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

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

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Premier P570 Q16
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Jul 2014, 10:48, edited 1 time in total.
Edited the question.
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Re: Is |15 - m| + |m - 15| > 15? [#permalink]

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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.

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

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New post 08 Mar 2016, 10:11
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.

Answer: B.


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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New post 08 Mar 2016, 11:02
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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.

Answer: B.


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 08 Mar 2016, 11:16
I realized my mistake! Thanks, Bunuel :)
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Re: Is |15 - m| + |m - 15| > 15? [#permalink]

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New post 08 Mar 2016, 19:32
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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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New post 09 Mar 2016, 07:31
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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Re: Is |15 - m| + |m - 15| > 15?   [#permalink] 11 Aug 2017, 21:35
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