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.



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