Hard Statistics Problem with Solution

Today I would like to give a solution to yesterday’s statistics problem. Before reading the solution, you may want to review the following article: Changing Averages to Sums

Here is the problem once again, followed by a solution.

Level 5 Statistics

Suppose that the average (arithmetic mean) of a, b, and c is h, the average of b, c, and d is j, the average of c, d, and e is k, and the average of d, e, and f is m. What is the value of (a + c) – (d + f ) ?

A) h – j + k – m
B) 3(h – j + k – m)
C) 3/4 (h – j + k – m)
D) 3(h + j + k + m)
E) 3/4 (h + j + k + m)

Solution by changing averages to sums:  We have

a + b + c = 3h

b + c + d = 3j

c + d + e = 3k

d + e + f = 3m

We subtract the second equation from the first equation to get

a – d = 3h – 3j

We subtract the fourth equation from the third equation to get

c – f = 3k – 3m

We now add these last two equations to get

a – d + c – f = 3h – 3j + 3k – 3m

This is equivalent to choice B.

More SAT and ACT Math Problems with Explanations

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