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

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If Pat saved $600 of his earnings last month, how much did [#permalink] New post 30 Jul 2012, 01:23
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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] New post 30 Jul 2012, 01:23
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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.
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 30 Jul 2012, 19:41
I'm going to go with
[Reveal] Spoiler:
A
.

He spent 1/2 of his earnings and he saved 1/3 of the remaining 1/2 --> \(1/6E = 600\)
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 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] New post 03 Aug 2012, 05:24
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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.
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 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] New post 05 Oct 2012, 03:30
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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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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 05 Oct 2012, 03:49
Bunuel wrote:

(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

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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 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.

Looking forward to your reply.

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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 05 Oct 2012, 05:24
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vinnik wrote:
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.
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 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] New post 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.

Answer: A.



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] New post 31 Oct 2013, 00:34
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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.

Answer: A.


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.
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 31 Oct 2013, 09:30
Thank you B, just another simple question that i over analyzed
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 18 May 2014, 09:54
(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.
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 03 Jun 2015, 01:46
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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] New post 03 Jun 2015, 02:25
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
Re: If Pat saved $600 of his earnings last month, how much did   [#permalink] 03 Jun 2015, 02:25
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