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# GMAT Diagnostic Test Question 18

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GMAT Diagnostic Test Question 18 [#permalink]

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06 Jun 2009, 22:56
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GMAT Diagnostic Test Question 18
Field: statistics
Difficulty: 700

Is the mean of set S greater than its median?

(1) All members of S are consecutive multiples of 3
(2) The sum of all members of S equals 75

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient
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Last edited by Bunuel on 07 Oct 2013, 00:20, edited 2 times in total.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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05 Aug 2009, 22:14
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A property in AP says...

If a series is in Airthmetic Progression then the series will have A.Mean = Median

In this case, series has multiples of 3 i.e. AP... So A.Mean = Median.

Thanks
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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20 Jul 2009, 21:17
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Expert's post
topher wrote:
Seriously, these questions are testing the fine little details, but I guess that's important to get top Quant scores.

And did you expect anything less from a 750-level question?
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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08 Jan 2011, 23:59
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Its a good question but definitely not a 750 level question. It should be in 650-700.

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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01 Jul 2009, 12:40
Explanation:

Statement 1 is sufficient. If this set contains an odd number of elements, say, 3, 6 and 9, then median of a set will equal its mean (both will equal the middle element). If set S contains an even number of elements, the median, as well as the mean of this set, will equal the mean of the two middle elements.

Statement 2 is insufficient. If we know only the sum of elements of set S, we can't be sure if the mean is greater than the median. Consider these two sets:

1. 25, 25, 25 --> mean is 25, median is 25, mean is not greater than median
2. 1, 2, 3, 4, 65 --> mean is 15, median is 3, mean is clearly greater than median
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Last edited by bb on 28 Sep 2013, 13:24, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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17 Jul 2009, 10:54
Hello!

I have a little question regarding the explanation,
the statement (1) says: All members of S are consecutive multiples of 3

and you say:
Quote:
Statement 1 is sufficient. If this set contains an odd number of elements [...]

and finally i ask: couldn't be possible that the set contained for example 3, 6, 9, 12? In other words, the statement
doesn't say that the number of elements is odd, am I right?

Thank you for your time guys =)
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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17 Jul 2009, 12:33
Hi,

You're right, it doesn't anywhere say that the number of elements is either odd or even. I was just going through the options. I've elaborated on either way in the explanation. You can see the highlighted part
dzyubam wrote:
Explanation:
 Rating:

Statement 1 is sufficient. If this set contains an odd number of elements, say, 3, 6 and 9, then median of a set will equal its mean (both will equal the middle element). If set S contains an even number of elements, the median, as well as the mean of this set, will equal the mean of the two middle elements.

Statement 2 is insufficient. If we know only the sum of elements of set S, we can't be sure if the mean is greater than the median. Consider these two sets:

1. 25, 25, 25 --> mean is 25, median is 25, mean is not greater than median
2. 1, 2, 3, 4, 65 --> mean is 15, median is 3, mean is clearly greater than median

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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17 Jul 2009, 14:33
This is a priceless lesson for my GMAT preparation haha
sorry!
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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20 Jul 2009, 21:08
Seriously, these questions are testing the fine little details, but I guess that's important to get top Quant scores.

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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06 Aug 2009, 00:02
Good one, thank you. +1.
walkman4mba wrote:
A property in AP says...

If a series is in Airthmetic Progression then the series will have A.Mean = Median

In this case, series has multiples of 3 i.e. AP... So A.Mean = Median.

Thanks
T.

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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28 Aug 2009, 06:36
bb wrote:
topher wrote:
Seriously, these questions are testing the fine little details, but I guess that's important to get top Quant scores.

And did you expect anything less from a 750-level question?

What is really confusing me is that I am getting more of the supposed "750" questions right and the supposed "easier" questions wrong.

Can this be??... I think that my mind works in reverse - it helps me in my line of current work, but not sure how it will help me with this test!

Any suggestions?

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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03 Oct 2009, 12:23
can you really say that the answer is A? I would have thought E. if Mean=Median, as it is with a set 3, 6, 9, then you can't really say Mean>median. Can you?

3, 6, 9. median = 6; mean = 6. so is mean greater than median? no

1, 3, 6, 9. Median = 9/2; mean = 19/4. so is mean greater than median? yes

insufficient.

Does the Gmat test that mean=median is similar to mean>median? Please let me know.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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03 Oct 2009, 12:34
azule45 wrote:
can you really say that the answer is A? I would have thought E. if Mean=Median, as it is with a set 3, 6, 9, then you can't really say Mean>median. Can you?

