senior Manager
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 302 [0], given: 10

Location: India
GMAT 1: 760 Q50 V44
Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

16 Nov 2015, 03:02
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

Given: √(xy) = xy
(xy)^2 - xy = 0
xy = 0 or 1 - (i)

Required: x + y = ?

Statement 1: x = -1/2
From the given equation (i), we can have two different values of y.
Hence two different values of x + y
INSUFFICIENT

Statement 2: y is not equal to 0
No information about x
INSUFFICIENT

Combining Statement 1 and Statement 2: x = -1/2 and y is not equal to 0
From (i), xy cannot be 0 since both x and y are not = 0
Hence xy = 1
y = -2
x + y = $$-\frac{5}{2}$$
SUFFICIENT

Option C
_________________

Reach out to us at bondwithus@gmatify.com

Kudos [?]: 302 [0], given: 10

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17173

Kudos [?]: 263 [0], given: 0

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

14 Apr 2017, 06:13
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.
_________________

Kudos [?]: 263 [0], given: 0

Director
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 881

Kudos [?]: 494 [0], given: 44

Location: Viet Nam
If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

14 Apr 2017, 07:13
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

The trick here is from $$\sqrt{xy}=xy$$ anyone could easily deduce that $$xy=1$$ or $$xy=0$$ and just consider one of these cases.

Here is my solution:
$$\sqrt{xy}=xy \implies \sqrt{xy}-xy=0 \implies \sqrt{xy}(\sqrt{xy}-1)=0$$
Hence we have $$xy=0$$ or $$xy=1$$.

(1) If $$x=-\frac{1}{2}$$, we need to consider two cases:

Case 1: If $$xy=0\implies y=0 \implies x+y = -\frac{1}{2}$$

Case 2: If $$xy=1 \implies y=-2 \implies x+y = -\frac{5}{2}$$

It's clear that (1) is insufficient.

(2) If $$y \neq 0$$, we still need to consider two cases:

Case 1: If $$xy=0\implies x=0 \implies x+y = y$$.

If $$y=1 \implies x+y = 1$$
If $$y=2 \implies x+y = 2$$

Hence, (2) is insufficient.

Now combine (1) and (2):
Since $$x \neq 0$$ and $$y \neq 0$$ hence $$xy \neq 0 \implies xy=1$$

Since $$x= -\frac{1}{2} \implies y = -2 \implies x+y = -\frac{5}{2}$$

Hence (1) & (2) are sufficient.
The answer is C.
_________________

Kudos [?]: 494 [0], given: 44

Director
Joined: 05 Mar 2015
Posts: 965

Kudos [?]: 256 [1] , given: 41

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

14 Apr 2017, 07:34
1
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

Bunuel / moderators

please move the question to DS section

thanks

Kudos [?]: 256 [1] , given: 41

Math Expert
Joined: 02 Sep 2009
Posts: 41058

Kudos [?]: 119439 [0], given: 12020

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

### Show Tags

14 Apr 2017, 07:54
rohit8865 wrote:
Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

Bunuel / moderators

please move the question to DS section

thanks

Done. Thank you for noticing.
_________________

Kudos [?]: 119439 [0], given: 12020

Re: If √(xy) = xy, what is the value of x + y?   [#permalink] 14 Apr 2017, 07:54
Similar topics Replies Last post
Similar
Topics:
What is the value of 3^(x-y) ? 3 29 Mar 2016, 03:04
23 If xy = - 6, what is the value of xy(x+y)? 15 21 Apr 2016, 16:14
8 If root(xy) = xy what is the value of x + y? 10 21 Nov 2016, 13:11
9 If x and y are integers, what is the value of x+y? 8 22 Apr 2017, 05:51
4 If xy = -6 , what is the value of xy(x+y ) ? 5 09 Jun 2015, 08:44
Display posts from previous: Sort by

# If √(xy) = xy, what is the value of x + y?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.