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M17-01

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M17-01  [#permalink]

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New post 16 Sep 2014, 00:00
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If set \(S\) consists of positive integers, is the median of set \(S\) larger than its range?


(1) All elements of set \(S\) are smaller than 40.

(2) All elements of set \(S\) are larger than 20.

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Re M17-01  [#permalink]

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New post 16 Sep 2014, 00:00
Official Solution:


Statement (1) by itself is insufficient. The range can be smaller than median (as in one-element set) or bigger than median (if the elements are spread wide enough: \({1, 39}\)).

Statement (2) by itself is insufficient. The range can be smaller than median (as in one-element set) or bigger than median (if the elements are spread wide enough: \({21, 100}\)).

Statements (1) and (2) combined are sufficient. If all the elements are confined between 21 and 39, the range of the set cannot exceed \(39 - 21 = 18\), whereas the median is between 21 and 39. Thus, the median of set \(S\) is larger than its range.


Answer: C
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Re: M17-01  [#permalink]

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New post 17 Aug 2016, 03:38
Bunuel wrote:
If set \(S\) consists of positive integers, is the median of set \(S\) larger than its range?


(1) All elements of set \(S\) are smaller than 40.

(2) All elements of set \(S\) are larger than 20.


I did it this way:

Let's say Median = M, Smallest element = S, and Largest element = L

Q: is M > L - S? or M + S > L?

(1) L <= 39, S & M unknown. Not Sufficient

(2) All elements > 20, so L, M & S unknown. Not sufficient

Together (1) & (2)
From (1) we know that L>=39, so let's say L is the maximum possible integer, so L = 39

From (2), we know that S could be any positive integer from 21 to 39, so let's say S is the smallest possible integer in the range, S = 21. We are left with M. Let's keep M as low as S, so M= S = 21

Q: Q: is M > L - S? or M + S > L? 21 > 39 -21? or 21 + 21 > 39? Yes. SUFFICIENT.

Hope this way of getting to the answer is ok.
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M17-01  [#permalink]

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New post 03 Dec 2016, 11:39
but what if all the elements are same? I think you had to emphasize that set contains of distinct numbers.
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Re: M17-01  [#permalink]

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New post 05 Dec 2016, 00:55
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Tuvshinbagana wrote:
but what if all the elements are same? I think you had to emphasize that set contains of distinct numbers.


It does not matter whether the elements are distinct or not. Please re-read:
If all the elements are confined between 21 and 39, the range of the set cannot exceed \(39 - 21 = 18\), whereas the median is between 21 and 39. Thus, the median of set \(S\) is larger than its range.
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Re: M17-01  [#permalink]

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New post 11 Apr 2017, 11:20
Bunuel wrote:
Tuvshinbagana wrote:
but what if all the elements are same? I think you had to emphasize that set contains of distinct numbers.


It does not matter whether the elements are distinct or not. Please re-read:
If all the elements are confined between 21 and 39, the range of the set cannot exceed \(39 - 21 = 18\), whereas the median is between 21 and 39. Thus, the median of set \(S\) is larger than its range.



Hi Bunuel.
What if the set has only one integer.

In that case => Median = Range ??
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Re: M17-01  [#permalink]

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New post 11 Apr 2017, 11:23
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stonecold wrote:
Bunuel wrote:
Tuvshinbagana wrote:
but what if all the elements are same? I think you had to emphasize that set contains of distinct numbers.


It does not matter whether the elements are distinct or not. Please re-read:
If all the elements are confined between 21 and 39, the range of the set cannot exceed \(39 - 21 = 18\), whereas the median is between 21 and 39. Thus, the median of set \(S\) is larger than its range.



Hi Bunuel.
What if the set has only one integer.

In that case => Median = Range ??


The range of a single-element set is 0.
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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 M17-01  [#permalink]

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New post 03 Sep 2018, 21:25
I think this is a high-quality question and I agree with explanation.
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Re M17-01 &nbs [#permalink] 03 Sep 2018, 21:25
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