Question: Number of Routes

Comment on Number of Routes

Is this kind of question likely to come up?
gmat-admin's picture

This would be a valid GMAT question on test day, although I wouldn't say that it's a "common" question type.

I should also note that this is a 700+ level question so, given the adaptive nature of the GMAT, the only students who would see a question like this would be those who are doing really well on the quant section.

Hey Brent,

I dont quite understand why to use the Mississippi rule.

I thought in this question its about finding unique ways to arrange the letters and RRRRDDD is not the same as DDDRRRR for example. with using the mississippi rule, wouldnt be make them the same ?
gmat-admin's picture

The MISSISSIPPI rule doesn't treat RRRRDDD as the same as DDDRRRR.

I tried solving a different way and I'm curious why it didn't work. I treated every upper left hand corner as a point where a decision between two options takes place (right or down) and since there are 12 upper left hand corners, I said 12 X 2 = 24. Where are the other 11 possibilities coming from?
gmat-admin's picture

If you try using that technique with a 2 by 2 grid, you'll find that it doesn't yield the correct answer either.

The problem is that each intersection isn't equal. For example, there's only 1 way to reach the intersection that's 1 block to the right of point A. However, there are 2 ways to reach the intersection that's diagonal from point A.

Dear Brent, I solved this question with different both answer and approach.

- We have 7 spots of movement from A to B
- We only can use 2 movements (either right or down) in each spot.
- Therefore, we use FCP : 2 X 2 X 2 X 2 X 2 X 2 X 2, which is 128.

Can you please elaborate what is wrong with this approach?
gmat-admin's picture

The problem with that solution is that there are situations in which we DON'T have two options (right or down)

To see what I mean, let's start at point A.
We have two directions to go (right or down).
Let's go DOWN

From here, we have two directions to go (right or down).
Let's go DOWN again

From here, we have two directions to go (right or down).
Let's go DOWN again

Now we're at the bottom left corner.

From here, we can go in only ONE direction: right

In fact, every move from that point on must be right.

Ahhh I see. Well noted then. Thanks for your explanation!

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