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

It is currently 16 Oct 2019, 18:34

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

What is root(x^2•y^2) if x < 0 and y > 0?

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
Joined: 16 Nov 2013
Posts: 28
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 21 Nov 2013, 01:51
6
37
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

66% (00:52) correct 34% (01:06) wrong based on 1467 sessions

HideShow timer Statistics

What is \(\sqrt{x^2 y^2}\) if x < 0 and y > 0?

A) -xy
B) xu
C) -|xy|
D) |y|x
E) No solution
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 21 Nov 2013, 08:26
11
19
Nai222 wrote:
hey,

Can you please explain why it is negative? I thought when the two number are enclosed within an absolute value bracket, it becomes positive.


\(-xy\) is not negative it's positive. \(xy\) is negative, thus \(-xy=-(negative)=positive\).

THEORY:
\(\sqrt{x^2}=|x|\).

The point here is that as square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
_________________
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 21 Nov 2013, 01:53
4
11
Manager
Manager
avatar
Joined: 29 Sep 2013
Posts: 108
GPA: 3.86
WE: Asset Management (Investment Banking)
GMAT ToolKit User Reviews Badge
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 21 Nov 2013, 08:21
hey,

Can you please explain why it is negative? I thought when the two number are enclosed within an absolute value bracket, it becomes positive.
Manager
Manager
avatar
Joined: 29 Sep 2013
Posts: 108
GPA: 3.86
WE: Asset Management (Investment Banking)
GMAT ToolKit User Reviews Badge
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 21 Nov 2013, 08:37
WOW!!! Thank you for that explanation. I definitely get it now.

:-D :-D :-D :-D :-D :-D :-D 8-)
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 20 Dec 2014, 20:06
Hi Nai222,

Since your post was from over a year ago, you might not still be around to read this. This question can be solved by TESTing VALUES:

We're told X < 0 and Y > 0

Let's TEST:
X = -2
Y = +2

So, we'd have \sqrt{(4)(4)} = +4

Using those values in the answers, we get...

Answer A: -(-2)(2) = +4 This IS a match

Answer B: (-2)(2) = -4 NOT a match

Answer C: - |(-2)(2)| = -4 NOT a match

Answer D: |2|(-2) = -4 NOT a match

Answer E: No solution. NOT a match

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 22 Dec 2014, 02:04
for |xy| we have 4 options

xy, x-y, -xy, -x-y

A
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 10 Mar 2016, 11:14
Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 70
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 06 Sep 2017, 02:25
Bunuel wrote:
Nai222 wrote:
hey,

Can you please explain why it is negative? I thought when the two number are enclosed within an absolute value bracket, it becomes positive.


\(-xy\) is not negative it's positive. \(xy\) is negative, thus \(-xy=-(negative)=positive\).

THEORY:
\(\sqrt{x^2}=|x|\).

The point here is that as square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).



How is mod of -x equal to -x? Shouldnt it be x?
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 3544
What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 07 Sep 2017, 16:48
3
1
sinhap07 wrote:
Bunuel wrote:
Nai222 wrote:
hey,

Can you please explain why it is negative? I thought when the two number are enclosed within an absolute value bracket, it becomes positive.

\(-xy\) is not negative it's positive. \(xy\) is negative, thus \(-xy=-(negative)=positive\).

THEORY:
. . .
What function does exactly the same thing [as the square root sign]? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\)...

sinhap07 How is mod of -x equal to -x? Shouldnt it be x?

sinhap07 , I assume you refer to
Quote:
\(|x|= -x\) , if \(x<0\)

For me, the rule can be counterintuitive. I've seen a few ways to think about the rule. Maybe they will help.

If x is negative, then |x| = -x

Possible ways to think about the rule:

1. "The negative of a negative is positive."

Think of the negative sign as signifying "opposite."

That is, the negative sign functions as "the negative of a negative number." And the negative of a negative number is positive. See Bunuel above in bold.

Let x = -3. Per |x| = -x:

|-3| = 3, and +3 is the opposite of -3, thus +3 = -(-3)

2. OR think: "The negative sign on RHS means (-1) multiplied by a negative number \(x\)," thus

|x| = -x
|x| = (-1)(x)
|x| = (-1)(negative #)
|x| = a positive number

3. OR think (similar to #1): "in this rule there is a hidden minus sign."

With a number, the "two negatives" are easy to see

|-3| = 3
|-3| = -(-3)

BUT: |x| = -(x) = -x

With variable \(x\), it is easy to forget that there ARE two negative signs.

