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

 It is currently 20 Mar 2019, 08:31

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

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

### Hide Tags

Manager
Joined: 07 Nov 2009
Posts: 239
Is sqrt ((x-3)^2) = 3-x?  [#permalink]

### Show Tags

22 Mar 2010, 22:37
1
5
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:29) correct 42% (01:55) wrong based on 288 sessions

### HideShow timer Statistics

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

(1) x not equal to 3
(2) -x|x| > 0

Let me rephrase it a bit to test my basics:
is sqrt ((x-3)^2) = x-3?

--> |x-3| = x-3
This will be true only if x>= 3 .. Am i correct?
Math Expert
Joined: 02 Sep 2009
Posts: 53734
Re: Redesign sqrt ((x-3)^2) = 3-x  [#permalink]

### Show Tags

23 Mar 2010, 06:14
3
2
rohitgoel15 wrote:
This question has been discussed many times ...

is sqrt ((x-3)^2) = 3-x?
1) x not equal to 3
2) -x|x| > 0

Let me rephrase it a bit to test my basics:
is sqrt ((x-3)^2) = x-3? Incorrect

--> |x-3| = x-3
This will be true only if x>= 3 .. Am i correct? Correct

Remember: $$\sqrt{x^2}=|x|$$.

$$\sqrt{(x-3)^2}=|x-3|$$. So the question becomes is $$|x-3|=3-x$$.

When $$x>3$$, then RHS (right hand side) is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.

When $$x\leq{3}$$, then $$LHS=|x-3|=-x+3=3-x=RHS$$, hence in this case equation holds true.

Basically question asks is $$x\leq{3}$$?

(1) x is not equal to 3. Clearly insufficient.

(2) $$-x|x| >0$$, basically this inequality implies that $$x<0$$, hence $$x<3$$. Sufficient.

_________________
##### General Discussion
Manager
Joined: 13 Dec 2009
Posts: 221
Re: Redesign sqrt ((x-3)^2) = 3-x  [#permalink]

### Show Tags

24 Mar 2010, 00:12
1
rohitgoel15 wrote:
This question has been discussed many times ...

is sqrt ((x-3)^2) = 3-x?
1) x not equal to 3
2) -x|x| > 0

Let me rephrase it a bit to test my basics:
is sqrt ((x-3)^2) = x-3?

--> |x-3| = x-3
This will be true only if x>= 3 .. Am i correct?

|x-3| = 3-x => we have to prove if x <= 3

Stmt1: x not equal to 3 doesnt say if x <3 or >3 so insufficient.
Stmt2: -x |x| > 0
In this case |x| is always going to be postive and to make the expression positive it means -x is also positive so -x>0
or x < 0 from this we can say dat is x <0 it must be < 3 too hence answer is B
_________________

My debrief: done-and-dusted-730-q49-v40

Senior Manager
Joined: 12 Mar 2009
Posts: 280

### Show Tags

28 Mar 2010, 10:08
pl help
Attachments

GMAT prep_ds.docx [53.01 KiB]

Manhattan Prep Instructor
Joined: 28 Aug 2009
Posts: 154
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Re: gmat prep_inequality  [#permalink]

### Show Tags

28 Mar 2010, 12:38
2
1
One important thing to know about the square root of a square term:
(1) If it's a number under the square root sign, the answer is only the positive root: sqrt[(-3)^2] = sqrt[(3)^2] = sqrt[9] = 3.
(2) If there are variables under the square root sign, you must consider the fact that the squared "thing" may have been either pos or neg to begin with: sqrt[(-x)^2] = sqrt[(x)^2] = |x|. We are still looking for the positive root, but we don't know whether +x or -x is actually greater than zero--that depends on the sign of x.

So for this question: Is sqrt[(x-3)^2] = 3-x?

Rephrase to: Is |x-3| = 3-x?

If stuff in the absolute value sign is positive or zero, this becomes:
Is x-3 = 3-x?
Is 2x = 6?
Is x = 3?

If stuff in the absolute value sign is negative, this becomes:
Is -(x-3) = 3-x?
Is -x+3 = 3-x?
The answer is yes for all x, but remember this was just "all x" such that x-3 was negative, or x < 3: So we ask "Is x < 3?"

Put the two cases together for the final rephrase: "Is x =<3 ? "

(1) x is not 3, but no info on whether it is less than or greater than 3. INSUFF.
(2) -x|x| > 0.
|x| is positive, so -x would have to be positive too (pos*pos > 0, but neg*pos < 0). Thus, x is negative. If x is negative, it is definitely less than 3. The answer is definitely Yes. SUFF.

The answer is B.
_________________

Emily Sledge | Manhattan GMAT Instructor | St. Louis

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | Manhattan GMAT Reviews

Manager
Joined: 27 Dec 2009
Posts: 138
Re: gmat prep_inequality  [#permalink]

### Show Tags

25 Apr 2010, 01:03
Thanks esledge . I have got one important take away.
Intern
Joined: 05 Aug 2014
Posts: 29
Is √(x-3)^2 = 3 - x ?  [#permalink]

### Show Tags

Updated on: 31 Jul 2015, 09:36
Is $$\sqrt{(x-3)^2}$$ = 3 - x

1. x $$\neq$$ 3
2. -x |x|>0

Originally posted by naeln on 31 Jul 2015, 09:24.
Last edited by ENGRTOMBA2018 on 31 Jul 2015, 09:36, edited 1 time in total.
Formatted the question
CEO
Joined: 20 Mar 2014
Posts: 2624
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Is √(x-3)^2 = 3 - x ?  [#permalink]

### Show Tags

31 Jul 2015, 09:41
naeln wrote:
Is $$\sqrt{(x-3)^2}$$ = 3 - x

1. x doesn't equal 3
2. -x |x|>0

$$\sqrt{(x-3)^2}$$ = 3 - x ONLY IF, $$x\leq3$$

FYI, $$\sqrt{a^2} = |a|$$

Per statement 1, $$x\neq3$$ but is x<3 ? No information. Thus this statement is not sufficient.

Per statement 2, -x|x| > 0 ---> only case possible is for x<0. Thus we have a definite yes for $$x \leq 3$$. B is the correct answer.
Non-Human User
Joined: 09 Sep 2013
Posts: 10153
Re: Is sqrt ((x-3)^2) = 3-x?  [#permalink]

### Show Tags

01 Oct 2018, 06:06
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: Is sqrt ((x-3)^2) = 3-x?   [#permalink] 01 Oct 2018, 06:06
Display posts from previous: Sort by

# Is sqrt ((x-3)^2) = 3-x?

 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®.