# GMAT OFFICIAL GUIDE DS – Last year, if Arturo spent…

## Solution:

We are given that Arturo spent \$12,000 on his mortgage payments, real estate taxes, and home insurance. We need to determine how much he spent on his real estate taxes. Let’s define some variables.

m = money spent on mortgage payments

t = money spent on real estate taxes

h = money spent on home insurance

Thus, we can create the following equation:

m + t + h = 12,000

t = 12,000 – m –  h

t = 12,000 – (m + h)

If we determine a value for m + h, we can determine a value for t.

Statement One Alone:

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.

Using the information in statement one, we can create the following equation:

t + h = 0.33m

Since t + h = 0.33m, we can substitute 0.33m for t + h in the equation m + t + h = 12,000 to obtain m + 0.33m = 12,000. This enables us to solve for m, but we still do not have enough information to determine the value of t. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

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.

Using the information in statement two, we can create the following equation:

t = 0.2(m + h)

Since t = 0.2(m + h), we can substitute 0.2(m + h) for t in the equation t = 12,000 – (m + h)

0.2(m + h) = 12,000 – (m + h)

0.2m + 0.2h = 12,000 – m – h

1.2m + 1.2h = 12,000

1.2(m + h) = 12,000

m + h = 12,000/1.2

m + h = 10,000

We see that t = 12,000 – 10,000 = 2,000.

Statement two is sufficient to answer the question.