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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If \(X \ge 1\) , then the inequality turns into \(X - 1 \lt 1\) or \(X \lt 2\) . If \(X \lt 1\) , then the inequality turns into \(1 - X \lt 1\) or \(X \gt 0\) . Combine the intervals to get the answer.

If \(X \ge 1\) , then the inequality turns into \(X - 1 \lt 1\) or \(X \lt 2\) . If \(X \lt 1\) , then the inequality turns into \(1 - X \lt 1\) or \(X \gt 0\) . Combine the intervals to get the answer.

\(|1-x|<{1}\) --> key point is \(x=1\) (key points are the values of \(x\) when absolute values equal to zero), thus two ranges to check:

\(x<1\) --> \(|1-x|=1-x\) and \(|1-x|<{1}\) becomes: \(1-x<{1}\) --> \(x>0\); \(x\geq{1}\) --> \(|1-x|=-1+x\) and \(|1-x|<{1}\) becomes: \(-1+x<{1}\) --> \(x<2\);

So \(|1-x|<{1}\) holds true for \(0<x<2\).

Answer: D.

As for your question: \(x\) can not equal to 2, because \(0<x<2\) means that \(x\) MUST be less than 2 (and more than zero), for ANY \(x\) from this range given inequality will hold true.

I guess (0,2) should be changed to \(0<x<2\) (as well as all other options) to avoid confusion whether 0 and 2 are inclusive in the range.

If \(X \ge 1\) , then the inequality turns into \(X - 1 \lt 1\) or \(X \lt 2\) . If \(X \lt 1\) , then the inequality turns into \(1 - X \lt 1\) or \(X \gt 0\) . Combine the intervals to get the answer.

\(|1-x|<{1}\) --> key point is \(x=1\) (key points are the values of \(x\) when absolute values equal to zero), thus two ranges to check:

\(x<1\) --> \(|1-x|=1-x\) and \(|1-x|<{1}\) becomes: \(1-x<{1}\) --> \(x>0\); \(x\geq{1}\) --> \(|1-x|=-1+x\) and \(|1-x|<{1}\) becomes: \(-1+x<{1}\) --> \(x<2\);

So \(|1-x|<{1}\) holds true for \(0<x<2\).

Answer: D.

As for your question: \(x\) can not equal to 2, because \(0<x<2\) means that \(x\) MUST be less than 2 (and more than zero), for ANY \(x\) from this range given inequality will hold true.

Hope it helps.

Thanks for the quick reply! Your explanation with the key-point value is very helpful!

Also, I was not aware, that if they talk about "range" the values given are excluded (hence \(0<x<2\) )

" I guess (0,2) should be changed to 0<x<2 (as well as all other options) to avoid confusion whether 0 and 2 are inclusive in the range. "

This correction is needed IMO. when we say (0,2) we mean than the numbers are included. Also another alternative would be to change the question to |1-x|<=1
_________________

Cheers !!

Quant 47-Striving for 50 Verbal 34-Striving for 40