3, 6, 9. median = 6; mean = 6. so is mean greater than median? no

1, 3, 6, 9. Median = 9/2; mean = 19/4. so is mean greater than median? yes

insufficient.

Does the Gmat test that mean=median is similar to mean>median? Please let me know.

1 is not a multiple of 3. Consider {3, 6, 9, 12}.
Here mean = 30/4 = 7.5 and median = 15/2=7.5
A is sufficient.

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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05 Oct 2009, 06:58
hgp2k wrote:
azule45 wrote:
can you really say that the answer is A? I would have thought E. if Mean=Median, as it is with a set 3, 6, 9, then you can't really say Mean>median. Can you?

3, 6, 9. median = 6; mean = 6. so is mean greater than median? no

1, 3, 6, 9. Median = 9/2; mean = 19/4. so is mean greater than median? yes

insufficient.

Does the Gmat test that mean=median is similar to mean>median? Please let me know.

1 is not a multiple of 3. Consider {3, 6, 9, 12}.
Here mean = 30/4 = 7.5 and median = 15/2=7.5
A is sufficient.

Oh i get it now. so it will always be mean=median. Great!! thanks for this. i appreciate it. Looks like its A.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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18 Oct 2009, 10:12
dzyubam wrote:
Explanation:
 Rating:

Statement 1 is sufficient. If this set contains an odd number of elements, say, 3, 6 and 9, then median of a set will equal its mean (both will equal the middle element). If set S contains an even number of elements, the median, as well as the mean of this set, will equal the mean of the two middle elements.

Statement 2 is insufficient. If we know only the sum of elements of set S, we can't be sure if the mean is greater than the median. Consider these two sets:

1. 25, 25, 25 --> mean is 25, median is 25, mean is not greater than median
2. 1, 2, 3, 4, 65 --> mean is 15, median is 3, mean is clearly greater than median

What's the difference between your rational between statement 1 and 2?

3,6,9, yes mean = median but
25, 25, 25 is also yes i.e. mean = median but yet you say median is not greater than median.

I think the right answer is C, since 9 + 12 + 15 + 18 + 21 = 75 where mean = median, no negatives will work since the sum is +75.

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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19 Oct 2009, 04:51
By the two examples after S2 in the OE I meant to prove that S2 is not sufficient. In the first example, "3, 6, 9", the median = mean. In the second, "25, 25, 25", mean is greater than median. These examples are only related to S2. S1, on the contrary, is sufficient to answer the question. With S1 in mind we're sure that median will always equal the mean.

I hope it helps to clear the doubts .
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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02 Apr 2010, 12:19
bb wrote:
GMAT Diagnostic Test Question 18
Field: statistics
Difficulty: 750
 Rating:

Is the mean of set S greater than its median?

(1) All members of S are consecutive multiples of 3
(2) The sum of all members of S equals 75

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient

I see! consecutive multiples of 3 => 3(x, x+1, x+2,...x+n)
3, 6, 9 => 3(1, 2, 3) The AP's (series of Arithmetic Progression) have mean = median.
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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20 Apr 2010, 15:11
Shouldn't the answer be C because statement A does not answer the question? I understand your explanation for statement A but isn't the purpose of data sufficiency to verify whether the information provided is sufficient to answer the question asked with a specific answer, in this case, yes or no?

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Re: GMAT Diagnostic Test Question 18 [#permalink]

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21 Apr 2010, 09:42
cyrusthegreat wrote:
Shouldn't the answer be C because statement A does not answer the question? I understand your explanation for statement A but isn't the purpose of data sufficiency to verify whether the information provided is sufficient to answer the question asked with a specific answer, in this case, yes or no?

cheers

Is the mean of set S greater than its median?

(1) All members of S are consecutive multiples of 3
(2) The sum of all members of S equals 75

Stamt1: all members of S are consecutive multiples of 3
x-2, x-1, x, x+1, x+2, x+3: let x = 1
-3, 0, 3, 6, 9, 12
3(-1, 0, 1, 2, 3, 4)
for this set, mean = median
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Re: GMAT Diagnostic Test Question 18 [#permalink]

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09 Jan 2011, 02:12
Thanks for the feedback!
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Re: GMAT Diagnostic Test Question 18   [#permalink] 09 Jan 2011, 02:12

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# GMAT Diagnostic Test Question 18

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