Thread: SAT practice: fractions of two groups

Problem: on a certain college faculty, (4/7) of the professors are male, and the ratio of the professors older than 50 years to the professors less than or equal to 50 years is 2:5. If (1/5) of the male professors are older than 50 years, what fraction of the female professors are less than or equal to 50 years?

I was able to find (female and less than or equal to 50 yrs) which is (9/35). The official solution involved dividing this fraction by (3/7). I don't quite understand the extra step of dividing 9/35 by 3/7.

Code:

              m                  f                   t
             40                 30                  70

> 50          8                 12                  20
=<50         32                 18                  50

females =<50 = 18 / 30 = 3/5

9/35 / (3/7) = 9/35 * 7/3 = 3/5

The solution is much clearer when the fractions are turned into whole numbers. The fractions way is less intuitive to me.

Originally Posted by Frederick

The solution is much clearer when the fractions are turned into whole numbers. The fractions way is less intuitive to me.

And to me also!
With that type of problem, I always start off by finding integers that "fit" given fractions and ratios.