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Last year, if Arturo spent a total of $12,000 on his mortgage payments [#permalink]

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23 Mar 2011, 07:24

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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 1/3 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 he spent on his mortgage payments and home insurance.

Re: Last year, if Arturo spent a total of $12,000 on his mortgage payments [#permalink]

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23 Mar 2011, 07:39

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gtr022001 wrote:

88. 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 he spent on mortgage payments and home insurance.

i'll add OA later

Let we denote the spending by M,R and I

M+R+I=12000

R=?

1. R+I=0.33M R= 0.33M-I M+R+I=12000 We just have two equations and 3 variables. Also, we can't get rid of any variable from the given conditions. Not Sufficient.

Re: Last year, if Arturo spent a total of $12,000 on his mortgage payments [#permalink]

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08 Nov 2011, 12:59

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given : r+m+h = 12,000 What is r? (1) \(r+h = 1/3 m\) substituting in the given equation gives: m + m/3 = 12000. We can only solve for m but can go no further. Insufficient (2) \(r= 20/100 (m+h)\) 5r = m+h. substituting in the given equation 5r + r = 12000 r = 2000. Sufficient.

Re: Last year, if Arturo spent a total of $12,000 on his mortgage payments [#permalink]

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05 Dec 2011, 22:16

T+M+I=12K

Statement 2: T= .2(M+I)= .2(12k-T) can be solved for T. sufficient. Statement 1: T+I=.33M using stem, we can solve for M, but we still have 2 variable to solve. Not Sufficient.

Re: Last year, if Arturo spent a total of $12,000 on his mortgage payments [#permalink]

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01 Mar 2015, 12:33

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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.

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 1/3 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 he spent on his mortgage payments and home insurance.

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 M, R, and H be the amounts that Arturo spent on mortgage payments, real estate taxes, and home insurance, respectively.

Given: M + R + H = 12,000. Question: R??

(1) Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33 1/3 percent of the amount that he spent on his mortgage payments --> 33 1/3 percent is 1/3 rd, thus given that R + H = M/3 --> M + R + H = M + M/3 = 12,000 --> M = 9,000 --> R + H = 12,000 - 9,000 = 3,000. R can take more than one value. Not sufficient.

(2) Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount he spent on his mortgage payments and home insurance --> given that R = (M + H)/5 --> 5R = M + H --> M + R + H = 5R + R = 12,000 --> 6R = 12,000 --> R = 2,000. Sufficient.

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