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GMAT Prep- Faster Way for average?

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GMAT Prep- Faster Way for average?

by nsuen » Sun Jun 12, 2016 11:06 pm
Hi-

What is the average ( arithmetic mean) of eleven consecutive integers?
1) The average of the first nine integers is 7
2) The average of the last nine integers is 9

With statement 1, the sum is 63, so I think there is a way for 9 consecutive integers to be = to 63, but I dont know will there be more than 1 way, ends up 3+4+5+6+7+8+9+10+11 will get me that, then I know the average as I know what are the two remaining number. For statement 2, the sum is 81, so there is a way to have the consecutive integers to be 81, but same as statement 1, I dont know if there is only one way to do so. Then, I ran out of time so I had to make a guess. The answer is D each statement alone is sufficient.

Is there a faster way to do this? Thanks in advance.
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by GMATGuruNY » Mon Jun 13, 2016 1:59 am
nsuen wrote:What is the average ( arithmetic mean) of eleven consecutive integers?
1) The average of the first nine integers is 7
2) The average of the last nine integers is 9
For any EVENLY SPACED SET:
average = median.

Statement 1:
Thus, average = median = 7, implying that the first 9 integers are 3, 4, 5, 6, 7, 8, 9, 10, 11 and that all 11 integers are 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Thus, for all 11 integers, median = average = 8.
SUFFICIENT.

Statement 2:
Thus, average = median = 9, implying that the last 9 integers are 5, 6, 7, 8, 9, 10, 11, 12, 13 and that all 11 integers are 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Thus, for all 11 integers, median = average = 8.
SUFFICIENT.

The correct answer is D.
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by [email protected] » Mon Jun 13, 2016 8:51 am
Hi nsuen,

When you look at this question, if you find yourself unsure of where to "start", it might help to break down everything that you know into small pieces:

1st: We're told that we have 11 consecutive integers. That means the 11 numbers are whole numbers that are in a row. If we can figure out ANY of the numbers AND it's place "in line", then we can figure out ALL of the other numbers and answer the question that's asked (the average of all 11 = ?)

2nd: Fact 1 tells us that the average of the FIRST 9 integers is 7. For just a moment, ignore the fact that there are 9 consecutive integers and let's just focus on the average = 7.

What would have to happen for a group of consecutive integers to have an average of 7?

Here are some examples:

7

6, 7, 8

5, 6, 7, 8, 9

Notice how there are the SAME number of terms below 7 as above 7. THAT'S a pattern.

With 9 total terms, that means there has to be 4 above and 4 below:

3, 4, 5, 6,.......7.......8, 9, 10, 11

Now we have enough information to figure out the other 2 terms (12 and 13) and answer the question. So Fact 1 is SUFFICIENT

With this same approach, we can deal with Fact 2.

The key to tackling most GMAT questions is to be comfortable breaking the prompt into logical pieces. Don't try to do every step at once and don't try to do work in your head. Think about what the information means, take the proper notes and be prepared to "play around" with a question if you're immediately certain about how to handle it.

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