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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.
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.
Dmitry Farber | Manhattan GMAT Instructor | New York
Re: Last year if Arturo spent a total of $12,000 on his mortgage [#permalink]
06 Oct 2015, 18:44
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