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# A race car driver has to drive from the intersection A to in

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A race car driver has to drive from the intersection A to in  [#permalink]

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03 Jun 2011, 09:23
3
00:00

Difficulty:

55% (hard)

Question Stats:

45% (01:34) correct 55% (01:56) wrong based on 33 sessions

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A race car driver has to drive from the intersection A to intersection B along the route that is confined to the square grid of four touchstones and three avenues shown in the map above. How many routes from A to B can the racer take that have minimum possible length?

A. 7
B. 9
C. 10
D. 14
E. 18

http://s3.amazonaws.com/production.grockit.com/content_images/production/1264222415/40_a.jpg

cant we solve this by combinatorics ? grockit gives solution via counting which is cumbersome.

Attachment:

40_a.jpg [ 9.39 KiB | Viewed 353 times ]

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Re: A race car driver has to drive from the intersection A to in  [#permalink]

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03 Jun 2011, 09:37
bblast wrote:
A race car driver has to drive from the intersection A to intersection B along the route that is confined to the square grid of four touchstones and three avenues shown in the map above. How many routes from A to B can the racer take that have minimum possible length?

7
9
10
14
18

http://s3.amazonaws.com/production.grockit.com/content_images/production/1264222415/40_a.jpg

cant we solve this by combinatorics ? grockit gives solution via counting which is cumbersome.

Count the number of columns, say c
Count the number of rows, say r

$$Ways = C^{(c+r)}_{c}$$
OR
$$Ways = C^{(c+r)}_{r}$$

In this figure,
c=2
r=3
c+r=5
$$Ways = C^{5}_{3} = 10$$

Ans: "C"
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Re: A race car driver has to drive from the intersection A to in  [#permalink]

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03 Jun 2011, 09:51
2
UUULL (shortest possible way includes 3 UPs and 2 Lefts)
No. of arrangement includes = 5! / (3! * 2!) = 10
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Re: A race car driver has to drive from the intersection A to in  [#permalink]

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11 Apr 2019, 10:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A race car driver has to drive from the intersection A to in   [#permalink] 11 Apr 2019, 10:59
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