Problem Solving

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

Source: GMAT Prep Now
Difficulty level: 500-600

Answer: E

Brent@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

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 ANY 6 odd integers will ALWAYS be 10, so the correct answer is E


That said, we can also use the information about q 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

Matt@VeritasPrep wrote: Take the set {1, 3, 5, 7, 9, 11}, then the set {5, 7, 9, 11, 13, 15}. In each case the range is 10, so you're ... set! (I really need to retire this pun.)

I don't think you should retire that pun; it has many humorous elements ......