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If the average (arithmetic mean) of six consecutive odd

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If the average (arithmetic mean) of six consecutive odd integers is 4q + 2, what is the difference between the greatest and least of the six integers?

A. 6q + 4
B. 10q
C. 6q/(q – 6)
D. 6
E. 10

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[Reveal] Spoiler: OA

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Re: If the average (arithmetic mean) of six consecutive odd [#permalink]

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Since the 6 integers are consecutive odd integers,
first integer = 2n + 1
sixth integer = 2n + 1 + (5*2) = 2n + 11

Difference = 2n + 11 - (2n + 1) = 10

There is no need to consider the expression mentioned in the question.

Answer: E

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Re: If the average (arithmetic mean) of six consecutive odd [#permalink]

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New post 15 Feb 2017, 09:45
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GMATPrepNow wrote:
If the average (arithmetic mean) of six consecutive odd integers is 4q + 2, what is the difference between the greatest and least of the six integers?

A. 6q + 4
B. 10q
C. 6q/(q – 6)
D. 6
E. 10

*Kudos for all correct solutions


For any six consecutive even/odd integers, the difference between the highest and smallest will always remain 10. Hence, I don't find this question too appropriate as there is excess of information in form of q which is unlike GMAT style.

Answer : Option E
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Re: If the average (arithmetic mean) of six consecutive odd [#permalink]

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GMATinsight wrote:
For any six consecutive even/odd integers, the difference between the highest and smallest will always remain 10. Hence, I don't find this question too appropriate as there is excess of information in form of q which is unlike GMAT style.


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
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Re: If the average (arithmetic mean) of six consecutive odd [#permalink]

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New post 15 Feb 2017, 10:17
GMATPrepNow wrote:
GMATinsight wrote:
For any six consecutive even/odd integers, the difference between the highest and smallest will always remain 10. Hence, I don't find this question too appropriate as there is excess of information in form of q which is unlike GMAT style.


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. :)
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If the average (arithmetic mean) of six consecutive odd [#permalink]

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GMATPrepNow wrote:
If the average (arithmetic mean) of six consecutive odd integers is 4q + 2, what is the difference between the greatest and least of the six integers?

A. 6q + 4
B. 10q
C. 6q/(q – 6)
D. 6
E. 10


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
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Re: If the average (arithmetic mean) of six consecutive odd [#permalink]

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New post 22 Mar 2017, 00:36
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
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Re: If the average (arithmetic mean) of six consecutive odd [#permalink]

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New post 08 Aug 2017, 02:53
N
N+2
N+4
N+6
N+8
N+10


Hence the difference will always be 10...


Hence E.
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Re: If the average (arithmetic mean) of six consecutive odd   [#permalink] 08 Aug 2017, 02:53
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