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# What is the average of eleven consecutive integers? 1. The

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What is the average of eleven consecutive integers? 1. The [#permalink]  25 May 2008, 07:49
What is the average of eleven consecutive integers?
1. The average of first nine integers is 7
2. The averge of the last nine integers is 9
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Re: GMAT Prep maths- Integers again [#permalink]  25 May 2008, 08:16

Q. You have to calculate average of 11 consecutive integers OR (11x + 55)/11, lets say it equation 1. Solution is below.

1. The average of first nine integers is 7....says that:

Take the first number as 'x' so second number will be 'x+1'........similarly u can take all the first 9 numbers in this way....adding 1 to each preceding number. Sum of first 9 numbers will be 9x + 36. And their average will be (9x + 36)/9 = 7. You can solve it for x and put it in the equation 1.

2. The average of the last nine integers is 9.

In this statement take 11x + 55 and subtract first two numbers i.e. (x + x + 1), which is ((11x + 55) - (2x +1)) = 9x + 54.
And we are give than (9x + 54)/9 = 9. Solve for x and put it in equation 1.

So u r getting ur answer from both the statements independently. Therefore answer is D.
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Re: GMAT Prep maths- Integers again [#permalink]  25 May 2008, 08:23
Expert's post
other way:

Average of odd consecutive integers will be equal to middle number (median).
For example, the average of 11 numbers is 6th number, the average of 9 numbers is 5th number in the sequence.

So, both conditions along give us 5th or 7th number in the sequence of 11 consecutive numbers and we can find average=6th number = 5th number + 1 = 7th number - 1.

D
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Re: GMAT Prep maths- Integers again   [#permalink] 25 May 2008, 08:23
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