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# Is |15 - m| + |m - 15| > 15?

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Is |15 - m| + |m - 15| > 15?  [#permalink]

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Updated on: 06 Jul 2014, 11:48
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3
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Difficulty:

55% (hard)

Question Stats:

62% (01:48) correct 38% (01:58) wrong based on 185 sessions

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Is |15 - m| + |m - 15| > 15?

(1) m > 6
(2) m < 7

Premier P570 Q16

Originally posted by goodyear2013 on 06 Jul 2014, 09:13.
Last edited by Bunuel on 06 Jul 2014, 11:48, edited 1 time in total.
Edited the question.
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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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06 Jul 2014, 11:53
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Is |15 - m| + |m - 15| > 15?

First of all since $$|15 - m| = |m - 15|$$, then the question asks whether $$|15 - m| + |15 - m| > 15$$ --> is $$2*|15 - m| > 15$$? --> $$|15 - m| > 7.5$$? --> is $$15 - m > 7.5$$ or $$-(15 - m) > 7.5$$? --> is $$m<7.5$$ or is $$m>22.5$$?

(1) m > 6. Not sufficient.

(2) m < 7. Sufficient.

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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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08 Mar 2016, 11:11
Bunuel wrote:
Is |15 - m| + |m - 15| > 15?

First of all since $$|15 - m| = |m - 15|$$, then the question asks whether $$|15 - m| + |15 - m| > 15$$ --> is $$2*|15 - m| > 15$$? --> $$|15 - m| > 7.5$$? --> is $$15 - m > 7.5$$ or $$-(15 - m) > 7.5$$? --> is $$m<7.5$$ or is $$m>22.5$$?

(1) m > 6. Not sufficient.

(2) m < 7. Sufficient.

Hi Bunuel,

Since in the question stem, it is not mentioned that m is an integer, why can't we use m=6.5?
Thus,
15-6.5 !>7.5
Thus, even the option (2) is not sufficient, Answer should be E.

Please correct me if I am wrong. This is the main confusion I have in DS questions, when to use fractions and when to not!
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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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08 Mar 2016, 12:02
1
diviGmat wrote:
Bunuel wrote:
Is |15 - m| + |m - 15| > 15?

First of all since $$|15 - m| = |m - 15|$$, then the question asks whether $$|15 - m| + |15 - m| > 15$$ --> is $$2*|15 - m| > 15$$? --> $$|15 - m| > 7.5$$? --> is $$15 - m > 7.5$$ or $$-(15 - m) > 7.5$$? --> is $$m<7.5$$ or is $$m>22.5$$?

(1) m > 6. Not sufficient.

(2) m < 7. Sufficient.

Hi Bunuel,

Since in the question stem, it is not mentioned that m is an integer, why can't we use m=6.5?
Thus,
15-6.5 !>7.5
Thus, even the option (2) is not sufficient, Answer should be E.

Please correct me if I am wrong. This is the main confusion I have in DS questions, when to use fractions and when to not!

If m=6.5, still $$|15 - m| > 7.5$$ holds true: $$(|15 - 6.5|=8.5) > 7.5$$?
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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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08 Mar 2016, 12:16
I realized my mistake! Thanks, Bunuel
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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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08 Mar 2016, 20:32
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diviGmat wrote:

Hi Bunuel,

Since in the question stem, it is not mentioned that m is an integer, why can't we use m=6.5?
Thus,
15-6.5 !>7.5
Thus, even the option (2) is not sufficient, Answer should be E.

Please correct me if I am wrong. This is the main confusion I have in DS questions, when to use fractions and when to not!

I think you got your doubt clarified.
As a general rule on DS, consider the variables as integers only if it is written else you can consider fractions too
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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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09 Mar 2016, 08:31
Here The best approach is to find the range of the question using the modulus equality relationship.
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Re: Is |15 - m| + |m - 15| > 15?  [#permalink]

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11 Aug 2017, 22:35
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Re: Is |15 - m| + |m - 15| > 15?   [#permalink] 11 Aug 2017, 22:35
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