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

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arshu27
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Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post   16 Jun 2015, 07:44
Bunuel wrote:
arshu27 wrote:
Hi Bunuel,

if we substitute p=0 then the answer must be 6. There can be no other answer right?


Not sure I understand what you mean...

p = 0, as well as any other value of p less than or equal 6 satisfies |p − 6| + p = 6.



thanks Bunuel..i have got it now... i wasn't seeing it the right way!!
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Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post   16 Jun 2015, 08:58
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arshu27 wrote:
Hi Bunuel,

if we substitute p=0 then the answer must be 6. There can be no other answer right?



You are wrong here Ashu,

There can be infinite many answers for this equation and the answer will fall in the range 0<p<6

I hope it answers your query!
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Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post   16 Sep 2017, 16:28
It's simple property of Absolute Value: if \(|x| = y\), then \(y>= 0\);

Here the given equation can be rearranged as, \(|p-6| = 6-p\)
which implies, \(6-p >=0\)
or \(p<=6\). Hence E.

I hope this clarifies some doubts.
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Re: If |p6|+p=6, which of the following must be true? [#permalink] New post   26 Apr 2022, 10:23
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|a-b| = |b-a| = the DISTANCE between b and a
b-a = the DIFFERENCE between b and a
Rule:
The distance between two values will be equal to the difference between the two values as long as the difference is NONNEGATIVE.

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

A. p=0
B. p=-6
C. p=6
D. p>-6
E. p<=6


|p−6|+p=6
|6-p| = 6-p
In words:
The distance between 6 and p is equal to the difference between 6 and p.
Since distance = difference as long as the difference is nonnegative, we get:
6-p ≥ 0
6 ≥ p

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Re: If |p6|+p=6, which of the following must be true? [#permalink] New post   31 Aug 2023, 04:19
bagdbmba wrote:
Bunuel wrote:
debayan222 wrote:
Bunuel-Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?


When \(p\leq{6}\), then \(|p-6|=-(p-6)=6-p\).
When \(p\geq{6}\), then \(|p-6|=p-6\).


So, only 6 satisfies both |p−6|= (p-6) and |p−6|=-(p-6)

Then why the answer is not ONLY 6 for the above qs?


Because 6 is a solution definitely, but that is not the only solution, any value less than or equal to 6 is possible for this question. You have to address all solution particularly when all solutions is given in the question.

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Re: If |p6|+p=6, which of the following must be true? [#permalink]
31 Aug 2023, 04:19
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