If Pat saved $600 of his earnings last month, how much did

The question asks us to find the Pat's earnings. Let us assume the Variable E for his earnings.

Statement (1): From the Information given we can set up the equation: (1/3) (E*(1/2))= 600. E can be calculated (E= 3600). -> SUFFICIENT

Statement (2): This statement only tells us that the amount of tax he payed was twice the amount of money he saved. This information does not help us calculate Pat's earnings.-> NOT SUFFICIENT

Ans(A).

SOLUTION

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

Let E be Pat's earnings last month.

(1) Pat spent 1/2 of his earnings last month for living expenses and saved 1/3 of the remainder. Pat spent \(\frac{E}{2}\), so \(E-\frac{E}{2}=\frac{E}{2}\) remained. We are told that 1/3 of that amount, or \(\frac{E}{6}\), was saved. Since we know that Pat saved $600 of his earnings last month, then we have that \(\frac{E}{6}=600\) --> \(E=3,600\). Sufficient.

(2) Of his earnings last month, Pat paid twice as much in taxes as he saved. Since Pat saved $600 of his earnings last month, then he paid 2*$600=$1,200 in taxes. But this info is not sufficient to determine Pat's earnings last month.

Answer: A.

Hi Bunuel,

I was just researching on this question and got your explanation. I got why (A) is correct. But I didn't understand B. I thought (B) was also the correct answer, so eventually i selected D, which was incorrect.

So, here's my reasoning for (B). I want to know where i am going wrong.

Pat saved $600, and paid $1200 for taxes. If Earnings= Taxes + Savings, then Earnings= $1800.

Were there any expenses that i could have assumed in (B) ? Because in (A), the explanation says there were expenses, so (A) is clear.

Thanks & Regards
Vinni

(2) is not sufficient because we don't know how much of his earnings last month Pat spent for living expenses.

Thanks Bunuel. Got your point

Regards
Vinni

Bunuel, I got your point. But one more question. As it is a DS question, we are not given anything about expenses in B. So, why there is a need to assume living expenses.

Looking forward to your reply.

Regards
Vinni

It's the other way around: if you are saying that (2) is sufficient, then you are assuming that there are no living expenses at all. Plus, assuming that is against common sense and the first statement.

Hmm. okay. I got your point.
Thanks
Vinni

Why are we assuming that their are no other expenses per month than living expenses?

I got E simple because i told myself the following:
Expenses (per month) = Living Expenses + Utility + mortgage + Car Lease...etc
1) only gave us the living expenses (i.e.: food and beverages???)

Am I over assuming things?

We are not assuming that. Stem says that Pat saved $600. Next, (1) says that Pat spent half of his earnings on something and saved 1/3 of the remainder (so Pat saved 1/3 of the remaining half of his earnings). This implies that 1/3*(earnings/2)=600 --> earnings=3,600.

Hope it's clear.

Thank you B, just another simple question that i over analyzed

(1) Savings = 1/3*(1-1/2)*Earnings = 600: Sufficient -> We can solve for earnings

(2) Taxes = 2*Savings = 2*600 = 1200. We are not told how taxes or savings relate to earnings: Insufficient -> There's no way to solve for earnings without a relationship.

Hence A.

very easy one
1/3 of 1/2 = 1/6x = 600
x = 3600 A is sufficient
B only tells that taxes = 1200 but gives no clue about earnings
so A it is

I am sorry to "reactivate" this old post, but I believe I am assuming things and I really shouldn't be:

On Statement 2:
I assumed that Taxes (T) were his total expenses, so out of his Earnings (E), he would have Saved (S) $ 600. Since the T = 2S = 2.$600 = $ 1,200, with that in mind E - T = S, then E = S + T, then E = $600 + $ 1,200 = $ 1,800.

I believe I should NOT assume that Taxes are his total Expenses on Statement 2 since, it does not mention that ?

Yes, exactly . Statement 2 does not provide you any information about living exp or any other expenses apart from the taxes. Statement 1 is straightforward as we dont have to worry about the actual division of his "expenditures".

Earning = Savings + Expenses

Read Bunuel's replies above: if-pat-saved-600-of-his-earnings-last-month-how-much-did-136568.html#p1128207

if-pat-saved-600-of-his-earnings-last-month-how-much-did-136568.html#p1128252

if-pat-saved-600-of-his-earnings-last-month-how-much-did-136568.html#p1286244

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.

Answer: A

Difficulty would not be 650 I presume.