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M30-04

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M30-04 [#permalink]

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What is the median of data set A?



(1) No number in data set A is less than the average (arithmetic mean) of the set.

(2) The average (arithmetic mean) of data set A is equal to the range of the set.
[Reveal] Spoiler: OA

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Re M30-04 [#permalink]

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Official Solution:


What is the median of data set A?

(1) No number in data set A is less than the average (arithmetic mean) of the set.

Since no number is less than the average, then no number is more than the average, which implies that the list contains identical elements: A={x, x, x, ...}. From this it follows that (the average)=(the median). But we don't know the value of \(x\), thus this statement is NOT sufficient.

(2) The average (arithmetic mean) of data set A is equal to the range of the set.

Not sufficient: if A={0, 0, 0, 0}, then (the median)=0, but if A={1, 2, 2, 3}, then (the median)=2.

(1)+(2) From (1) we have that the list contains identical elements. The range of all such sets is 0. Therefore, from (2) we have that (the average)=(the range)=0 and since from (1) we also know that (the average)=(the median), then (the median)=0. Sufficient.


Answer: C
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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

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Re: M30-04 [#permalink]

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New post 22 Oct 2016, 15:11
Shouldn't the mention of Set A in (2) be Set S instead?
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Re: M30-04 [#permalink]

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New post 22 Oct 2016, 23:37
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Re: M30-04 [#permalink]

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New post 14 Jan 2018, 08:01
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Bunuel
M28-47 and M30-04 are the same question
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Re: M30-04 [#permalink]

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New post 14 Jan 2018, 22:00
Re: M30-04   [#permalink] 14 Jan 2018, 22:00
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