In Set A above, if positive integer x is subtracted from the 3 largest

Question

Set A: {7, 4, 1, 0, 5, 8, 10, 9, 13, 21}

In Set A above, if positive integer x is subtracted from the 3 largest numbers in the list and x is added to the 3 smallest even numbers in the list, which of the following will be true?

A. The average of the set will stay the same.
B. There will be no mode in the new set.
C. The standard deviation of the set will stay the same.
D. The median of the set will stay the same.
E. The median of the set will increase by x.

philipssonicare · Answer

Set A: {7, 4, 1, 0, 5, 8, 10, 10, 13, 21}

In Set A above, if positive integer x is subtracted from the 3 largest numbers in the list and x is added to the 3 smallest even numbers in the list, which of the following will be true?

A. The average of the set will stay the same.
Arithmetic mean is  \frac{(sum of all number)}{(# of numbers)} . The sum doesn't change, just the distribution. A is correct

B. There will be no mode in the new set.
This may or may not be true. x could be some absurd number like 100 whereby there is no mode, or it could be 1 where '1' would be the mode.

C. The standard deviation of the set will stay the same.
Standard deviation is the spread from the mean. As with mode, could perhaps coax the numbers for it to be the same, but it is likely to not be the same.

D. The median of the set will stay the same.
Currently the median is 7.5
If x=1
1, 1, 5, 7, 9, 9, 10, 12, 20
Median is now 9.

E. The median of the set will increase by x.
As just shown above.

A

sting8 · Answer

"x is subtracted from the 3 largest numbers"

But there is 10 which is the third largest number, thus should x be subtracted from 4 numbers, 10,10,13,21 ?

In such case mean should change, as x is subtracted 4 times, but added only 3 times.

If that is not the case, then how can we conclude x should be subtracted from only one 10, from the language in the question stem ?

Bunuel   chetan2u  please help

IanStewart · Answer

That's a great point, and you're completely right - there's no way to know precisely how to interpret "x is subtracted from the three largest numbers" with this particular list, when two values are tied for 3rd-largest (it's also not a "Set", despite what the question says, since it has repeated values). It's a prep company question, and prep companies often don't design questions properly. This is one example of that.

sting8 · Answer

IanStewart Thanks for your reply Looks like this is yet another classic case of "Stick to official stuff"

chetan2u · Answer

Yes, you are correct with your observation. 
The question requires to be edited. Thank you

IanStewart · Answer

If the question was correctly transcribed from the source, shouldn't it be left alone? If the question is edited, gmatclub is attributing to the source a question that the source didn't write, for one thing. For another, test takers might use questions on this forum to make decisions about which prep products to buy. If moderators edit company questions to make them better, test takers might think the company produces better questions than it actually does, and might be shocked to find a lot of errors when they buy the company's product.

Test takers who see this thread will presumably see the discussion about the error in the original question (assuming the question was transcribed correctly the first time, which I'm not sure of).

chetan2u · Answer

I would agree with you completely on both the accounts. However, what happens to students who do not go through discussions and use these questions for quiz only. The timer shows that 80% answered it correctly even though the OA was incorrect. 
We can either tag them as questions of poor quality or find another way to give them the corrected version.

In Set A above, if positive integer x is subtracted from the 3 largest

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