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

 It is currently 03 May 2015, 01:55

### 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

# Is sqrt[(x-5)^2] = 5-x?

Author Message
TAGS:
Director
Joined: 18 Feb 2005
Posts: 674
Followers: 1

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

Is sqrt[(x-5)^2] = 5-x? [#permalink]  05 May 2005, 17:37
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
This question is from OG.

Is sqrt[(x-5)^2] = 5-x?

i) -x|x|>0
ii) 5-x>0

Please correct my approach if it is wrong. I am having some confusion with this problem.
From 1)

since |x| is always positive -x|x| > 0 only if x<0

==>> sqrt[(x-5)^2] = 5-x means (x-5)<0

from 2) 5-x>0 means (x-5)<0

So we can get from 1 and 2 .

Is this approach correct??
VP
Joined: 25 Nov 2004
Posts: 1495
Followers: 6

Kudos [?]: 38 [0], given: 0

Re: DS: Inequalities [#permalink]  05 May 2005, 20:56
let me do this way. first simplify the question. remember this is yes/no question.

given that sqrt[(x-5)^2] = 5-x is equivalant to x=5? because sqrt [(x-5)^2] = x-5 (because sqrt of something is always positive. so it is x-5).
so the enequality is x-5 = 5-x......after simplification, x=5.

i) -x|x|>0
from this, x is -ve. so x is definitely not 5. sufficient...............

from ii, 5>x. this also means x is not equal to 5. it is also sufficient............
Senior Manager
Joined: 14 Apr 2005
Posts: 419
Location: India, Chennai
Followers: 1

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

MA, your approach is easy fine.

I got the same answer (D) by picking up numbers.

1) From statement 1, we get x to be negative. I tried substituting the original formulas, for various numbers, and the base statement was true. Hence statement 1 is sufficient.

2) From statement 2, we get X < 5. I substituted x to be a positive number less than 5, and a negative number, and the statement still holds good.

But having looked at your post, felt there was a better way of doing it. Thanks.
Senior Manager
Joined: 19 Sep 2004
Posts: 371
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: DS: Inequalities [#permalink]  06 May 2005, 00:29
MA wrote:
because sqrt [(x-5)^2] = x-5 (because sqrt of something is always positive. so it is x-5).
..

I didn't understand what u mean by that

Sqrt (9) = +- 3 rt?

Kindly explain

Saurabh Malpani
Manager
Joined: 05 May 2005
Posts: 92
Location: Kyiv, Ukraine
Followers: 1

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

sqrt[(x-5)^2] = 5-x

what if we rewrite it as (x-5)^2=(5-x)^2, and then it would mean (x-5)^2=(-(x-5))^2, right? (x-5)^2=(x-5)^2 thus, it might be concluded that x can be any number, which makes the answer D since it does not really matter what they put in st1 or st2.
Director
Joined: 18 Feb 2005
Posts: 674
Followers: 1

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

Thanks guys ....The OA is D
VP
Joined: 25 Nov 2004
Posts: 1495
Followers: 6

Kudos [?]: 38 [0], given: 0

Re: DS: Inequalities [#permalink]  06 May 2005, 06:18
saurabhmalpani wrote:
MA wrote:
because sqrt [(x-5)^2] = x-5 (because sqrt of something is always positive. so it is x-5).
..

I didn't understand what u mean by that
Sqrt (9) = +- 3 rt?
Kindly explain. Saurabh Malpani

saurabh,
Sqrt (9) = always and only +3 not -3.
Director
Joined: 18 Feb 2005
Posts: 674
Followers: 1

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

Re: DS: Inequalities [#permalink]  06 May 2005, 08:37
MA wrote:
saurabhmalpani wrote:
MA wrote:
because sqrt [(x-5)^2] = x-5 (because sqrt of something is always positive. so it is x-5).
..

I didn't understand what u mean by that
Sqrt (9) = +- 3 rt?
Kindly explain. Saurabh Malpani

saurabh,
Sqrt (9) = always and only +3 not -3.

Can you figure out if there are any flaws in my reasoning? That would be of great help to me.....Also suggestions on where to find more "Inequalities" problems....
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 181 [0], given: 2

D for me

the key here is that we need to make sure X is less than 5!

if that is the case then we can solve the problem...

I and II both say X is less than 5, therefore sufficient!
Senior Manager
Joined: 21 Mar 2004
Posts: 444
Location: Cary,NC
Followers: 2

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

D for me too !

From the question LHS is always = + ( x-5)

A. -x|x| > 0

=> -x>0 because |x| is always +ve
=> 5-x>5 or 5-x>0

LHS is not = RHS .........A is suff

B.

LHS = +(x-5)
5-x > 0 implies (x-5)<0
LHS not = RHS
B is sufficient.

ans is D
_________________

ash
________________________
I'm crossing the bridge.........

VP
Joined: 25 Nov 2004
Posts: 1495
Followers: 6

Kudos [?]: 38 [0], given: 0

Re: DS: Inequalities [#permalink]  06 May 2005, 16:48
gmat2me2 wrote:
This question is from OG.
Is sqrt[(x-5)^2] = 5-x?
i) -x|x|>0
ii) 5-x>0

Please correct my approach if it is wrong. I am having some confusion with this problem.
From 1) since |x| is always positive -x|x| > 0 only if x<0
==>> sqrt[(x-5)^2] = 5-x means (x-5)<0
from 2) 5-x>0 means (x-5)<0
So we can get from 1 and 2 . Is this approach correct??

i think, there is nothing wrong with your approach. you only did not simplified the given inequality in the question. if the given inequality is complex and multiple variables, it better to simplify to the possible extent. if you simplifiy the question, you can get the answer.
Director
Joined: 18 Feb 2005
Posts: 674
Followers: 1

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

Re: DS: Inequalities [#permalink]  06 May 2005, 18:21
MA wrote:
gmat2me2 wrote:
This question is from OG.
Is sqrt[(x-5)^2] = 5-x?
i) -x|x|>0
ii) 5-x>0

Please correct my approach if it is wrong. I am having some confusion with this problem.
From 1) since |x| is always positive -x|x| > 0 only if x<0
==>> sqrt[(x-5)^2] = 5-x means (x-5)<0
from 2) 5-x>0 means (x-5)<0
So we can get from 1 and 2 . Is this approach correct??

i think, there is nothing wrong with your approach. you only did not simplified the given inequality in the question. if the given inequality is complex and multiple variables, it better to simplify to the possible extent. if you simplifiy the question, you can get the answer.

Thanks a bunch MA for your review
Re: DS: Inequalities   [#permalink] 06 May 2005, 18:21
Similar topics Replies Last post
Similar
Topics:
6 If 5^x = y, what is x? 6 04 Nov 2014, 09:03
3 (3^5x + 3^5x + 3^5x)(4^5x + 4^5x + 4^5x + 4^5x) = 3 04 Nov 2014, 08:43
Is root(5-x)^2=5-x? 9 02 May 2010, 14:51
Which of the following is perpendicular to y=5x? 1) y = -5x 1 05 May 2006, 22:03
Is Sqrt (x-5)^2 = 5 - x 5 22 Sep 2005, 12:41
Display posts from previous: Sort by