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

Question

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

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

Luckisnoexcuse · Answer

mean is ~8

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

Hence C

Skywalker18 · Answer

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

Answer C

pikolo2510 · Answer

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

ScottTargetTestPrep · Answer

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

Adarsh_24 · Answer

Let x be the smallest value of largest.
X has to be smallest then others have to be largest as possible . But, all are distinct.
So x+x-1+x-2+x-3+x-4=5x-10=39
X=9.something 
So we need to try something where others are still max possible. So we reduce the lowest a little bit. x-5 instead of x-4.
If we reduce x-1 then each one below that has to be reduced further due to them being distinct and it will sway too much away from our intention of keeping others maximum as possible.
5x-11=39
X=50/5=10

Dereno · Answer

Since all the five numbers have to be different.

a , a+1, a+2 , a+3 , a+4

Sum = 5a + 10 = 39

This gives, 5a = 29 , and a is not an integer.

If we are able to allot 4 more than the earlier ones (29-4=25), we get sum as a multiple of 5.

Let’s allocate the last 4 values an extra 1 each.

We get, a, a+2, a+3 , a+4, a+5

New sum = 5a + 14

5a+14 = 39

5a = 25

a = 5

Then a+5, the wining candidate value = (5+5) =  10

Option C

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

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

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