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Last year if Arturo spent a total of $12,000 on his mortgage

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

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New post 07 Dec 2012, 06:54
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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.
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Re: Last year if Arturo spent a total of $12,000 on his mortgage  [#permalink]

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New post 07 Dec 2012, 07:00
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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?

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.

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

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New post 26 May 2014, 18:43
Walkabout wrote:
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.


Problem: Tax+Morg+Ins=T+M+I=12 000

(1) T+I=331/3% x (12 000 -T -I) -------- (M=12 000 - T - I) Not sufficient.

(2) T=0.2 x (12 000 - T) --------------------(M+I=12 000 - T) Sufficient.

T+0.2T=2 400
T=2 400/1.2=2 000
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Re: Last year if Arturo spent a total of $12,000 on his mortgage  [#permalink]

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New post 28 May 2014, 11:48
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Quick version:

1) This statement lumps together T and I, so we'll never find T. Insufficient.

2) This relates T to the rest. T = .20(M+I). The ratio of T to other is 1 to 5, so the ratio of T to total is 1 to 6. We can now solve (1/6 of $12,000 is $2,000), but as soon as we see that we know the relation of T to the other parts (when we already know the total), we can stop. Sufficient.
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Last year if Arturo spent a total of $12,000 on his mortgage  [#permalink]

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New post 22 Aug 2018, 08:03
Bunuel wrote:
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.



Answer: B.


when it says "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 "

I expressd the red part like this (R+H)0.30 = M why this equality didn't work ? :?


Same question applies for second statement "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 "

i expressed the red part of sentance like this (M+H)0.20= R

here again it didnt work my equality :? why ?


what is the difference the way bunuel expressed R + H = M/3, R = (M + H)/5 and my equalities (R+H)0.30 = M , (M+H)0.20= R :? :)
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Last year if Arturo spent a total of $12,000 on his mortgage  [#permalink]

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New post 22 Aug 2018, 10:02
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dave13 wrote:
Bunuel wrote:
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.



Answer: B.


when it says "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 "

I expressd the red part like this (R+H)0.30 = M why this equality didn't work ? :?


Same question applies for second statement "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 "

i expressed the red part of sentance like this (M+H)0.20= R

here again it didnt work my equality :? why ?


what is the difference the way bunuel expressed R + H = M/3, R = (M + H)/5 and my equalities (R+H)0.30 = M , (M+H)0.20= R :? :)



1st statement: R+H = \(\frac{33+\frac{1}{3}}{100}* M = \frac{1}{3} * M\) --> (R+H)*3 = M --> this is 3, not 0.3

2nd statement: \(R=\frac{20}{100}*(M+H)=\frac{1}{5}*(M+H)=0.2*(M+H)\) --> Legend Bunuel 's expression and your expression are the same. You're right in this case.

Hope it's clear.
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