If Pat saved $600 of his earnings…
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.