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pradeepkaushal9518: Legendary Member; Posts: 1309; Joined: Wed Mar 17, 2010 11:41 pmFollowed by: 5 members; Thanked: 33 times

by pradeepkaushal9518 » Tue Aug 03, 2010 4:17 am

plz explain i m confused

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Source: Beat The GMAT — Problem Solving | Tue Aug 03, 2010 4:17 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Tue Aug 03, 2010 4:23 am

OG Explanation looks good for me.

30 cities will have 900 squares.

diadonal will have 30 squares without dots.
Hence 900-30 = 870

Now half will have dots and half do not.

870/2 = 435

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Tue Aug 03, 2010 4:32 am

Note that 5 cities have 25 entries.

For 30 cities there ll be 900 entries.

30 entries along the diagonal are not needed?Why?

Because they are entries bw the same city like City A--City A,City B--City B

900-30=870

In 870 entries there ll be pairs of distance bw same cities[for ex city A--City B and City B]

there should be only one entry bw 2 city.

-->870/2=435 entries.

You can easily understand if u apply this concept in the diagram shown.

Pick B

--Anand--

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Vipulvp: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Tue Jun 22, 2010 6:52 am; Thanked: 1 times; GMAT Score:760

by Vipulvp » Wed Aug 04, 2010 4:07 am

pradeepkaushal9518 wrote:plz explain i m confused

You can probably start small. In case of three cities, we have three entries. In case of four cities, we need six entries. In case of five cities, we need ten entries. If we are able to see the pattern, we can easily apply it to thirty cities.
3 --> 3C2 (=3)
4 --> 4C2 (=6)
5 --> 5C2 (=10)
Hence 30 --> 30C2 = 435

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