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# A set of numbers has an average of 50. If the largest

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Manager
Joined: 25 Aug 2011
Posts: 196
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
A set of numbers has an average of 50. If the largest [#permalink]

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12 Mar 2012, 22:38
1
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Difficulty:

75% (hard)

Question Stats:

55% (02:37) correct 45% (02:23) wrong based on 56 sessions

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A set of numbers has an average of 50. If the largest element is 5 greater than 3 times the smallest element and if the median equals the mean . what is largest possible value in the set

A. 85
B. 86
C. 88
D. 91
E. 92

If median = mean does’nt it imply an evenly spaced set?
[Reveal] Spoiler: OA
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4128

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13 Mar 2012, 10:29
3
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Expert's post
Hi, there. I'm happy to help with this.

This is a diabolically evil question, much much harder than anything the GMAT will ask you. In addition to that, the question is flawed. What is the source of this extremely poor question?

First, to answer your parenthetical question --- mean = median does not imply evenly spaced. Evenly-spaced is an extremely special condition -- if that's true, it's also true that mean - median, but there are scads of sets with mean = median that don't have this special condition.

In this question, we want a set that satisfies two conditions:
1) mean = median = 50
2) the largest element is 5 greater than 3 times the smallest element

Here are some sets that satisfy those conditions:
{27, 28, 50, 59, 86}
{29, 29, 50, 50, 92}
{30, 30, 45, 50, 50, 50, 95}
{33, 34, 36, 37, 50, 51, 52, 53, 104}

So, I was able to create a set that satisfies this condition with a highest value of 104. I am sure I could make sets with higher values, but I don't know how high could go (possibly 152?) (Notice, BTW, all of those set have mean = median, and none are evenly spaced, or even close)

The point is: the question, as posed, does not contain the correct answer among the answer choices. It may be that the author intended further restrictions (e.g. only five elements, elements are integers, all elements are distinct, etc etc.) that have not been stated. It is the mark of a poor question when the author has in mind further conditions that are not explicitly stated. The GMAT will never do that to you.

So, don't worry about this particular question ---- and in fact, you might be suspicious of any other question you got from that source. Here's a more GMAT-like question about median:

When you submit your answer to that question, the next page will have a video explanation.

Does everything I've set here make sense? Please let me know if you have any further questions.

Mike
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Mike McGarry
Magoosh Test Prep

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Joined: 13 Mar 2012
Posts: 358
Concentration: Operations, Strategy
Re: A set of numbers has an average of 50. If the largest [#permalink]

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14 Mar 2012, 02:07
Before reading the post from mike i tried to solve by rejecting options i.e.

3x+5 the largest in the set

only B and E are possible and among those E is higher so marked that

@mike
its a nice analysis;
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If there's a loophole in my analysis--> suggest measures to make it airtight.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India
Re: A set of numbers has an average of 50. If the largest [#permalink]

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14 Mar 2012, 03:33
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Expert's post
devinawilliam83 wrote:
A set of numbers has an average of 50. If the largest element is 5 greater than 3 times the smallest element and if the median equals the mean . what is largest possible value in the set

A. 85
B. 86
C. 88
D. 91
E. 92

If median = mean does’nt it imply an evenly spaced set?

Mike has already given a great analysis of this question. Let me add one more bit here:

The question says 'a set of numbers', not integers so a member of the set can be 49.9999.
The limiting value of the smallest number is 50. As long as the smallest number is a tiny bit less than 50, you can have the greatest number a tiny bit less than 50*3 + 5 = 155.

I would have respected this question much more if instead, they had asked "which of the following numbers cannot be in the set?" and had provided 155 or a greater value as an option.

And the median = mean condition doesn't hold much relevance (to create a median of 50, you can add any number of 50s to the set).

Also, for an evenly spaced set, mean = median but not vice versa.
e.g.
2, 3, 4, 4, 7 - mean = median = 4
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Re: A set of numbers has an average of 50. If the largest   [#permalink] 14 Mar 2012, 03:33
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# A set of numbers has an average of 50. If the largest

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