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Average Problem

by CaptainOats » Wed Oct 27, 2010 2:41 am
Hey Guys,

I am faced with the following average question from a testbook...can u help me?

"The average of 11 games is 50. The average of the first 6 is 49, and the last 6 is 52.
->What is the result of the 6th game?"

Cheers
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by kmittal82 » Wed Oct 27, 2010 2:52 am
Let the games be a1,a2....a11

a1 + a2 + a3 + ...... a11
------------------------------ = 50
11

Thus, a1 + a2 + .... .a11 = 550

>The average of the first 6 is 49
Using similar logic, a1 + a2... + a6 = 294

>and the last 6 is 52
a6 + a7 + a8 + a9 + a10 + a11 = 312

Add the above two equations, and you will get (a1 + a2 +.... 2xa6 + a7+ ... a11 ) = 606
We know that a1+a2+a3+a4+.... a11 = 550, so we can deduce that

a6 + 550 = 606 => a6 = 56
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by CaptainOats » Wed Oct 27, 2010 3:00 am
Thanks dude!
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by Abhishek009 » Wed Oct 27, 2010 3:09 am
CaptainOats wrote:Hey Guys,

I am faced with the following average question from a testbook...can u help me?

"The average of 11 games is 50. The average of the first 6 is 49, and the last 6 is 52.
->What is the result of the 6th game?"

Cheers
Since kmittal82 has wonderfully explained the basics let me work out the shortcut which we can adopt easily:

Sum of all the 11 games = 550

Sum of first 6 games = 294

Sum of last 6 games is = 312

Value of the 6th game is the one which is calculated twice ( Value of a6 ) is (312+294) - 550 = 56
Abhishek
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by GMATGuruNY » Wed Oct 27, 2010 3:12 am
CaptainOats wrote:Hey Guys,

I am faced with the following average question from a testbook...can u help me?

"The average of 11 games is 50. The average of the first 6 is 49, and the last 6 is 52.
->What is the result of the 6th game?"

Cheers
Another approach would be to plug in the answer choices, one of which would say that the result of the 6th game was 56.

Sum of all 11 games = (number of games)*(average) = 11*50 = 550.

Sum of first 6 games = (number of games)*(average) = 6*49 = 294
Thus, sum of first 5 games = 294 - 6th game = 294-56 = 238.

Sum of last 6 games = (number of games)*(average) = 6*52 = 312
Thus, sum of last 5 games = 312 - 6th game = 312-56 = 256.

Sum of all 11 games = sum of first 5 games + 6th game + sum of last 5 games = 238 + 56 + 256 = 550. Success!
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