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Fudge

by manik11 » Fri Jan 29, 2016 6:08 am
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.
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by MartyMurray » Fri Jan 29, 2016 6:46 am
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.
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by manik11 » Fri Jan 29, 2016 8:40 am
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. :)
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by Matt@VeritasPrep » Sun Feb 14, 2016 10:16 pm
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.)
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