10RS Math ? help

Discus: SAT/ACT Tests and Test Preparation: March 2004 Archive: 10RS Math ? help
 By Eagles122 (Eagles122) on Monday, March 22, 2004 - 04:04 pm: Edit

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?

ALSO
#15 in the Quantitative Comparision of the Saturday, May 1997 in the 3rd edition of 10 real sats. thanks.

 By Kewlkiwi102 (Kewlkiwi102) on Monday, March 22, 2004 - 04:16 pm: Edit

For the p/n question:
This one isnt really very hard, you just have to know how to deal with average questions (try using Grubers math review). Here goes:

Avg for class one. x is total of all the scores, p is students, 70 is the average.
x/p=70
x=70p

Avg for class two. y is total of all the scores, n is number of students, 92 is the average.
y/n=92
y=92n

The average for both classes. (x+y) is the total points earned by all the people. (n+p) is the total number of students.
(x+y)/(n+p)=86

Sub in 70p for x, and 92n for y
(70p+92n)/(n+p)=86

Cross multiply:
70p+92n=86n+86p

Subtract and divide and mess around with the above equation to get:
6n=16p
p/n=6/16=3/8

Long explanation for an easy concept!
(I hope i didnt make any typos!)
~Kiwi

 By Nwx (Nwx) on Monday, March 22, 2004 - 04:32 pm: Edit

Because the area of a triangle, regardless which base or which altitude is used, is 1/2bh, b and h have an inverse relationship. Since 1/2(AC)(BD) is the area and 1/2(AB)(EC) is the area as well, the two expressions are equal. Because, AC is larger than AB, BD would have to be smaller than EC. So, EC is greater and B is the answer.

 By Romastaflex (Romastaflex) on Monday, March 22, 2004 - 05:07 pm: Edit

yo kiwi...i got everythin til the last step. how did u get 3/8 from 6n=16p for p/n??

 By Eagles122 (Eagles122) on Monday, March 22, 2004 - 05:28 pm: Edit

awesome... i get it.
thanks.

 By Romastaflex (Romastaflex) on Monday, March 22, 2004 - 08:04 pm: Edit

nvm i get it now..i didnt see that for some reason. thnks newayz

 By Whtx (Whtx) on Monday, March 22, 2004 - 08:22 pm: Edit

Nwx, where did it say that the triangles are equal? That what i dont get

 By Nwx (Nwx) on Monday, March 22, 2004 - 09:39 pm: Edit

There is only one triangle, not two. The two lines are two altitudes of the same triangle. BD can be thought of as the height if you were to use base AC to calculate the area. CE is then the height if you were to use base AB to calculate that same area. But, since the area is the same either way, if AC is bigger, BD would have to be smaller to compensate. Therefore, CE is the larger segment.