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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Wed Jan 25, 2012 7:12 pm

A sequence: 2, 4, 6, ...22. Sequence M contains eight numbers, which are elements of the former sequence. What is the standard deviation of M?
1) Two sequences have the same average value.
2) M does contain 22

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Source: Beat The GMAT — Data Sufficiency | Wed Jan 25, 2012 7:12 pm

MBACenter: GMAT Instructor; Posts: 56; Joined: Thu Jun 30, 2011 12:54 amFollowed by: 4 members; Location: Paris, FRANCE; Thanked: 16 times; GMAT Score:740

by MBACenter » Thu Jan 26, 2012 3:03 am

sud21 wrote:A sequence: 2, 4, 6, ...22. Sequence M contains eight numbers, which are elements of the former sequence. What is the standard deviation of M?
1) Two sequences have the same average value.
2) M does contain 22

The original sequence contains 11 elements. To find the standard deviation of a new set, we need to know which elements are in the new sequence.

The original sequence is an arithmetic sequence, so its median is equal to its mean. This will be the 6th term, or 12.

The new sequence, however, is not guaranteed to be arithmetic!

Statement 1 alone is not sufficient. For example, we COULD have 2, 4, 6, 8, 16, 18, 20, 22 or we could have 2, 4, 6, 10, 14, 18, 20, 22 or 4, 6, 8, 10, 14, 16, 18, 20...

Statement 2 alone is not sufficient. We could have 2, 4, 6, 8, 16, 18, 20, 22 or 2, 4, 6, 10, 14, 18, 20, 22 or even the non-symmetrical 4, 6, 10, 12, 14, 18, 20, 22...

Even together the statements are not sufficient; we could still have 2, 4, 6, 8, 16, 18, 20, 22 or 2, 4, 6, 10, 14, 18, 20, 22.

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by [email protected] » Mon Apr 30, 2012 5:52 pm

Even after considering both the Statements 1 and 2, we get overall 2 sets i.e

(i) {2, 4, 6, 8, 16, 18, 20, 22}

OR

(ii) {2, 4, 6, 10, 14, 18, 20, 22}

Because of that the correct answer is E and not C...

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