SAT Math VI

The average of the last six numbers is 4 because 24/6=4. So, the total average is the average of the average of the first and the average of the last six numbers. So, it's (15+4)/2= 19/2=9.5

Use an average every time the question uses the word average . An average pie looks like this:

A circle that is divided into three sections:

1. A semicircle top representing the Total.
2. A half-semicircle bottom-left representing the #of things.
3. A half-semicircle bottom-right representing the Average.

In this case we end up with the following average pies that use the information in the question (1,2,3 - as in above) (draw them so you can see them):

First Six: (90,6,15)

+

Last Six: (24,6,4)

=

(114,12,95)

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We need an average pie for the first six numbers: the six numbers' average is 15, so the total of those six numbers is $15\times 6=90$ The last six have an average of $4$ , so the total of those six numbers is $4 \times 6\ =24$ . Now take the two totals and add them together for the final mention of the word average . The total for all 12 numbers is 114, so to find the average, divide 114 by 12, which gives $\boxed{9.5}$ .

(You could also reduce the fraction $\frac{114}{12}$ , since the numberator and denominator are both divisible by 6, to $\frac{19}{2}=\boxed{9.5}$