Hello

While working on some practice PSAT questions, I came across this question:

The various averages (arithmetic means) of three of the four numbers c, d, e, and f are calculated, and are arranged from greatest to least as follows

The average of c, d, and e

The average of d, e, and f

The average of e, f, and c

The average of f, c, and d

Which of the following correctly orders c, d, e, and f from greatest to least?

(A) c > d > f > e

(B) d > f > e > c

(C) d > e > c > f

(D) e > c > f > d

(E) e > d > c > f

My answer was (A), but the correct answer was (E). I do not see how my work was wrong, other than I might have perhaps used the wrong method. I set it up like you do when you solve equations with two variables by subtracting one whole equation from another. Of course, I'm not totally positive if you can do this with inequalities, but I honestly don't see why not. Here's my work for clarity's sake:

c + d + e > d + e + f

-(d+ e + f > f + c + d)

-----------------------

f > e

d + e + f > e + f + c

-(e + f + c > f + c + d)

------------------------

c > e

So, I found that both c and f are greater than e and picked the only choice that had this written, (A).

Anyone want to tell me if I'm doing this wrong, and, if so, how it is actually supposed to be done? Thanks.