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If x is a positive integer, is the mean of set S greater tha

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S = {1, 2, 5, 7, x}

If x is a positive integer, is the mean of set S greater than 4?

(1) The median of set S is greater than 2
(2) The median of set S is equal to the mean of set S
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Apr 2014, 02:08, edited 1 time in total.
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S = {1, 2, 5, 7, x}

If x is a positive integer, is the mean of set S greater than 4?


The mean = (1 + 2 + 5 + 7 + x)/5 = (15 + x)/5. The question asks whether (15 + x)/5 > 4 --> is x > 5.

(1) The median of set S is greater than 2:

The median of a set with odd number of elements is the middle element when arranged in ascending/descending order. Hence the median of set S can be:
2, when \(x\leq{2}\), {x, 1, 2, 5, 7}
x, when \(2\leq{x}\leq{5}\), {1, 2, x, 5, 7};
5, when \(x\geq{5}\), {1, 2, 5, 7, x}.

So, the median of the set will be greater than 2, when x > 2. Hence this statement is not sufficient to say whether x > 5. Not sufficient.


(2) The median of set S is equal to the mean of set S:

The mean = (15 + x)/5 = 3 + x/5.

Since we know that the median of set S must be an integer (2, x, or 5), then the mean, which is 3 + x/5 must also be an integer --> x must be a multiple of 5. The least positive multiple of 5 is 5 itself. If x=5, then S={1, 2, 5, 5, 7} --> mean=4 and the median=5. So, x is not 5, which implies that it must be 10 (the next multiple of 5) or greater. Sufficient.

Answer: B.

Hope it's clear.
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Re: If x is a positive integer, is the mean of set S greater tha [#permalink]

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New post 18 Oct 2015, 21:20
ANS is b clearly ;

Quick question Bunnel :- if number are in AP mean = median ; so according to this q the vic-versa doesnt hold true i should believe that ???
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rohitkumar77 wrote:
ANS is b clearly ;

Quick question Bunnel :- if number are in AP mean = median ; so according to this q the vic-versa doesnt hold true i should believe that ???


Yes. If in a set mean = median, the elements in the set are not necessarily in A.P. For example, {1, 1, 3, 3, 7}.
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Re: If x is a positive integer, is the mean of set S greater tha [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

S = {1, 2, 5, 7, x}

If x is a positive integer, is the mean of set S greater than 4?

(1) The median of set S is greater than 2
(2) The median of set S is equal to the mean of set S

If we modify the original condition, (1+2+5+7+x)/5>4? ==> (15+x)/5>4? ==> 15+x>20, so we want to know whether x>5
There is one variable (x) so we need one equation, when there are 2 equations are provided . Therefore, there is high chance D will be our answer.
From condition 1, the sequence can be 2,x,5. 2 cannot be the median. If median=x, x>2, so this is insufficient.
From condition 2, the mean=(1+2+5+7+x)/5=(15+x)/5 --> 2=(15+x)/5. If x=-5 it is an negative number so it is out of scope. There is also no integer that satisfies x=(15+x)/5.
for 5=(15+x)/5, x=10>5, and the answer to the question is 'yes', so this is a sufficient condition and the answer is (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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