Data Sufficiency

Five friends recently visited a famous chocolatier, and collectively purchased a total of 16 pounds of fudge. Did any one friend purchase more than 5 pounds of fudge?

(1) No two friends purchased the same amount of fudge.

(2) The minimum increment in which the chocolatier sells fudge is one pound.

OA : C
Source : Veritas Prep

Experts....could you guys show how statement 2 is insufficient. I just can't come up with a test case to eliminate it.

manik11 wrote:Experts....could you guys show how statement 2 is insufficient. I just can't come up with a test case to eliminate it.

Did you somehow let Statement 1 sneak into Statement 2? Sometimes people make the mistake of letting information from one statement affect the way they see the other one.

In any case, here's a way to show that Statement 2 is insufficient.

To minimize the largest purchase, maximize some of the purchases, keeping them below the number in question, 5. Four friends could purchase 4, 4, 4, and 3 pounds, leaving just one pound for the last one.

To maximize the largest purchase, minimize the rest. Four friends could purchase 1, 1, 1, and 1 pounds, leaving 12 for the last guy.

So the maximum could be above or below 5.

Marty Murray wrote:

manik11 wrote:Experts....could you guys show how statement 2 is insufficient. I just can't come up with a test case to eliminate it.

Did you somehow let Statement 1 sneak into Statement 2? Sometimes people make the mistake of letting information from one statement affect the way they see the other one.

In any case, here's a way to show that Statement 2 is insufficient.

To minimize the largest purchase, maximize some of the purchases, keeping them below the number in question, 5. Four friends could purchase 4, 4, 4, and 3 pounds, leaving just one pound for the last one.

To maximize the largest purchase, minimize the rest. Four friends could purchase 1, 1, 1, and 1 pounds, leaving 12 for the last guy.

So the maximum could be above or below 5.

Thanks a lot Marty!
You're right on the money. I did let the info from statement 1 sneak into my analysis of the second one.
I was so focussed on the minimum increment of 1 pound thing that I never tested a case in which more than one friend could buy same amount of
fudge.
Gotta work on this.

manik11 wrote: I was so focussed on the minimum increment of 1 pound thing that I never tested a case in which more than one friend could buy same amount of
fudge.
Gotta work on this.

The testwriters know that we like to assume that numbers are integers, positive, even, etc. and tend to exploit this in DS, so be careful! (Easier said than done, I know, but it's incredible how often something like this comes up on the test.)