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In a close election, there were five candidates-John, Bill,

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by Anaira Mitch » Sat Jan 14, 2017 2:33 pm
In a close election, there were five candidates-John, Bill, Steph, Jen, and Amanda- who each finished in that order and received atleast one vote. If each candidate was at least 10 votes apart from any other candidate and 114 votes were cast, did John receive more than 50 votes?

a) 62
b) 56
c) 50
d) 70
e) 80

Please help with this problem.
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by [email protected] » Sat Jan 14, 2017 2:39 pm
Hi Anaira Mitch,

To start, the answers don't match the question that's asked - so I'll ignore that for now. Since each candidate received at least one vote, and they're each separated by at least 10 votes, we can use a bit of 'brute force' to derive the pattern behind this prompt. To start, I'm going to give the MINIMUM possible number of votes to each candidate:

Amanda = 1 vote
Jen = 11 votes
Steph = 21 votes
Bill = 31 votes
John = 41 votes
Total = 105 votes

Since the actual total number of votes is 114, there can't be that many way to assign the remaining 9 votes to these 5 people (AND still keep each pair of numbers at least 10 votes apart.

IF we assigned all 9 of the remaining votes to John, then he COULD have 41+9 = 50 votes. As such, the answer to the immediate question is NO. If the question was meant to ask "what is the maximum number of votes that John could have received, then the answer is 50.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by Anaira Mitch » Sat Jan 14, 2017 2:54 pm
[email protected] wrote:Hi Anaira Mitch,

To start, the answers don't match the question that's asked - so I'll ignore that for now. Since each candidate received at least one vote, and they're each separated by at least 10 votes, we can use a bit of 'brute force' to derive the pattern behind this prompt. To start, I'm going to give the MINIMUM possible number of votes to each candidate:

Amanda = 1 vote
Jen = 11 votes
Steph = 21 votes
Bill = 31 votes
John = 41 votes
Total = 105 votes

Since the actual total number of votes is 114, there can't be that many way to assign the remaining 9 votes to these 5 people (AND still keep each pair of numbers at least 10 votes apart.

IF we assigned all 9 of the remaining votes to John, then he COULD have 41+9 = 50 votes. As such, the answer to the immediate question is NO. If the question was meant to ask "what is the maximum number of votes that John could have received, then the answer is 50.

GMAT assassins aren't born, they're made,
Rich
Thank you...It was from Veritas Prep Book- Word Problems and Answers were provided like this only
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