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Source: — Data Sufficiency |
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by muzali » Tue Nov 25, 2008 11:39 am
Let the eleven numbers be x, x+1, x+2,...,x+10

We need to find [x+(x+1)+ (x+2)+...+(x+10)]/11, i.e, if we know x, we can find the mean of these elven numbers.

STM1: Avg of first nine numbers is 7
=> [x+(x+1)+ (x+2)+...+(x+10)]/9 = 7 we can calculate x
(you don't need to do this, but (9x+36)/9=11, so x=3)

STM2: Avg of last nine numbers is 9
In a similar fashion as above, we can calculate x.

So both STMs are sufficient, therefore answer is D.
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by California4jx » Tue Nov 25, 2008 12:05 pm
Thanks !
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by Stuart@KaplanGMAT » Tue Nov 25, 2008 1:01 pm
The above solution is certainly correct, but seems like a lot of work. As experienced GMAT writers, we've all learned to hate extra work! 8)

Instead, let's use our knowledge of consecutive integers to answer the question:

Every set of n consecutive integers will have a unique average. So, if we know the average and the number of terms, we can figure out the exact set.

(1) n = 9, average is 7. Only one set of consecutive integers will fit this rule. We can just add on the next two integers to fill out our set of 11: sufficient.

(Note: if this were a problem solving question and we wanted to figure out the set, we'd see that we have an odd number of terms, which means that the average, 7, is the middle term, so our set must be {3, 4, 5, 6, 7, 8, 9, 10, 11}. Since it's data sufficiency, we couldn't care less what the members of the set are!)

(2) n = 9, average is 9. Only one set of consecutive integers will fit this rule. We can just add on the previous two integers to fill out our set of 11: sufficient.

Each of (1) and (2) are sufficient alone: choose (D).
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by California4jx » Tue Nov 25, 2008 2:46 pm
wonderful ! :)
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by vittalgmat » Tue Nov 25, 2008 3:11 pm
Yep got D here.
Here is my approach.

Stmt 1. Avg of first 9 ints is 7.
ie first int is x and the last int is 8.
We know avg of n consecutive ints = (first# + last#)/2
So here it is x + x+8 = 7 *2.
2x +8 = 14
x = 3
So we know the first element of the sequence. Now we derive the entire sequence and get anything else we want..
So sufficient.

Stmt 2. Similar to above. So sufficient.

So D

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