NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 22:24 It is currently 23 Apr 2024, 22:24
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is ((x-3)^2)^(1/2) = 3-x? (1) x ≠ 3 (2) -x|x| > 0

SORT BY:
Date
Kudos
   1   2   3 
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
P
jabhatta2
VP
VP
Joined: 15 Dec 2016
Posts: 1376
Own Kudos [?]: 207 [0]
Given Kudos: 189
Send PM
Is ((x-3)^2)^(1/2) = 3-x? (1) x 3 (2) -x|x| > 0 [#permalink] New post   Updated on: 13 Mar 2022, 15:34
Hi avigutman - doubt on the question stem. When i did using the rules of inequality and algebra - I first re-phrased the question stem as Is x <= 3 ? and then saw S2 was sufficient.

How do you rephrase the question stem using graphs specifically ?

When i drew the question stem first to see the overlap between |3-x| and (3-x) - the lines do overlap. The overlap is the blue line (when x <=3)

Thus i thought my rephrase of the question stem intead should be instead

Are the values of x as per the arrows in green - the values on the blue line (when x=< 3)
Attachments

screenshot 2.JPG
screenshot 2.JPG [ 89.92 KiB | Viewed 1158 times ]


Originally posted by jabhatta2 on 13 Mar 2022, 13:47.
Last edited by jabhatta2 on 13 Mar 2022, 15:34, edited 8 times in total.
User avatar
P
jabhatta2
VP
VP
Joined: 15 Dec 2016
Posts: 1376
Own Kudos [?]: 207 [0]
Given Kudos: 189
Send PM
Is ((x-3)^2)^(1/2) = 3-x? (1) x 3 (2) -x|x| > 0 [#permalink] New post   13 Mar 2022, 14:53
When i saw S2 and graphed S2 (x <= 0) -- it ALL THE area in the green

Thus i thought S2 in the graphical method was not sufficient because S2 represents ALL the green area where i am looking for x to be only values on the blue line only (within the black box)
Attachments

picture 4.JPG
picture 4.JPG [ 88.74 KiB | Viewed 1140 times ]

User avatar
D
avigutman
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2285 [0]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: Is ((x-3)^2)^(1/2) = 3-x? (1) x 3 (2) -x|x| > 0 [#permalink] New post   13 Mar 2022, 16:02
Expert Reply
jabhatta2 wrote:
Are the values of x as per the arrows in green - the values on the blue line (when x=< 3)
When i saw S2 and graphed S2 (x <= 0) -- it ALL THE area in the green
Thus i thought S2 in the graphical method was not sufficient because S2 represents ALL the green area where i am looking for x to be only values on the blue line only (within the black box)


jabhatta2 you drew the graphs very well. I think the issue is with your rephrasing of the question stem. The blue line is made up of points, each of which has a x-coordinate and a y-coordinate. The question isn't interested in y-coordinates, though. In fact, the concept of y isn't anywhere in the question or statements. It's a concept that you introduced into the problem for your own purposes. The problem itself is 1-dimensional, not 2-dimensional.
You're right that the question is asking whether we're on the blue line, but, that's the same thing as asking whether x<=3. Think of it this way: it's given that we're somewhere on either the blue line or the red line, and we're just trying to figure out which? Blue or Red?
User avatar
P
jabhatta2
VP
VP
Joined: 15 Dec 2016
Posts: 1376
Own Kudos [?]: 207 [0]
Given Kudos: 189
Send PM
Is ((x-3)^2)^(1/2) = 3-x? (1) x 3 (2) -x|x| > 0 [#permalink] New post   14 Mar 2022, 17:38
thanks so much avigutman for responding.

I think the way to re-phrase the question stem specifically is the following way

Is LHS = RHS ?

From the graph
if x cordinate is
+ 6 - answer to question is No
+ 5 - answer to question is No
+ 4 - answer to the question is NO
+ 3 - answer to the question is Yes
+ 2 - answer to the question is Yes
+ 1 - answer to the question is Yes
+ 0 - answer to the question is Yes
- 1 - answer to the question is Yes
- 2 - answer to the question is Yes
- 3 - answer to the question is Yes
User avatar
P
jabhatta2
VP
VP
Joined: 15 Dec 2016
Posts: 1376
Own Kudos [?]: 207 [0]
Given Kudos: 189
Send PM
Re: Is ((x-3)^2)^(1/2) = 3-x? (1) x 3 (2) -x|x| > 0 [#permalink] New post   15 Mar 2022, 08:38
^^ when it comes to S2 -- the answer is always "Yes" as the lines are always overlapping
avatar
B
vinayakjjw
Intern
Intern
Joined: 02 Apr 2022
Posts: 11
Own Kudos [?]: 14 [0]
Given Kudos: 11
Send PM
Re: Is ((x-3)^2)^(1/2) = 3-x? (1) x 3 (2) -x|x| > 0 [#permalink] New post   10 Jul 2022, 11:24
[quote="esledge"]
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?"

Can you please explain me how did you get to the conclusion that x<3. When I consider -
Is -(x-3) = 3-x? I get the answer as x=0. Then if i substitute these back in the equation we still get both of them as possible solutions. Why didn't you think that this equation has two solutions x=0, x=3. I wanted to understand the thought process behind getting to x<3
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32635
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: ps - abs. value [#permalink] New post   28 Jun 2023, 02:50
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
gmatclubot
Re: ps - abs. value [#permalink]
28 Jun 2023, 02:50
   1   2   3 
Moderator:
Bunuel
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions