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In an election for class president, each of 32 students vote

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by BTGmoderatorDC » Tue Sep 17, 2019 4:34 pm

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Answers

A

B

C

D

E

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Difficulty—

In an election for class president, each of 32 students voted for exactly one candidate, Ann, Bob or Carl. Did Bob receive the most votes?

(1) Bob received 9 votes.

(2) Carl received 13 votes.

OA A

Source: Magoosh
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Sep 17, 2019 8:46 pm
BTGmoderatorDC wrote:In an election for class president, each of 32 students voted for exactly one candidate, Ann, Bob or Carl. Did Bob receive the most votes?

(1) Bob received 9 votes.

(2) Carl received 13 votes.

OA A

Source: Magoosh
Let's take each statement one by one.

(1) Bob received 9 votes.

=> Ann and Carl received 32 - 9 = 23 votes. Since 23 is more than double the votes Bob got, either Ann or Carl must hev got more than 9 votes. Exact half of 23 is 11.5, which is greater than 9. If Ann gets 12 or greater than 12 votes, the answer is no, Bob did not receive the most votes and if Carl gets 12 or greater than 12 votes, the answer is no, Bob did not receive the most votes. In either case, the answer is No. Sufficient.

(2) Carl received 13 votes.

Case 1: Say Bob got 14 votes; thus, Carl got 32 - 13 - 14 = 5 votes. The answer is yes, Bob got the most votes.
Case 2: Say Carl got 14 votes; thus, Bob got 32 - 13 - 14 = 5 votes. The answer is no, Bob did not get the most votes.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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