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30 Jul 2012, 02:23
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:51) correct 15% (01:00) wrong based on 1522 sessions

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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. Practice Questions Question: 10 Page: 275 Difficulty: 650 _________________ Math Expert Joined: 02 Sep 2009 Posts: 47946 Re: If Pat saved$600 of his earnings last month, how much did  [#permalink]

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30 Jul 2012, 02:23
3
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. _________________ Manager Joined: 28 Sep 2011 Posts: 64 Location: United States GMAT 1: 520 Q34 V27 GMAT 3: 690 Q47 V38 GPA: 3.01 WE: Information Technology (Commercial Banking) Re: If Pat saved$600 of his earnings last month, how much did  [#permalink]

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30 Jul 2012, 20:41
I'm going to go with .

He spent 1/2 of his earnings and he saved 1/3 of the remaining 1/2 --> $$1/6E = 600$$
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03 Aug 2012, 06:24
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. Answer: A. _________________ Manager Joined: 14 Dec 2011 Posts: 75 Re: If Pat saved$600 of his earnings last month, how much did  [#permalink]

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05 Oct 2012, 04:20
1
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 Math Expert Joined: 02 Sep 2009 Posts: 47946 Re: If Pat saved$600 of his earnings last month, how much did  [#permalink]

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05 Oct 2012, 04:30
1
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. _________________ Manager Joined: 14 Dec 2011 Posts: 75 Re: If Pat saved$600 of his earnings last month, how much did  [#permalink]

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05 Oct 2012, 04:49
Bunuel wrote:

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

Regards
Vinni
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05 Oct 2012, 06:24
1
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.

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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30 Oct 2013, 19:59
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? Math Expert Joined: 02 Sep 2009 Posts: 47946 Re: If Pat saved$600 of his earnings last month, how much did  [#permalink]

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31 Oct 2013, 01:34
1
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. 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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18 May 2014, 10:54
(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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25 Jul 2015, 12:57
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, 12:17
1
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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Re: If Pat saved $600 of his earnings last month, how much did [#permalink] ### Show Tags 18 Jul 2017, 03:37 Difficulty would not be 650 I presume. Re: If Pat saved$600 of his earnings last month, how much did &nbs [#permalink] 18 Jul 2017, 03:37

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