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# GMAT Diagnostic Test Question 18

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Senior Manager
Joined: 19 Apr 2011
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Schools: Booth,NUS,St.Gallon
Re: GMAT Diagnostic Test Question 18 [#permalink]

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06 Feb 2012, 22:30
Nice explanation everyone !!had got this question wrong !!
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+1 if you like my explanation .Thanks

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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07 Feb 2012, 01:32
The answer is A. Very good Q.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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08 Feb 2012, 02:08
and what if the members of S are negative numbers? nothing in the question states that S is composed of at least one positive number... am I mistaken? in that case, we need both statements: answer is C ... (????????)

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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08 Feb 2012, 04:27
Expert's post
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nbrianco wrote:
and what if the members of S are negative numbers? nothing in the question states that S is composed of at least one positive number... am I mistaken? in that case, we need both statements: answer is C ... (????????)

Hi and welcome to GMAT Club! Below is an answer to your doubt.

Is the mean of set S greater than its median?

First of all:
The median of a set with odd # of terms is just a middle term (when ordered in ascending/descending order).

The median of a set with even # of terms is the average of two middle terms (when ordered in ascending/descending order).

Next, one of the most important properties of evenly spaced set (aka arithmetic progression):
In any evenly spaced set the arithmetic mean (average) is equal to the median and can be calculated by the formula $$mean=median=\frac{a_1+a_n}{2}$$, where $$a_1$$ is the first term and $$a_n$$ is the last term. Given the set $$\{7,11,15,19\}$$, $$mean=median=\frac{7+19}{2}=13$$.

(1) All members of S are consecutive multiples of 3 --> S is an evenly spaced set, thus its mean equals to its median. Sufficient.

To address your question, lets check whether it's true if S consists with negative numbers:
{-6, -3} --> mean=-4.5=median;
{-9, -6, -3} --> mean=-6=median;
{-6, -3, 0, 3} --> mean=-1.5=median.

(2) The sum of all members of S equals 75. Clearly insufficient.

For more on this topic check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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08 Feb 2012, 04:44
Thanks so much! I feel terrible as i completely misread the first assumption. This was not difficult indeed... sorry

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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22 Feb 2012, 13:17
I solved it in a similar fashion. This was not bad at all...

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Re: GMAT Diagnostic Test Question 18   [#permalink] 22 Feb 2012, 13:17

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# GMAT Diagnostic Test Question 18

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