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If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 30 Jul 2012, 01:23 Expert's post 4 This post was BOOKMARKED 00:00 Difficulty: 5% (low) Question Stats: 83% (01:48) correct 17% (01:01) wrong based on 988 sessions ### HideShow timer Statistics 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.

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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 30 Jul 2012, 01:23 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.

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31 Jul 2012, 01:32
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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).
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 03 Aug 2012, 05:24 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.

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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 05 Oct 2012, 03:20 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.

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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 05 Oct 2012, 03:30 1 This post received KUDOS Expert's post vinnik wrote: 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.
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05 Oct 2012, 05:21
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.

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05 Oct 2012, 05:47
Bunuel wrote:
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.
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 30 Oct 2013, 18:59 Bunuel wrote: 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.

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?
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 31 Oct 2013, 00:34 1 This post received KUDOS Expert's post PatrickS wrote: Bunuel wrote: 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.

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. _________________ Intern Joined: 15 Mar 2013 Posts: 23 Location: Canada Concentration: International Business, Finance WE: Information Technology (Consulting) Followers: 0 Kudos [?]: 22 [0], given: 6 Re: If Pat saved$600 of his earnings last month, how much did [#permalink]

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31 Oct 2013, 09:30
Thank you B, just another simple question that i over analyzed
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25 Jul 2015, 11:57
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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 ?
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22 Jul 2016, 11:17
Bunuel 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.

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.

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