Tricky questions - Needs logic rather than Algebra

HI nikhilgmat31,

These questions can all be solved by TESTing VALUES and thinking about the 'limits' involved (how big or small one number can be AND how that would impact the other numbers).

From the prompt, we know a number of facts:

1) There are 100 total votes.
2) Everyone got AT LEAST 1 vote.
3) A+B+C+D+E = 100
4) A>B>C>D>E
5) A = 40

The first question asks for the maximum and minimum number of votes that Bill could have received....We know that Bill got FEWER than 40, so let's start with 39 and see if we can make all the facts 'fit' together...

A = 40
B = 39

That leaves 21 votes for the other 3 people...there are a number of ways to distribute those votes. Here's one...

C = 15
D = 5
E = 1

So, Bill COULD have gotten 39 votes.

The minimum number of votes will be a little trickier to determine (we have to maximize all of the other numbers while still making Bill the biggest of those 4 numbers)...

B+C+D+E = 60

This means the average would be 60/4 = 15. Using that information, we can 'bunch' the numbers close...this means that the minimum number of votes for Bill would be a little more than 15....

IF....
B = 16
C = 15
D = 14
E = 13
Total = 58, which is NOT enough votes. Thus, Bill had to have received MORE than 16 votes...

IF....
B = 17
C = 16
D = 15
E = 12
Total = 60, so the minimum number of votes for Bill would have to be 17.

You can use a similar approach for each of the other questions.

GMAT assassins aren't born, they're made,
Rich