List A contains 16 distinct odd integers and 9 distinct even integers

Question

List A contains 16 distinct odd integers and 9 distinct even integers such that the average (arithmetic mean) of List A is 13.84. If each odd integer is doubled in magnitude, what is the new average (arithmetic mean) of List A?

(1) The average (arithmetic mean) of the even integers in List A is 10

(2) Before each odd integer is doubled in magnitude, the smallest odd integer in List A is 1 and the largest odd integer in List A is 31.

medic19 · Answer

Great question. Semantics are at play here.

gvij2017 · Answer

Can you explain why D is wrong?

IanStewart · Answer

If the answer is E here, this is not a good question at all. The GMAT is not going to try to 'trick' you in the way this question is trying to. The only reason the answer could be E is if by "double in magnitude" they mean "doubles its distance from zero" (so 3 could become 6 or -6). That's technically what "magnitude" means, but the GMAT is not going to test you on technicalities of mathematical definitions. Almost anyone reading this question would naturally assume we're just doubling each odd number's value, since in any real GMAT problem worded in a similar way, that's what you'd be doing. And if that's what we are doing here, the answer is D -- we can find the sum of the even integers and thus of the odd integers from Statement 1, and thus find the sum of all the values after we double the odd integers. Statement 2 tells us exactly what the odd integers are (they must be the consecutive odd integers from 1 through 31), so we can find their sum, find the sum of the even numbers, and find the sum of the set after we double the odd integers.

But of course if you interpret "magnitude" the way they're intending, the answer is E without requiring any work, since there's no predicting what's in the set after doubling each odd number's "magnitude".

It's a much better (more realistic) question if you simply assume you're doubling each odd number.

But of course if you interpret "magnitude" the way they're intending, the answer is E without requiring any work, since there's no predicting what's in the set after doubling each odd number's "magnitude".

It's a much better (more realistic) question if you simply assume you're doubling each odd number.

baru · Answer

The OA is indeed D , I made a mistake while posting it

baru · Answer

OA is D , made a mistake while posting

IanStewart · Answer

Then it's a much better question, but then they're misusing the word "magnitude", so there's still an issue with the wording. It's hard to know what the right answer is to a question when you have to guess what it means.

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List A contains 16 distinct odd integers and 9 distinct even integers

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List A contains 16 distinct odd integers and 9 distinct even integers

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