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The median length of the 13 logs in shipment x was 84 inches

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The median length of the 13 logs in shipment x was 84 inches [#permalink] New post 01 Apr 2013, 06:43
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The median length of the 13 logs in shipment x was 84 inches, and the median length of the 21 logs in shipment y was 85 inches. If the two longest logs in shipment Y were transferred to shipment X, what would be the median length, in inches, of the 15 logs in shipment X after the transfer?

1) The two logs transferred had lengths of 91 and 92 inches, respectively.

2) The longest log that was in shipment x before the transfer had length 90 inches.

+1 if u like the Q :-D
[Reveal] Spoiler: OA
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Re: The median length of the 13 logs in shipment x was 84 inches [#permalink] New post 01 Apr 2013, 07:49
The question tells us that the median of the 13 logs in shipment x is 84 inches. This implies that the length of the seventh log, when all logs are arranged in ascending order, is 84.
The question also tells us that the median of the 21 logs in shipment y is 85 inches. This implies that the length of the 12th log, when all logs are arranged in ascending order of length, is 85 inches.
Now, two longest logs are shifted from shipment y to shipment x. We need to find the median length of the 15 logs in shipment x.
1. This tells is the length of the longest two logs transferred. However, to find the median of the fifth log, we need to know the length of the 8th log which must be greater than 84 inches. However, we cannot be sure of its length. Hence, INSUFFICIENT.

2. This tells us that the longest log is shipment x has a length of 90 inches. However, this does not tell us the lengths of the logs longer than 84 inches. Hence, INSUFFICIENT.

Together, the statements still do not tell us anything about the length of the 8th log in shipment X so still insufficient.
Answer:E

thinktank wrote:
The median length of the 13 logs in shipment x was 84 inches, and the median length of the 21 logs in shipment y was 85 inches. If the two longest logs in shipment Y were transferred to shipment X, what would be the median length, in inches, of the 15 logs in shipment X after the transfer?

1) The two logs transferred had lengths of 91 and 92 inches, respectively.

2) The longest log that was in shipment x before the transfer had length 90 inches.

+1 if u like the Q :-D

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Re: The median length of the 13 logs in shipment x was 84 inches [#permalink] New post 01 Apr 2013, 08:41
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thinktank wrote:
The median length of the 13 logs in shipment x was 84 inches, and the median length of the 21 logs in shipment y was 85 inches. If the two longest logs in shipment Y were transferred to shipment X, what would be the median length, in inches, of the 15 logs in shipment X after the transfer?

1) The two logs transferred had lengths of 91 and 92 inches, respectively.

2) The longest log that was in shipment x before the transfer had length 90 inches.

+1 if u like the Q :-D


Be weary of a question like this because you could think it's solvable if you confuse median with mean. The median is the middle term (or average of two middle terms in an even-numbered set), so adding terms at the end does not mean (pun intended) that we know the new median.

If this question asked about the average, then you could think it would be (13* 84)+91+92 and then divide the whole thing by 15, and this is tempting because the math is tough so it lends itself well to a data sufficiency question. If you identify the word median properly and don't get confused with the concept of mean, this question becomes significantly easier.

Hope this helps!
-Ron
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Re: The median length of the 13 logs in shipment x was 84 inches   [#permalink] 01 Apr 2013, 08:41
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