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Help!! Mgmat 5th edition Guide 3 Chapter 7-Problem 6!!!

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by mallika hunsur » Sun Dec 07, 2014 11:02 am
Hi all,
It'd be great if anyone can help me understand this problem (and the graph) from MGMAT WOrd problems CHapter 7 guide-
I've attached a snapshot of the graph and the question.
Any help with this is greatly appreciated!!

Many thanks,
Mallika Hunsur
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Source: — Quantitative Reasoning |

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by Brent@GMATPrepNow » Sun Dec 07, 2014 11:05 am
Hi Mallika,

Looks like you forgot the attachment.

Cheers,
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by mallika hunsur » Sun Dec 07, 2014 11:09 am
Hi Brent,

Some problem with the drive- I've attached a PDF now :) looks like there were multiple uploads!
Thanks so much!!

Best,
Mallika Hunsur
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by mallika hunsur » Sun Dec 07, 2014 10:01 pm
Brent@GMATPrepNow wrote:Hi Mallika,

Looks like you forgot the attachment.

Cheers,
Brent
Hi Brent,
I've attached a PDF!! :)

Best,
Mallika
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by [email protected] » Thu Dec 11, 2014 11:29 pm
Hi Mallika,

This question has a minor bit of "interpretative bias" in it. When the question states "within 6 pages", I'm going to assume that it really means "up to 6 pages" and not "fewer than 6 pages"

That having been said, the data gives us the number of students and the "ranges" of pages in each of their theses:

0-9 pages ==> 1 student
10-19 pgs ==> 4 students
20-29 pgs ==> 6 students
30-39 pgs ==> 7 students
40-49 pgs ==> 2 students

We have a total of 20 students, so the median number of pages will be based on the "highest 2" numbers in the 20-29 range, although we do have to consider the possibility of duplicate numbers. To figure out the "least" and "greatest" number of students within 6 pages of the median, we will have to TEST VALUES. Here's how to do it:

Since we're dealing with ranges of pages, we can send all of the students within a particular range to either extreme end of that range.

To figure out the LEAST number within 6 pages of the median....

In the 20-29 page range....
If we have 20, 20, 20, 20, 29, 29
then the median = 29
AND
in the 30-39 page range...
if we have ALL 39s

Then there are only 2 seniors with a page count within 6 pages of the median: the two with 29 pages each.

To figure out the GREATEST number within 6 pages of the median....


In the 20-29 page range...
if we have ALL 25s: 25, 25, 25, 25, 25, 25
then the median = 25
AND
in the 10-19 page range....
if we have ALL 19s: 19, 19, 19, 19
AND
in the 30-39 page range...
if we have ALL 30S: 30, 30, 30, 30, 30, 30, 30

Then there are 6 + 4 + 7 = 17 seniors that have a page count within 6 pages of the median

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Rich
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by mallika hunsur » Mon Dec 22, 2014 8:29 am
[email protected] wrote:Hi Mallika,

This question has a minor bit of "interpretative bias" in it. When the question states "within 6 pages", I'm going to assume that it really means "up to 6 pages" and not "fewer than 6 pages"

That having been said, the data gives us the number of students and the "ranges" of pages in each of their theses:

0-9 pages ==> 1 student
10-19 pgs ==> 4 students
20-29 pgs ==> 6 students
30-39 pgs ==> 7 students
40-49 pgs ==> 2 students

We have a total of 20 students, so the median number of pages will be based on the "highest 2" numbers in the 20-29 range, although we do have to consider the possibility of duplicate numbers. To figure out the "least" and "greatest" number of students within 6 pages of the median, we will have to TEST VALUES. Here's how to do it:

Since we're dealing with ranges of pages, we can send all of the students within a particular range to either extreme end of that range.

To figure out the LEAST number within 6 pages of the median....

In the 20-29 page range....
If we have 20, 20, 20, 20, 29, 29
then the median = 29
AND
in the 30-39 page range...
if we have ALL 39s

Then there are only 2 seniors with a page count within 6 pages of the median: the two with 29 pages each.

To figure out the GREATEST number within 6 pages of the median....


In the 20-29 page range...
if we have ALL 25s: 25, 25, 25, 25, 25, 25
then the median = 25
AND
in the 10-19 page range....
if we have ALL 19s: 19, 19, 19, 19
AND
in the 30-39 page range...
if we have ALL 30S: 30, 30, 30, 30, 30, 30, 30

Then there are 6 + 4 + 7 = 17 seniors that have a page count within 6 pages of the median

GMAT assassins aren't born, they're made,
Rich

Thanks so much for your prompt response Rich!!

We should be looking at the median of the pages data and in this case it means that the median of number of students happens to fall in the page range 20-29 that also houses the median number of pages.
Do you think I've understood this right..?

Thanks,
Mallika
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by [email protected] » Mon Dec 22, 2014 12:53 pm
Hi Mallika,

Since the questions both involve the median number of pages, and we have 20 students, the median value will be the average of the 10th and 11th student's pages (once those values are in order from least to greatest). From the table, we KNOW that those two students are in the 20-29 page range; however, we DON'T know how many pages are associated with either of them.

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by abduabd » Wed Feb 18, 2015 12:14 pm
I just came across this question. Thanks, Rich, for posting the detailed response. I understand why you would chose "25 pages" for the second question. For the first, however, if I were to choose any number of pages between 27 and 30, would I not get the same result? I just want to make sure that I am not missing any underlying principle here.

Thanks.
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by [email protected] » Wed Feb 18, 2015 12:59 pm
Hi abduabd,

In that question, we're trying to MINIMIZE the number with 6 PAGES of the median.

To answer your immediate question, you COULD have made the 10th and 11th values into 27s or 28s, but not 30s (since 30 is outside the 'range' for that group) and still have gotten the correct answer. You have to keep in mind that the values that you choose for the median can't be too low (if you made the median 25, for example, then EVERY value in that range would be within 6 of the median) and that would NOT minimize the answer.

GMAT assassins aren't born, they're made,
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