how many different victory circles are possible

[abhi332]

In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the
second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of
a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top
two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is
awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together
with their medals to form a victory circle, how many different victory circles are possible?

A)24
B)52
C)96
D)144
E)648
[spoiler]
OA:B[/spoiler]

[harsh.champ]

In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the
second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of
a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top
two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is
awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together
with their medals to form a victory circle, how many different victory circles are possible?

A)24
B)52
C)96
D)144
E)648
[spoiler]
OA:B[/spoiler]

Case 1:-All 3 different -3!
Case 2:-1st place tied - 3C2 + 1(All3 coming first)
Case 3:-2nd place tied - 3C2
Total = 13 ways


Now,any 3 can be selected for medal standings in 4 ways. 4C3

[spoiler]Hence,answer is 4C3 x 13 =52 ways B[/spoiler]

[harsh.champ]

Hey abhi,
This is an incomplete ques.
What if the 3rd place is tied??
No pre-requisite for this condition is given in the question..
I guess this will not be a probable GMAT question.
Whats the source??

[abhi332]

[spoiler]Source: Manhattan Challenge Question[/spoiler]

[harsh.champ]

[spoiler]Source: Manhattan Challenge Question[/spoiler]

I guess,you understand my doubt over here..
I don't think Manhattan designed it to resemble like a GMAT problem.
The other day,a guy was telling me that some of the Manhattan problems do not resemble GMAT like questions.
Does anybody has any idea which test-prep has the most resemblance???
Am I wrong over here??

[abhi332]

I heard from my friends that Kaplan is very close to GMAT format. Manhattan is quite difficult compare to actual GMAT.

[harsh.champ]

I heard from my friends that Kaplan is very close to GMAT format. Manhattan is quite difficult compare to actual GMAT.

Hey,thanks for the info.
Still,if in any way some expert can help us out here.
Can this thread be highlighted in the forum so that we can get responses from instructors or experts??

[Testluv]

Because the question tells us to assume that exactly three medals are awarded, we have to assume that a third place tie does not happen. If we did have a third place tie, we would have to hand out four medals, which would contradict the assumption the question told us to make. While the question is technically fine, I doubt a GMAT question would be phrased like this. If this question came on the GMAT, it would almost certainly also instruct you to assume that there is never a third place tie.