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.

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:

Re: If |p−6|+p=6, which of the following must be true? [#permalink]
30 Jun 2013, 17:08

If |p−6|+p=6, which of the following must be true?

There are two ways to solve, one of which is to just pick numbers.

The other way: |p-6|+p=6 |p-6| = 6-p |p-6| = -(p-6) |x| = -x (i.e. the value inside the absolute value bars is negative) So, (p-6) is negative when p≤6

Re: If |p−6|+p=6, which of the following must be true? [#permalink]
01 Jul 2013, 13:39

without plugging in numbers, how would you know that this |p-6| = -(p-6) would be p<=6 and not just p<6? the way i'm solving it, this |x| = -x condition would be met when (p-6)<0 and therefore -(p-6)<0 yields p<6. but why also p=6?

Re: If |p−6|+p=6, which of the following must be true? [#permalink]
01 Jul 2013, 13:42

Expert's post

nancerella wrote:

without plugging in numbers, how would you know that this |p-6| = -(p-6) would be p<=6 and not just p<6? the way i'm solving it, this |x| = -x condition would be met when (p-6)<0 and therefore -(p-6)<0 yields p<6. but why also p=6?

thanks!

Because when x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}.

We have |p-6|=-(p-6), thus p-6\leq{0} --> p\leq{6}.
_________________