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by GMATGuruNY » Fri Jan 09, 2015 7:30 am
DATA:
1 student --> 0-9 pages
4 students --> 10-19 pages
6 students --> 20-29 pages
7 students --> 30-39 pages
2 students --> 40-49 pages

There are a total of 20 students.
Thus, there are a total of 20 page lengths.
The median = average of the 10th and 11th page lengths.
The 10th and 11th page length fall within the RED RANGE above.

What is the LEAST possible number of pages lengths within 6 pages of the median length?
Strategy:
Put the 10th and 11th page lengths AS CLOSE TO EACH OTHER AS POSSIBLE, with the 18 remaining page lengths AS FAR AS POSSIBLE from the 10th and 11th page lengths.
The data points could be as follows:
0, 10, 10, 10, 10, 20, 20, 20, 20, 29, 29, 39, 39, 39, 39, 39, 39, 39, 49, 49.
Here:
Median = (29+29)/2 = 29.
Only the 2 values in green are within 6 pages of the median.
Final answer: 2

What is the GREATEST possible number of pages lengths within 6 pages of the median length?
Strategy:
Put the 10th and 11th page lengths AS FAR FROM EACH OTHER AS POSSIBLE, with the 18 remaining page lengths AS CLOSE AS POSSIBLE to the 10th and 11th page lengths.
The data points could be as follows:
9, 19, 19, 19, 19, 20, 20, 20, 20, 20, 29, 30, 30, 30, 30, 30, 30, 30, 40, 40.
Here:
Median = (20+29)/2 = 24.5.
All 17 values in green are within 6 pages of the median.
Final answer: 17
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by Brent@GMATPrepNow » Fri Jan 09, 2015 8:13 am
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Each senior in a college course wrote a thesis. The lengths, in pages, of those seniors' theses are summarized in the graph above.

a. What is the least possible number of seniors whose theses were within six pages of the median length?

b. What is the greatest possible number of seniors whose theses were within six pages of the median length ?
First determine the median thesis length. This seems a little tricky (since we have RANGES for the thesis lengths), but we could still list the ranges in ascending order.
We get: (0-9),(10-19),(10-19),(10-19),(10-19),(20-29),(20-29),(20-29),(20-29),(20-29),(20-29)...

Since there are 20 papers altogether (1 + 4 + 6 + 7 + 2 = 20), the median will be the mean (average) of the 10th and 11th terms.
So, the median can have several possible values.

a. What is the least possible number of seniors whose theses were within six pages of the median length?
Here's one way to minimize this value:
{2,11,11,11,11,20,20,20,20,29,29,39,39,39,39,39,39,39,49,49}
Here, the median = (29+29)/2 = 29.
So, there were only 2 theses within six pages of the median length

a. What is the greatest possible number of seniors whose theses were within six pages of the median length?
IMPORTANT: If we make the median length right in the middle of the 20-29 range, then the theses in the ranges on either side will both be within 6 pages.
Here's what I mean.
{2,19,19,19,19,20,20,20,20,20,29,30,30,30,30,30,30,30,49,49}
Here, the median = (20+29)/2 = 24.5
So, there were 17 theses within six pages of the median length

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by neha shekhawat » Mon Jul 31, 2017 10:13 am
Is there any other way to solve this question ?
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by [email protected] » Mon Jul 31, 2017 10:55 am
Hi neha shekhawat,

GMAT questions will often include 'shortcuts' (and be solvable with alternative approaches) based on how the 5 answer choices are designed. With this prompt though, the two questions don't include answer choices, so we're essentially "stuck" performing a certain amount of analysis and doing 'math.' As it stands, the math isn't actually that difficult, but - under the circumstances - you have to do all of it to correctly answer the two questions.

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