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If set T was derived from set S when all elements of set S w

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by BTGmoderatorAT » Sat Feb 03, 2018 6:12 am
If set T was derived from set S when all elements of set S were multiplied by 2, is the median of set T greater than that of set S ?

(1) All elements of set S are positive
(2) The median of set S is positive

What's the best way to determine which statement is sufficient? Can any experts help?
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Sun Feb 04, 2018 8:21 am
ardz24 wrote:If set T was derived from set S when all elements of set S were multiplied by 2, is the median of set T greater than that of set S ?

(1) All elements of set S are positive
(2) The median of set S is positive

What's the best way to determine which statement is sufficient? Can any experts help?
Statement 1: Case 1
Set S: {1, 2, 3} Median = 2
Set T: {2, 4, 6} Median = 4

The answer is YES, T's median is greater.

Case 2:
Set S: {1/4, 1/3, 1/2} Median = 1/3
Set T {2/4, 2/3, 2/2} Median = 2/3
Again, the answer is YES, T's median is greater.

Now see the logic - if we're multiplying every element in Set S by 2 to derive Set T, it means we must also multiply the median by 2. If that median is positive, it will become greater. So statement 1 is sufficient.

Statement 2: Same logic. If the median is positive, when we multiply by it 2, it will be larger, thus the answer will always be YES

The answer is D, either statement alone is sufficient to answer the question.
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