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

 It is currently 15 Aug 2018, 09:43

### 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

# Is sqrt = 3-x ? 1) x is not equal to 3 2) -x*lxl > 0 why

Author Message
Retired Moderator
Joined: 18 Jul 2008
Posts: 893
Is sqrt = 3-x ? 1) x is not equal to 3 2) -x*lxl > 0 why  [#permalink]

### Show Tags

06 May 2009, 19:29
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

Is sqrt [(x-3)^2] = 3-x ?

1) x is not equal to 3
2) -x*lxl > 0

why am I not allowed to take the Square of both the left and the right side of the equation?

Then it would equal :

(x-3)^2 = (3-x)^2

If I do this, then A is true. I'm just not sure why you can't. (this is how I learned it back in HS).

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Intern
Joined: 02 Mar 2009
Posts: 42
Location: Austin

### Show Tags

06 May 2009, 19:44
Because:

sqrt [(x-3)^2] = (x-3) if (x>3)
and
sqrt [(x-3)^2] = -(x-3) if (x<3)

A:does not say if x is ">" than or "<" than 3
B:-x|x| > 0 implies x<0; hence B is sufficient
Manager
Joined: 08 Feb 2009
Posts: 139
Schools: Anderson

### Show Tags

07 May 2009, 14:21
Is sqrt [(x-3)^2] = 3-x ?

1) x is not equal to 3
2) -x*lxl > 0

why am I not allowed to take the Square of both the left and the right side of the equation?

Then it would equal :

(x-3)^2 = (3-x)^2

If I do this, then A is true. I'm just not sure why you can't. (this is how I learned it back in HS).

So,

Can you explain how you solved this question ?
Retired Moderator
Joined: 18 Jul 2008
Posts: 893

### Show Tags

08 May 2009, 06:47
The way I did it was wrong, unfortunately.

I squared both sides right away (I somehow remembered learning this method a LONG time ago *sigh*), the equation is true for any value of X. So for me, A was sufficient. It's going to be hard to unlearn it.

the OA is B.

goldeneagle94 wrote:
Is sqrt [(x-3)^2] = 3-x ?

1) x is not equal to 3
2) -x*lxl > 0

why am I not allowed to take the Square of both the left and the right side of the equation?

Then it would equal :

(x-3)^2 = (3-x)^2

If I do this, then A is true. I'm just not sure why you can't. (this is how I learned it back in HS).

So,

Can you explain how you solved this question ?
Manager
Joined: 08 Feb 2009
Posts: 139
Schools: Anderson

### Show Tags

08 May 2009, 08:38
The way I did it was wrong, unfortunately.

I squared both sides right away (I somehow remembered learning this method a LONG time ago *sigh*), the equation is true for any value of X. So for me, A was sufficient. It's going to be hard to unlearn it.

the OA is B.

goldeneagle94 wrote:
Is sqrt [(x-3)^2] = 3-x ?

1) x is not equal to 3
2) -x*lxl > 0

why am I not allowed to take the Square of both the left and the right side of the equation?

Then it would equal :

(x-3)^2 = (3-x)^2

If I do this, then A is true. I'm just not sure why you can't. (this is how I learned it back in HS).

So,

Can you explain how you solved this question ?

Old habits don't go away so easy.
I have the same issue as yours.
So, to overcome that, I have started taking the inequalities as is and first using the Substitution method.
For e.g.

In this problem, I would keep the question as is:
$$sqrt [(x-3)^2] = (3-x)$$

1) Substitute different values (e.g. x = -4, -1, 0, 1, 4) and check for its equality.

2) Subsitute different values in the statement itself to realize that x < 0. Then check the question for its equality with x = -4, -1,

This approach of NOT taking variables from LHS (left hand side of eqn) to RHS or vice-versa has been helping me.
If substitution doesn't work, then I go for shifting the variables from LHS or RHS to the other side.

Hope it helps you.
Retired Moderator
Joined: 18 Jul 2008
Posts: 893

### Show Tags

08 May 2009, 11:12
This is a good tip. Thank you.

*NOTE TO SELF* plug in numbers before manipulating equation!
Intern
Joined: 07 May 2009
Posts: 16

### Show Tags

17 May 2009, 14:50
Hi Guys... correct me if i am wrong, but... when x =1 then

lhs = 2 and rhs = 2, the two sides are equal... same thing goes for x = 1, x = 0 and x = -1 and so on

basically the lhs is always positive ... for any x, while the RHS will be positive for x < 3... not 0

i think that the answer is that neither of the statements are sufficient...
Intern
Joined: 07 May 2009
Posts: 16

### Show Tags

17 May 2009, 14:54
but then if x < 0 then it is less then 3 too so the answer is B... go it...

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Inequality rule check &nbs [#permalink] 17 May 2009, 14:54
Display posts from previous: Sort by

# Events & Promotions

 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®.