With the variable, there is only one minus sign on RHS... because the negative variable \(x\) already "contains" a minus sign.

We just don't (can't) write the minus sign twice with the variable.

|-3| = -(-3) = 3
|x| = -(x) = -x

Those two equations are functionally equivalent.

4. Summary - use any negative number, substituted for x, to see that, if x < 0 , then |x| = -x. Reasons:

|-3| = 3, where +3 is the opposite of -3 [+3 = -(-3)]; RHS is the negative of a negative number

|-3| = 3 = (-1)(-3)

|-3| = -(-3) = 3

The absolute value IS positive (or nonnegative). The sign of a negative variable can obscure that fact.

Hope that helps.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.




Choose life.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 07 Sep 2017, 17:02
3
genxer123 wrote:
sinhap07 wrote:
Bunuel wrote:
\(-xy\) is not negative it's positive. \(xy\) is negative, thus \(-xy=-(negative)=positive\).

THEORY:
. . .
What function does exactly the same thing [as the square root sign]? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\)...

sinhap07 How is mod of -x equal to -x? Shouldnt it be x?

sinhap07 , I assume you refer to
Quote:
\(|x|= -x\) , if \(x<0\)

For me, the rule can be counterintuitive. I've seen a few ways to think about the rule. Maybe they will help.

If x is negative, then |x| = -x

Possible ways to think about the rule:

1. "The negative of a negative is positive."

Think of the negative sign as signifying "opposite."

That is, the negative sign functions as "the negative of a negative number." And the negative of a negative number is positive. See Bunuel above in bold.

Let x = -3. Per |x| = -x:

|-3| = 3, and +3 is the opposite of -3, thus +3 = -(-3)

2. OR think: "The negative sign on RHS means (-1) multiplied by a negative number \(x\)," thus

|x| = -x
|x| = (-1)(x)
|x| = (-1)(negative #)
|x| = a positive number

3. OR think (similar to #1): "in this rule there is a hidden minus sign."

With a number, the "two negatives" are easy to see

|-3| = 3
|-3| = -(-3)

BUT: |x| = -(x) = -x

With variable \(x\), it is easy to forget that there ARE two negative signs.

With the variable, there is only one minus sign on RHS... because the negative variable \(x\) already "contains" a minus sign.

We just don't (can't) write the minus sign twice with the variable.

|-3| = -(-3) = 3
|x| = -(x) = -x

Those two equations are functionally equivalent.

4. Summary - use any negative number, substituted for x, to see that, if x < 0 , then |x| = -x. Reasons:

|-3| = 3, where +3 is the opposite of -3; RHS is the negative of a negative number

|-3| = (-1)(-3) = 3

|-3| = -(-3) = 3

The absolute value IS positive (or nonnegative). The sign of a negative variable can obscure that fact.

Hope that helps.


To add:

|-x| = |x|. One way to think about it is that |-x| is the distance between -x and 0 on the number line. Similarly, |x| is the distance between x and 0 on the number line. Obviously -x and x are the same distance from 0. For example, -3 and 3 are the same distance from 0; 2 and -2, are the same distance from 0...

Next, when x is 0 or negative, the rule says that |x| = -x. The absolute value cannot be negative and this rule is not violated here. For example, say x = -10, then |-10| = -(-10) = 10 = positive or generally when x is negative |x| = -x = -negative = positive. Or using the distance concept again |-10| is the distance from -10 to 0, which is 10.

Hope it helps.
_________________
Manager
Manager
User avatar
B
Joined: 21 Jun 2017
Posts: 82
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 13 Oct 2017, 09:51
registerincog wrote:
What is \(\sqrt{x^2 y^2}\) if x < 0 and y > 0?

A) -xy
B) xu
C) -|xy|
D) |y|x
E) No solution



If x<0, then x = (-)
if y > 0, then y = (+)
root x^2y^2 = (+), for, given the exponent is even, the power of (-) is (+)

B) xy = (-)(+) = (-) therefore insufficient
C) (-)(+) = (-)
D)(+)(-) = (-)

A) (-)(-) = (+)

Therefore, the answer is A-xy
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13210
Re: What is root(x^2•y^2) if x < 0 and y > 0?  [#permalink]

Show Tags

New post 31 Oct 2018, 10:52
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.
_________________
GMAT Club Bot
Re: What is root(x^2•y^2) if x < 0 and y > 0?   [#permalink] 31 Oct 2018, 10:52
Display posts from previous: Sort by

What is root(x^2•y^2) if x < 0 and y > 0?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne