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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Gmat Prep question

by gana » Mon Jan 24, 2011 6:02 pm
What is the average (arithmetic mean) of 11 consecutive integers?

1. the average of the first nine integer equals 7
2. the average of the last nune integer equals 9.
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by VivianKerr » Mon Jan 24, 2011 6:25 pm
This is a "value" DS question, so we need to know the exact average in order to have sufficiency.

Average = sum of terms/ # of terms

Avg = (a + b + c + d + e + f + g + h + i + j + k) / 11

We know the 11 numbers are consecutive, so we need to know at least one of the numbers and its placement to find the set.

STATEMENT 1.

7 = (a + b + c + d + e + f + g + h + i) / 9

63 = a + b + c + d + e + f + g + h + i

What 9 consecutive numbers sum to 63?

Let's call the middle number x. We can re-write the sequence as:

63 = (x - 4)+(x - 3)+(x - 2)+(x - 1)+(x)+(x + 1)+(x + 2)+(x + 3)+(x + 4)

63 = 9x

7 = x = middle number of the first 9 terms. We can find the other numbers now since we know they are consecutive integers.

The set is 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

SUFF.

STATEMENT 2.

The same logic applies. We can determine the set. The answer is (D).
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by gana » Mon Jan 24, 2011 7:08 pm
Hi, Thank you for your explanation. But why did you call x as middle number instead of the first number? Any difference?
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by tellsud » Tue Jan 25, 2011 3:44 am
4 5 6 7 8 9 10 [First 7]
_ _ 6 7 8 9 10 11 12 13 14 [Last 9]

so the number's are

4 5 6 7 8 9 10 11 12 13 14

So the Answer is: 9
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by VivianKerr » Wed Jan 26, 2011 10:46 am
@gana, I just called x the middle number to illustrate how a consecutive sequence would look. You could have called any number x.
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