## Monday, April 16, 2012

### rock and roll! got last week's MGRE problem correct!

I admit I felt shaky about my solution to last week's MGRE Math Beast Challenge problem, but I turned out to be correct. Here's MGRE's explanation:

Let’s put the words into equation form:

(Total Income – Exclusion)(Tax Rate) = Income Tax.

The question asks about total income, so we’ll solve the equation for Total Income:

Total Income – Exclusion = [Income Tax / Tax Rate]
Total Income = [Income Tax / Tax Rate] + Exclusion

To maximize total income, we’ll minimize Tax Rate (smaller denominator→larger value) and maximize the Exclusion:

Maximum Total Income = [\$8700/0.15] + \$9800 = \$58,000 + \$9,800 = \$67,800.

To minimize total income, we’ll maximize Tax Rate (larger denominator→smaller value) and minimize the Exclusion:

Minimum Total Income = [\$8700/0.35] + \$5200 = \$24,857.14 + \$5,200 = \$30,057.14.

The correct answers are C, D, E, and F.

The letters C, D, E, and F correspond to the values I had selected. MGRE arrived at the exact same range that I had arrived at, too: roughly \$30,057 at the bottom end, and \$67,800 at the top end.

Triomphe!

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