Veritas: Business School Case Competition

[vishalj]

Didn't find this question in the forum yet. So here I go.

In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000 and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible?

A) 18
B)20
C) 54
D) 84
E) 120

[Laura GMAT Tutor]

First, I have to say: this is a permutations question, and those generally don't show up on the test. (If anything, you just see combinations.) Further, in my experience the test doesn't test you on formal logic. I find this question completely untestlike, so don't stress over it if you find it hard. Study number properties and word translations.... not this one.

However, it's kind of a fun one so, here goes.

First, how many options are there that don't include A at all? It's possible to have B without A, it's not not possible to have A without B. So that means that the number of options that don't include A is 5x4x3 = 60.

Now, let's think about what would happen if it did include A. If it includes A, it must include B. So basically, the group would be ABX, where X represents one of {C, D, E, F}. How many ways can we arrange ABX? 3! = 6 ways. But each of those 6 ways could be written with a C, a D, an E, or an F. So that's 4 options for each of the 6 arrangements, so that's 6x4 = 24 ways that it could work out if it involved A.

The total options would be the sum of the ways that involve A and the ways that don't involve A. So that's 60 + 24 = 84.

[goyalsau]

First, how many options are there that don't include A at all? It's possible to have B without A, it's not not possible to have A without B. So that means that the number of options that don't include A is 5x4x3 = 60.

Can you please explain why you are not considering A, As A and B are in the top 3 so they have to be in the winning group, Or In the number of combination for the top 3 spots they must be there,

Please explain why the answer is not 24 ,

[Laura GMAT Tutor]

The part of my explanation that you quoted was the part talking about what would happen *if* A were not involved. I didn't say that that is the only thing going on. I wasn't "not considering" A just in general. I just was taking it step by step. In the next paragraph, there's some explanation of what would happen if A *were* involved.

There's no reason to believe that A must be involved. It only says that if A wins, so does B. It never says A must win. Check back in the wording of the question. It just says "IF A wins..." not "A wins."

Either A is involved or it isn't. The ways that A could be involved = 24. The ways that A isn't involved = 60. So the sum is 84.

[goyalsau]

The part of my explanation that you quoted was the part talking about what would happen *if* A were not involved. I didn't say that that is the only thing going on. I wasn't "not considering" A just in general. I just was taking it step by step. In the next paragraph, there's some explanation of what would happen if A *were* involved.

There's no reason to believe that A must be involved. It only says that if A wins, so does B. It never says A must win. Check back in the wording of the question. It just says "IF A wins..." not "A wins."

Either A is involved or it isn't. The ways that A could be involved = 24. The ways that A isn't involved = 60. So the sum is 84.

Thanks,

[vishalj]

Thanks for the great explanation