# If Pat saved \$600 of his earnings…

## Solution:

We are given that Pat saved \$600 worth of his earnings, and we need to determine how much he earned last month.

Statement One Alone:

Pat spent 1/2 of his earnings last month for living expenses and saved 1/3 of the remainder.

From the information in statement one, we can set up some variables and equations.

We are given that Pat spent ½ of his earnings last month for living expenses. So if we let L = living expenses, and E = total money earned last month, we can say:

½(E) = L

We are also given that Pat saved 1/3 of the remainder. Since we see that ½(E) went towards the living expenses, the remainder of that is E – ½(E) = ½(E). Remember, too, that we were initially told that Pat saved \$600. Thus, we can say:

1/3[1/2(E)] = 600

1/6(E) = 600

E = 3,600

We see that Pat earned \$3,600. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Of his earnings last month, Pat paid twice as much in taxes as he saved.

From statement two we can set up an equation in which T = taxes paid by Pat last month.

T = 2(600)

T = 1,200

Although we know how much Pat paid in taxes last month, we do not know how much Pat earned. Statement two is not sufficient to answer the question.