PS- number prop 264 600

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Xbond: Master | Next Rank: 500 Posts; Posts: 275; Joined: Wed Jul 02, 2008 4:19 am; Thanked: 4 times

by Xbond » Sat Sep 19, 2009 2:54 am

Hi there,

could you help to understand and resolve this PS in the simplest way

How many numbers that are not divisible by 6 divide evenly into 264,600?

(A) 9
(B) 36
(C) 51
(D) 63
(E) 72

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Source: Beat The GMAT — Problem Solving | Sat Sep 19, 2009 2:54 am

real2008: Legendary Member; Posts: 527; Joined: Thu May 01, 2008 12:06 am; Thanked: 7 times

by real2008 » Sat Sep 19, 2009 7:09 am

is that D?

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Xbond: Master | Next Rank: 500 Posts; Posts: 275; Joined: Wed Jul 02, 2008 4:19 am; Thanked: 4 times

by Xbond » Sat Sep 19, 2009 2:24 pm

I would like your full explanation, please

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praky_rules: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Wed Jun 11, 2008 4:25 pm; Thanked: 4 times; GMAT Score:730

by praky_rules » Sat Sep 19, 2009 4:38 pm

264600 = 2^3 x 5^2 x 3^3 x 7^2

Total number of factors that are not divisible by 6 = Total number of factors - Total number of factors divisible by 6.

Total number of factors = (3+1) x (2+1) x (3+1) x (2+1) = 144 (For 2^3 term, you can pick "2" 3 times or not pick it at all = (3+1))

Total Number of factor divisible by 6 = you have to pick 2 atleast once and 3 atleast once. So total possible factors = 3 x (2+1) x 3 x (2+1)
= 81

144-81 = 63. Can I get a hug?

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