Challenge PS Problem for GMATT Mondays tonight (3/17)

[Matt@VeritasPrep]

Hi all!

Here's a nifty probability question of a type you may not have seen before. If you have trouble solving it -- or can't see how you would even begin -- feel free to swing on by GMATT Mondays tonight, at the link provided in my sig file, where I'll walk you through intuitive approaches to fun, unusual problems like these. (We meet at 4PM Pacific, 7PM Eastern. This week's theme is probability, and there will be eight questions, four PS and four DS; hopefully I'll have time to go through all of them.)

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I'm at a birthday party and I'm blindfolded. (Uh oh.) I'm currently standing in the First Room of the four rooms of the house, as shown.

Door <-> First Room <-> Second Room <-> Third Room <-> Fourth Room, with Cake!

I'm wandering from room to room with the following probabilities:

1:: If I'm in the first room, there's a 25% chance I walk out the door and a 75% chance I walk to the second room.
2:: If I'm in the second room, there's a 50% chance I walk to the first room and a 50% chance that I walk to the third room.
3:: If I'm in the third room, there's a 75% chance I walk to the second room and a 25% chance I walk to the fourth room (with cake!)

If I make it to the room with cake, I get to remove the blindfold and pig out. If I walk out the door blindfolded, however, the door is locked behind me and I'm banished from the party, without cake.

What are the odds that I get to pig out on cake?

A:: 3/32 B:: 3/16 C:: 1/3 D:: 3/8 E:: 1/2

[Bill@VeritasPrep]

Oh man, this is a fun one.

[Matt@VeritasPrep]

Oh man, this is a fun one.

I thought so too, but no takers!

Here's a hint for those puzzling this one out. To solve it, you only have to multiply two numbers together. The first number is 3/4, as you may have gathered, so the only step left is figuring out what that second number is. The logic behind it is surprisingly intuitive: as often on the GMAT, if you're doing any real computation at all, you're missing something.