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The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86. What is the value of p/n?

I have never encountered this kind of problem before. How do i solve it?

By Serene (Serene) on Wednesday, August 13, 2003 - 12:01 am: Edit

this question's posted before

70p+92n=86p+86n
6n=16p

By Frugal81 (Frugal81) on Wednesday, August 13, 2003 - 12:06 am: Edit

Huh? can u explain how u arrived at that?

By Serene (Serene) on Wednesday, August 13, 2003 - 12:13 am: Edit

70p = total score of first class
92n = total score of second class
combined score of two classes = 70p+92n
combined number of students = p+n
new avg score = 86
thus combined score of two classes also = (p+n)*86

By Lurker (Lurker) on Wednesday, August 13, 2003 - 12:13 am: Edit

If the average test score for a class of p students is 70, then the sum of all the students' scores in the class is 70 x p (70p).

If the average test score for a class of n students is 92, then the sum of all the students' scores in the class is 92 x n (92n).

The average of these combined scores is the sum of the combined scores divided by the sum of the total number of students.
(70p + 92n) / (n + p) = 86.

Multiply both sides of the equation by (n + p) to get 70p + 92n = 86p + 86n.

Hope this helps.

By Frugal81 (Frugal81) on Wednesday, August 13, 2003 - 12:17 am: Edit

o i see now. where can i get practice for these kind of hard sat math problems?

By Serene (Serene) on Wednesday, August 13, 2003 - 12:29 am: Edit

There are several SAT math threads on this forum...
try
http://www.collegeconfidential.com/discus/messages/69/15818.html

By Aoe2guy (Aoe2guy) on Wednesday, August 13, 2003 - 12:58 pm: Edit

practice? do more real SATs! Frugal this is a perfect problem of where ETS takes a simple concept and checks if you really know what average is. Someone who solves this problem knows that it is referring to the formula for avg, which we all know from school. The way the problem is presented, however, might make an unfamiliar test taker baffled. I'm sure the Barron's Math Workbook or even the Kaplan one might have questions like this in their "average" section of their books- look towards the end. i haven't used these books but i know their format so try that out. personally, i think it's just a matter of applying the general formula here so try to simple things down if this happens again.