In an election to choose a class president from 5 candidates

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

In an election to choose a class president from 5 candidates

by Gmat_mission » Sun Jun 30, 2019 8:46 am

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In an election to choose a class president from 5 candidates, 39 votes were cast. If no two people received the same number of votes, what is the smallest number of votes that the winning candidate could have received?

A. 8
B. 9
C. 10
D. 11
E. 12

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun Jun 30, 2019 8:46 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Jul 06, 2019 4:54 pm

Gmat_mission wrote:In an election to choose a class president from 5 candidates, 39 votes were cast. If no two people received the same number of votes, what is the smallest number of votes that the winning candidate could have received?

A. 8
B. 9
C. 10
D. 11
E. 12

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

If the five candidates had each received the same number of votes, then they would have received approximately 8 votes each (notice that 39/5 = 7.8). Since each candidate actually received a different number of votesh, we can let the candidate with the median number of votes be 8. We then let 6, 7, 8, and 9 be the number of votes for the four losing candidates. This would make the winner's vote tally be 39 - (6 + 7 + 8 + 9) = 39 - 30 = 9. However, since no one received the same number of votes, the winner's number of votes can't be 9. So let's tweak it. We can change 6 to 5, so now the one who received the most votes is 39 - (5 + 7 + 8 + 9) = 39 - 29 = 10, which must be the minimum number of maximum votes since the numbers are as close as possible.

Answer: C

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