Data sufficiency

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Data sufficiency

by Newaz111 » Sun May 03, 2015 11:31 am
Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes?

(1)Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33 percent of the amount that he spent on his mortgage payments.
(2)Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount that he spent on his mortgage payments and home insurance.

Thank you..
:)

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by [email protected] » Sun May 03, 2015 12:17 pm
Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes?
Let's do some algebra. If we call mortgage payments "m," real estate taxes, "r," and home insurance "h," then we know that m + r + h = 12,000. And we want to know if we have enough info to find r.
(1)Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33 percent of the amount that he spent on his mortgage payments.
This tell us that r + h = .33m; now we could substitute .33m in place of r + h in our original equation to get: m + .33m = 12,000. This will allow us to solve for m. m + (1/3)m = 12,000; (4/3)m = 12,000; m = 9000. We'd also know that r + h would be 3000. But there's no way to know what r is. Could be the case that r = 1000 and h = 2000 or vice versa, etc. So Not Sufficient.
(2)Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount that he spent on his mortgage payments and home insurance.
This tell us that r = .20( m + h). We can rewrite this as r = (1/5)(m + h) or 5r = (m + h). Now we can substitute 5r in place of (m + h) in the original equation to get r + 5r = 12000. Clearly we can solve for r. (6r = 12,000; r = 2000.) Once we see that we have one linear equation and one variable, we know we can find a unique value for that variable, so we have Sufficiency.

Answer is B
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by [email protected] » Sun May 03, 2015 9:55 pm
Summing it up algebraically,

m = mortgage payments
r = real estate taxes
h = home insurance

From the prompt, we have m + r + h = 12,000.

S1 tells us that (r + h) ≈ (1/3)m.

Since we have m + (r + h) = 12,000, we can replace (r + h) with (1/3)m and get m + (1/3)m = 12,000. This gives us m, but not r or h individually; NOT SUFFICIENT.

S2 tells us that r = .2(m + h), or 5r = (m + h)

Substituting 5r for (m + h) in our first equation, we have r + 5r = 12,000, or r = 2000. SUFFICIENT!

The nice thing about this one is that once you see how S1 works, you know S2 will be sufficient, since it isolates r in the same way that S1 isolated m.

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by [email protected] » Mon May 04, 2015 11:48 am
Hi Newas111,

This question is a measure of your Algebra skills and whether you recognize when you have enough "comparison" information to answer a given question or not.

We're told that $12,000 was spent (in total) on mortgage payments, real estate taxes and home insurance. We're asked for the total spent on real estate taxes.

First, let's set up an equation:

M = money spent on mortgage payments
R = money spent on real estate taxes
H = money spent on home insurance

M + R + H = 12,000 We are asked for the value of R.

Fact 1: The amounts spend on real estate and home insurance are 33% of what was spent on mortgage payments.

From this information, we can create 1 equation:

R + H = .33(M)

From this, we can solve for M by substituting in the value of (R+H)....

M + (.33M) = 12,0000
1.33M = 12,000

HOWEVER, we CANNOT get the value of R from this.
Fact 1 is INSUFFICIENT

Fact 2: The amount spent on real estate is 20% of the total spent on mortgage payments and home insurance.

Here, we can also create 1 equation:

R = .2(M + H)
5R = (M+H)

We can now substitute in the value of (M+H)

R + 5R = 12,000
6R = 12,0000
R = 2,000, so we have answered the question.
Fact 2 is SUFFICIENT.

Final Answer: B

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Re: Data sufficiency

by [email protected] » Thu May 20, 2021 6:55 am
Newaz111 wrote:
Sun May 03, 2015 11:31 am
Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes?

(1)Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33 percent of the amount that he spent on his mortgage payments.
(2)Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount that he spent on his mortgage payments and home insurance.

Thank you..
:)
Solution:

Question Stem Analysis:


We can let r, m, and h be the amounts that Arturo spent on his real estate taxes, his mortgage payments, and his home insurance, respectively.

Thus, we know that r + m + h = 12,000. We want to find the value of r.

Statement One Alone:

From statement one, we know that r + h = (1/3)m. Thus, we know that:

r + m + h = 12,000

(1/3)m + m = 12,000

(4/3)m = 12,000

m = 9,000

We know that m = 9,000. However, we still don’t know the value of r. Statement one is not sufficient.

Statement Two Alone:

Statement two tells us that r = 0.2(m + h) = (m + h)/5. Solving for m + h, we obtain m + h = 5r. Substituting for m + h into the original equation, we have:

r + m + h = 12,000

r + 5r = 12,000

6r = 12,000

r = 2,000

We see that r = $2,000. Statement two alone is sufficient.

Answer: B

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Re: Data sufficiency

by Ian Stewart » Sat Jun 05, 2021 9:21 am
Statement 1 says the ratio of his tax and insurance expense to his mortgage payments was 1 to 3. So 3/4 of Arturo's total costs went to mortgage payments, and the remaining 1/4 is divided, in some unknown way, between taxes and insurance, and Statement 1 is not sufficient.

Statement 2 says the ratio of his tax expense to his insurance and mortgage expense was 1 to 5. So 1/6 of his total expense went to tax, and he spent (1/6)($12,000) = $2000 on tax, so the answer is B.
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