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PS: Pat and savings

by ikaplan » Tue Nov 22, 2011 11:51 am

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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.

Source: OG12

OA is A

I know that this is quite easy DS questions, but Statement (2) boggles my mind.
Pat saved $600, and paid $1200 for taxes. If Earnings= Taxes + Savings, then Earnings= $1800

My question is: Why B is incorrect? How do we know that Pat did not spend money on something else apart from taxes? Do we have to look at the information in Statement (1) to realize that the equation consists of living expenses as well? (I know that this is against the main DS rule- "avoid using information from one statement when considering another", but sometimes looking at the other statement helps).
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by user123321 » Tue Nov 22, 2011 2:16 pm

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IMO A

using A you can get A's earnings.
using B not much info is present to get his earnings.

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by ollapodrida » Tue Nov 22, 2011 8:09 pm

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ikaplan 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.

Source: OG12

OA is A

I know that this is quite easy DS questions, but Statement (2) boggles my mind.
Pat saved $600, and paid $1200 for taxes. If Earnings= Taxes + Savings, then Earnings= $1800

My question is: Why B is incorrect? How do we know that Pat did not spend money on something else apart from taxes? Do we have to look at the information in Statement (1) to realize that the equation consists of living expenses as well? (I know that this is against the main DS rule- "avoid using information from one statement when considering another", but sometimes looking at the other statement helps).
(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.

Earnings does not necessarily have to equal taxes + savings, so you cannot apply that formula here.
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by [email protected] » Mon Apr 02, 2018 3:56 pm

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Hi All,

We're told that Pat SAVED $600 of his earnings last month. We're asked how much Pat EARNED last month.

1) Pat spent 1/2 of his earnings last month for living expenses and saved 1/3 of the remainder.

Since we already know that Pat SAVED $600 last month, we can 'work backwards' based on the information in Fact 1 to determine how much Pat earned:

If 1/3 of X = $600, then X = ($600)(3) = $1800, so $1800 was what Pat had AFTER living expenses....
1/2 of Y = $1800, so Y = ($1800)(2) = $3600, so Pat EARNED $3600 last month.

Working forward, you can double-check this result if you like - and you'll see that it 'fits' all of the information that we've been given and answers the question.
Fact 1 is SUFFICIENT

2) Of his earnings last month, Pat paid twice as much in taxes as he saved.

The information in Fact 2 doesn't 'interact' with the $600 that we know that Pat saved, so there's no way to answer the question with this new information.
Fact 2 is INSUFFICIENT

Final Answer: A

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by Scott@TargetTestPrep » Sun Jul 22, 2018 5:10 pm

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ikaplan 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.

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.

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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