If the average (arithmetic mean) of six consecutive odd

You may be right. I thought it would be a fun question.
That said, there ARE official GMAT questions in which we can solve the question without using all of the given information.

For example, in this official GMAT question https://gmatclub.com/forum/for-any-posi ... 27817.html, we can solve the question without using the formula that's provided.

Cheers,
Brent

Very humbly, I beg to defer. The formula in the official question quoted is a "help" and not a "diversion" to confuse the GMAT aspirant. But I get the rationale of your posting your own question and I totally respect your rationale.

Yes, the question is a bit of a trick question, since we don't really need to know the part about the average equaling 4q+2.
The range of 6 odd integers will ALWAYS be 10.

That said, we can also use that information to solve the question.
We'll use the input-output approach.

So, let's see what happens when we analyze a random set of 6 consecutive odd integers.
How about {9, 11, 13, 15, 17, 19}
Here, the mean = 14
From the given information, this means that 4q + 2 = 14
Solve to get q = 3
Now, for this set of values, the difference between the greatest and least of the six integers = 19 - 9 = 10

In other words, when we INPUT q = 3, then the OUTPUT (the answer to the given question) is 10

Now, we'll plug q = 3 into the 5 answer choices and see which one yields an OUTPUT of 10
A. 6(3) + 4 = 22. We need 10, so eliminate
B. 10(3) = 30. We need 10, so eliminate
C. 6(3)/(3 – 6) = -6. We need 10, so eliminate
D. 6. We need 10, so eliminate
E. 10. PERFECT MATCH

Answer: E

Oh my god. I spent more than 2 minutes on this question.
lot of unnecessary information provided.

quite easy one; but can be time waster is not well approached

N
N+2
N+4
N+6
N+8
N+10


Hence the difference will always be 10...


Hence E.

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