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M21-05

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M21-05 [#permalink]

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New post 16 Sep 2014, 01:10
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What is the median of set \(S =\{a - b, b - a, a + b\}\) ?


(1) The mean of set \(S\) is equal to \(a + b\)

(2) The range of set \(S\) is equal to \(2b\)
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 01:10
Official Solution:


Statement (1) by itself is sufficient. The mean of set \(S = \frac{a - b + b - a + a + b}{3} = \frac{a + b}{3}\). This equals \(a + b\) only if \(a + b = 0\). \(a - b\) and \(b - a\) are either both zeros or have different signs. In either case, 0 is the median of set \(S\).

Statement (2) by itself is insufficient. Consider \(a = b = 0\) (the answer is 0) and \(a = 0\), \(b = 3\) (the answer is 3).


Answer: A
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Re: M21-05 [#permalink]

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New post 10 Nov 2017, 06:33
I really can't understand why the answer isn't D.
If the range(Highest - Lowest) is 2B, this means that the highest term of the set is a+b and the lowest is a-b.

If i know the highest and the lowest term of a 3 part set, i can know which one is the middle term, therefore, i know which term is the median, B-A. Even considering B=3 or B=0 this answer will work.

Can someone explain this to me?

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Re: M21-05 [#permalink]

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New post 10 Nov 2017, 06:38
pedrocaa wrote:
I really can't understand why the answer isn't D.
If the range(Highest - Lowest) is 2B, this means that the highest term of the set is a+b and the lowest is a-b.

If i know the highest and the lowest term of a 3 part set, i can know which one is the middle term, therefore, i know which term is the median, B-A. Even considering B=3 or B=0 this answer will work.

Can someone explain this to me?


This is a value DS question. When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".
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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: M21-05 [#permalink]

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New post 15 Nov 2017, 06:38
+1 for A.
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Re: M21-05   [#permalink] 15 Nov 2017, 06:38
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