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

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

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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