In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received.
(A) 0.06N + 3,200
(B) 0.1N + 7,200
(C) 0.4N + 7,200
(D) 0.1N + 8,000
(E) 0.06N + 8,000
Technically, this is a VIC (variables in choices), but back-solving isn’t going to work well here – the many specific numbers floating around means that we would spend precious time picking numbers that follow the constraints of the problem. We’re going to have to get our hands dirty.
The test writers use a typical misdirection here. We know that Ms. Robbins got 8,000 independent votes, and 10 percent of registered voters, but we don’t know anything about to total number of registered voters. What they tell us is the percent of total voters that are independent. It’s implied in the problem that you’re either independent or registered – there’s nothing in between (don’t let your real world knowledge interfere with GMAT world). So, if 40 percent are independent, then 60 percent are registered. That means that, in addition to the 8,000 independent votes, Ms. Robbins received 10 percent of 60 percent of the total number of votes cast:
\(8,000 + (0.1)(0.6)N = 8.000 + 0.06N\)
The correct answer is E.