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In a recent election, Ms. Robinson received 8000 voters cast [#permalink]

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12 Nov 2010, 22:55

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In a recent election, Ms. Robinson received 8000 voters 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 Mrs. Robbins received?

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Last edited by Bunuel on 29 Aug 2012, 04:10, edited 1 time in total.

In a recent election, Ms. Robinson received 8000 voters 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 Mrs. Robbins received? (A) .06N+3200 (B) .1N+7200 (C) .4N+7200 (D) .1N+8000 (E) .06N+8000

40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 10% votes so, 0.1*0.6*N plus 8,000 votes from independents: total=0.1*0.6*N+8,000=0.06*N+8,000.

Wordings is quite poor as the question does not state that Robinson received 100% of the votes cast by independent voters i.e. 0.4N = 8000.
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Solution 2: 8000/0.40 = 20,000 IV = 8000 Not IV = 12000 * 0.10 = 1200 8000 + 1200 = 9200 (total votes Ms. Robbins received)

Checking the answers by plugging in 20000 for N: A - out B - correct C - out D - out E - correct

B or E, from solution 1 I chose B?

Please advise,

Thank you

The highlighted part is not correct. The number of registered voters is not N - 8000, because the number of independent voters is not 8000. 8000 is the number of independent voters received by Ms. Robinson.
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In a recent election, Ms. Robinson received 8000 voters 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 Mrs. Robbins received?

We are given that Ms. Robinson received 8,000 votes cast by independent voters and 10% of the votes cast by voters affiliated with a party.

Since N is the total number of votes and 40% of the votes were cast by independent voters, 60% of the votes were cast by voters affiliated with a party.

Since Ms. Robinson received 10% of the votes cast by voters affiliated with a party, she received (0.1)(0.6)N = 0.06N of the votes by voters who are affiliated with a party. Since she also received 8,000 votes from independent voters, she received 0.06N + 8,000 total votes.

Answer: E
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