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# In an election to choose a class president from 5 candidates, 39 votes

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Math Expert
Joined: 02 Sep 2009
Posts: 46129
In an election to choose a class president from 5 candidates, 39 votes [#permalink]

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02 Aug 2017, 23:48
00:00

Difficulty:

75% (hard)

Question Stats:

59% (01:15) correct 41% (01:28) wrong based on 108 sessions

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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

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Joined: 18 Aug 2016
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GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: In an election to choose a class president from 5 candidates, 39 votes [#permalink]

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03 Aug 2017, 03:09
1
Bunuel 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

mean is ~8

now if highest is 10+9+8+7+5 = 39
if highest is 9+8+7+6+...not possible

Hence C
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Re: In an election to choose a class president from 5 candidates, 39 votes [#permalink]

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03 Aug 2017, 13:56
1
Bunuel 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

Mean of total number of votes is = 39/ 5 = 7.8
So to minimize the votes received by the winner, we need to keep the winner's vote to as close as possible to the mean.
10+9+8+7+5= 39
If 9 is the smallest for the winning candidate then , 9+8+7+6+5 = 35

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Re: In an election to choose a class president from 5 candidates, 39 votes [#permalink]

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17 Sep 2017, 23:03
Hey Bunuel,

Can you help to solve this sum? i couldn't understand the method used by folks who have posted their solution

Here's how I solved it

Let the largest number be x
There all remaining numbers will be smaller than x i.e. x-1, x-2, x-3 and x-4

x + x-1 + x-2 + x-3 + x-4 = 39
5*x - 10 = 39
5*x = 49
x = 9.8 ~ 10

Let's check using x=10

10 + 9 + 8 + 7 + 6
= 40

The equation doesn't satisfy. But if I replace 6 with 5, the equation will satisfy

10 + 9 + 8 + 7 + 5
= 39

Let me know if this is the correct approach
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Re: In an election to choose a class president from 5 candidates, 39 votes   [#permalink] 17 Sep 2017, 23:03
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