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

 It is currently 20 Apr 2019, 23:56

### 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 x>0? 1) x-3/|x-3|<1 2) 3x<y<2x

Author Message
TAGS:

### Hide Tags

Director
Joined: 23 Feb 2015
Posts: 845
GMAT 1: 720 Q49 V40
Is x>0? 1) x-3/|x-3|<1 2) 3x<y<2x  [#permalink]

### Show Tags

Updated on: 27 Mar 2019, 13:37
1
2
00:00

Difficulty:

65% (hard)

Question Stats:

42% (01:53) correct 58% (02:09) wrong based on 24 sessions

### HideShow timer Statistics

Is $$x>0?$$
1) $$\frac{x-3}{|x-3|}<1$$
2) $$3x<2x$$

_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Originally posted by AsadAbu on 14 Mar 2019, 08:13.
Last edited by AsadAbu on 27 Mar 2019, 13:37, edited 1 time in total.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1418
Re: Is x>0? 1) x-3/|x-3|<1 2) 3x<y<2x  [#permalink]

### Show Tags

14 Mar 2019, 09:53
1
In Statement 1, if x-3 were positive, then the absolute value wouldn't change x-3, and (x-3)/|x-3| would equal (x-3)/(x-3) which is 1. Statement 1 tells us that fraction is not equal to 1, so the absolute value must change x-3, and x-3 must be negative, so x-3 < 0, and x < 3. But x can be 2 or -5 so this is not sufficient.

I'm not sure what the "y" is doing in Statement 2, but ignoring it, we have 3x < 2x, which, subtracting 2x on both sides, tells us x < 0, so this is sufficient to give a 'no' answer to the question, and the answer is B.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Director
Joined: 23 Feb 2015
Posts: 845
GMAT 1: 720 Q49 V40
Re: Is x>0? 1) x-3/|x-3|<1 2) 3x<y<2x  [#permalink]

### Show Tags

27 Mar 2019, 13:39
IanStewart wrote:
In Statement 1, if x-3 were positive, then the absolute value wouldn't change x-3, and (x-3)/|x-3| would equal (x-3)/(x-3) which is 1. Statement 1 tells us that fraction is not equal to 1, so the absolute value must change x-3, and x-3 must be negative, so x-3 < 0, and x < 3. But x can be 2 or -5 so this is not sufficient.

I'm not sure what the "y" is doing in Statement 2, but ignoring it, we have 3x < 2x, which, subtracting 2x on both sides, tells us x < 0, so this is sufficient to give a 'no' answer to the question, and the answer is B.

removed y from statement 2.
Thanks (with +1) for your explanation...
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
Re: Is x>0? 1) x-3/|x-3|<1 2) 3x<y<2x   [#permalink] 27 Mar 2019, 13:39
Display posts from previous: Sort by