Question

Last year, if Arturo spent a total of 12,000$onhismortgagepayments,realestatetaxes,andhomeinsurance,howmuchdidhespendonhisrealestatetaxes?\left(1\right)Lastyear,thetotalamountthatArturospentonhisrealestatetaxesandhomeinsurancewas$33\frac{1}{3}$ 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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Let M, R, and H be the amounts that Arturo spent last year on mortgage payments, real estate taxes, and home insurance, respectively. Given that, M + R + H = 12000, determine the value of R.

1. Given that and M + R + H = 12000, then M = 9000. However, the value of R cannot be determined, since it is possible that R = 2000 (when M = 9000 and H = 1000) and it is possible that R = 1000 (when M = 9000 and H = 2000). Thus, not sufficient.
2. Given that , or 5R = M + H and M + R + H = 12000 which can be rewritten as (M + H) + R = 12000 , then 5R + R = 12000, or R = 2000; SUFFICIENT.

• The correct answer is B; statement 2 alone is sufficient