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

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.
_________________

I'm going to go with .

He spent 1/2 of his earnings and he saved 1/3 of the remaining 1/2 --> \(1/6E = 600\)

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.