How to solve these kind of problems efficiently?

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newgmattest: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed May 18, 2011 8:48 pm; Thanked: 4 times

by newgmattest » Tue Jun 28, 2011 12:28 am

Hi GMAT Experts,

Please help to elaborate on efficient way to solve these kind of problems:

A person starts from A and passes through B and C,arrives D at last. If he go forward only to east and north, in how many way can he finish the trip?

a.20
b.32.
c.36.
d. 56

OA : C

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Source: Beat The GMAT — Problem Solving | Tue Jun 28, 2011 12:28 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jun 28, 2011 12:45 am

Hi,
Let R be the operation to move 1 unit right and U be the operation to move 1 unit up

Consider the path from A to B.
Moving using only right and up operations we can reach A to B in 2 ways.
Path BC: We can reach from B to C by moving 2 units right and 1 unit up in any order.
So, R,R,U can be arranged in 3!/2! = 3 ways
Path CD: We can reach from C to D by mopving 2 units right and 2 units up in any order.
So, R,R,U,U can be arranged in 4!/2!2! = 6 ways
So, number of ways from A to D though B and C is (No.of ways from A to B)*(No.of ways from B to C)*(No.of ways from C to D) = 2*3*6 = 36

Hence, C

Cheers!

Things are not what they appear to be... nor are they otherwise

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casperkamal: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Mon May 31, 2010 3:29 am; Location: Hyderabad; Thanked: 2 times

by casperkamal » Tue Jun 28, 2011 3:04 am

I literally counted..but i think i could make it out

That A to B = 2
B to C = 3
C to D = 6
2*3*6

Kamal

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Tue Jun 28, 2011 3:06 am

1. from A-B E-1 N-1. total 2
2. from B-C E-2 N-1. total 3
3. from C-intermediate point E-1,N-1 total 2; Intermediate-D E-1,N-1 total 2 thus C-Intermediate-D = 4
and C-D direct path E-1 N-1 total 2.

total E-D = 4+2=6

thus 2*3*6 = 36.

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