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

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thinktank
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The median length of the 13 logs in shipment x was 84 inches, and the [#permalink] New post   01 Apr 2013, 07:43
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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.

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VeritasPrepRon
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Re: The median length of the 13 logs in shipment x was 84 inches, and the [#permalink] New post   01 Apr 2013, 09:41
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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, and the [#permalink] New post   09 Dec 2014, 03:42
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Basically in shipment X, if we put in ascending order, the 7th log is 84
and in Shipment Y, 11th log is 85 inches.

We need to find after the transfer, the length of 8th Log in shipment x.
Statement 1) The two logs transferred had lengths of 91 and 92 inches, respectively.
Now I don't know lengths of logs 8th to 13th. I don't know how to place them and find out the median -> Not Sufficient.


Statement 2) Longest log in Shipment X is 90. We don't know what is the length of logs transferred and length of logs from 8th to 13th. not Sufficient

Combining the two statements.
We just know in ascending order 13th, 14th and 15th with certainty and rest we don't know.

So E)
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Re: The median length of the 13 logs in shipment x was 84 inches, and the [#permalink] New post   01 Apr 2013, 08:49
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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, and the [#permalink] New post   14 Nov 2023, 23:37

OFFICIAL EXPLANATION


Let X and Y, respectively, denote the list of the lengths of the logs in shipments X and Y before the transfer (to shipment X) of the two longest logs in shipment Y. Also, let X* and Y*, respectively, denote the list of the lengths of the logs in shipments X and Y after the transfer (to shipment X) of the two longest logs in shipment Y. It is given that the median of list X is 84 and the median of list Y is 85. Determine the median of list X*.

(1) Given that the lengths of the two logs transferred were 91 and 92, it is not possible to determine the median of list X*. For example, suppose list X consisted of 13 occurrences of 84 while list Y consisted of 19 occurrences of 85, 1 occurrence of 91, and 1 occurrence of 92. Then the median of list X is 84, the median of list Y is 85, and the median of list X* is 84 (note that 84 is the 8th number when the 15 numbers in list X* are listed from least to greatest). On the other hand, suppose list X consisted of 7 occurrences of 84 and 6 occurrences of 85, while list Y consisted of 19 occurrences of 85, 1 occurrence of 91, and 1 occurrence of 92. Then the median of list X is 84, the median of list Y is 85, and the median of list X* is 85 (note that 85 is the 8th number when the 15 numbers in list X* are listed from least to greatest); NOT sufficient.

(2) Given that the greatest number in list X is 90, it is not possible to determine the median of list X*. For example, suppose list X consisted of 12 occurrences of 84 and 1 occurrence of 90, while list Y consisted of 19 occurrences of 85, 1 occurrence of 91, and 1 occurrence of 92. Then the median of list X is 84, the median of list Y is 85, and the median of list X* is 84 (note that 84 is the 8th number when the 15 numbers in list X* are listed from least to greatest). On the other hand, suppose list X consisted of 7 occurrences of 84, 5 occurrences of 85, and 1 occurrence of 90, while list Y consisted of 19 occurrences of 85, 1 occurrence of 91, and 1 occurrence of 92. Then the median of list X is 84, the median of list Y is 85, and the median of list X* is 85 (note that 85 is the 8th number when the 15 numbers in list X* are listed from least to greatest); NOT sufficient.

Given (1) and (2) together, the examples given in (2) above show that the median of list X* cannot be determined.

The correct answer is E; both statements together are still not sufficient.
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Re: The median length of the 13 logs in shipment x was 84 inches, and the [#permalink]
14 Nov 2023, 23:37
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