PS: Pat and savings

Hi All,

We're told that Pat SAVED $600 of his earnings last month. We're asked how much Pat EARNED last month.

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

Since we already know that Pat SAVED $600 last month, we can 'work backwards' based on the information in Fact 1 to determine how much Pat earned:

If 1/3 of X = $600, then X = ($600)(3) = $1800, so $1800 was what Pat had AFTER living expenses....
1/2 of Y = $1800, so Y = ($1800)(2) = $3600, so Pat EARNED $3600 last month.

Working forward, you can double-check this result if you like - and you'll see that it 'fits' all of the information that we've been given and answers the question.
Fact 1 is SUFFICIENT

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

The information in Fact 2 doesn't 'interact' with the $600 that we know that Pat saved, so there's no way to answer the question with this new information.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

ikaplan wrote:If Pat saved $600 of his earnings last month, how much did Pat earn last month?

(1) Pat spent 1/2 of his earnings last month for living expenses and saved 1/3 of the remainder
(2) Of his earnings last month, Pat paid twice as much in taxes as he saved.

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.

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.

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.

Answer: A