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# M21-05

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Math Expert
Joined: 02 Sep 2009
Posts: 44656
M21-05 [#permalink]

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16 Sep 2014, 01:10
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Difficulty:

65% (hard)

Question Stats:

52% (00:59) correct 48% (01:12) wrong based on 142 sessions

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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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Re M21-05 [#permalink]

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16 Sep 2014, 01:10
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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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10 Nov 2017, 06:33
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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?
Math Expert
Joined: 02 Sep 2009
Posts: 44656
Re: M21-05 [#permalink]

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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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GMAT 1: 640 Q48 V29
Re: M21-05 [#permalink]

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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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# M21-05

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