If the average (arithmetic mean) of six consecutive odd

Question

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

Kurtosis · Accepted Answer

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

GMATinsight · Answer

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

BrentGMATPrepNow · Answer

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

GMATinsight · Answer

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.

BrentGMATPrepNow · Answer

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

guialain · Answer

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

stonecold · Answer

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

Hence the difference will always be 10...

Hence E.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the average (arithmetic mean) of six consecutive odd

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the average (arithmetic mean) of six consecutive odd

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards