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Re: What is the average (arithmetic mean ) of eleven consecutive [#permalink]

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12 Aug 2013, 04:39

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zz0vlb wrote:

What is the average (arithmetic mean ) of eleven consecutive integers?

(1) The avg of first nine integers is 7 (2) The avg of the last nine integers is 9

Here is a neat little trick for such kind of problems:

Will be better illustrated using a numerical example: take the set {2,3,4,5,6}. Here the common difference (d)=1. The initial average = 4. Now, the averge of the set, after removing the last integer of the set(i.e. 6)will be reduced by exactly \(\frac{d}{2} units \to\) The new Average = \(4-\frac{1}{2} = 3.5\)

Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.

Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.

Back to the problem:

From F.S 1, we know that the average of the first 9 integers is 7. Thus, the average with the original 11 integers must have been 7+0.5+0.5 = 8. Sufficient.

From F.S 2, we know that the average of the last 9 integers is 9, thus the average with the initial 11 integers must have been 9-0.5-0.5 = 8. Sufficient.

Re: What is the average (arithmetic mean ) of eleven consecutive [#permalink]

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12 Aug 2013, 23:15

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zz0vlb wrote:

What is the average (arithmetic mean ) of eleven consecutive integers?

(1) The avg of first nine integers is 7 (2) The avg of the last nine integers is 9

As a general rule whenever there is a AP the average of the series is always the median of the series. Here it is a AP with difference 1

1. First 9 integers average is 7 . So the median that is the 5th digit is 7. Hence we can easily find the series and the average of the 11 consecutive digit series. Sufficient 2. Average of last 9 integers is 9 hence we know that for this subset of 9 integers the 5th integer would be 9 and we can find the series on the basis of this and the average. Sufficient

Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

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28 Aug 2014, 09:43

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Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

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09 Mar 2015, 19:15

I considered following approach

if the smallest number in set is x , then sum of 11 consecutive numbers = 11x+(1+2+...10)=11x+55--->A if largest number in set is x ,then sum of 11 consecutive numbers=11x-(1+2+10)=11x-55

Now as per statement 1 , average of first 9 numbers is 7 i.e sum =63 sum of 11 numbers =63+x+9+x+10----->B

Equating A& B 11X+55=63+X+9+10 ,which can be solved to get x=3

statement I is sufficient similar approach for Statement II 11X-55=8+2X-19 ,can be solved to get X=13

Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

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09 Mar 2015, 19:26

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Hi All,

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.

Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

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10 Mar 2016, 03:12

Hello from the GMAT Club BumpBot!

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