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# How many values can the integer p=|x+3|-|x-3| assume?

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Math Expert
Joined: 02 Sep 2009
Posts: 56371
Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

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06 Jan 2017, 07:14
Salvetor wrote:
What is the level of this question. Above 650?

Yes. You can check the difficulty level from the original post: how-many-values-can-the-integer-p-x-3-x-3-assume-152859.html#p1225434
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Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

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13 Feb 2017, 06:53
Zarrolou wrote:
How many values can the integer $$p=|x+3|-|x-3|$$ assume?

A)6
B)7
C)13
D)12
E)Infinite values

My own question, as always any feedback is appreciated

This is a copy of the following GMAT Club question: https://gmatclub.com/forum/if-y-x-5-x-5 ... 73626.html
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Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

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06 Apr 2018, 06:37
Zarrolou wrote:
Good job arpanpatnaik, vinaymimani!

Official explanation

The function $$|x+3|-|x-3|$$ for values $$\geq{}3$$ equals $$6$$, and for values $$\leq{}-3$$ equals $$-6$$
For the middle values it follows the equation $$2x$$ (as the users above correctly say)

However there is a quicker way to get to the answer than counting the possible values.

Its upper limit is $$6$$, its lower limit is $$-6$$ and the function $$2x$$ is monotonic and increasing (and continuous), so will assume all values between 6 and -6 included.
(This is not theory necessary for the GMAT, but if notice the fact that $$2x$$ must pass for all values between 6 and -6, you can save time)

So the values that the integer p can assume are $$-6,-5,...,0,...,5,6$$ TOT=$$13$$

For for clarity, below there is the graph of $$|x+3|-|x-3|$$ that will make my explanation more clear.

Can you please explain how you drew the graph with two variables. sort of struggling with that.
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Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

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25 May 2019, 20:15
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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).

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Re: How many values can the integer p=|x+3|-|x-3| assume?   [#permalink] 25 May 2019, 20:15

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