44 Is there a quicker way of doing calculating the function?

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ern5231: Master | Next Rank: 500 Posts; Posts: 226; Joined: Sun Aug 09, 2009 4:34 am

by ern5231 » Sat Oct 03, 2009 7:03 pm

There is a function f (2 ^ 6) = f (64) = 6 +4 = 10, What is the value of f (2 ^ 9 * 5 ^ 7) =?

The answer can be calculated by direct calculation as 4. Can you suggest a quick approach?

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Source: Beat The GMAT — Problem Solving | Sat Oct 03, 2009 7:03 pm

cbenk121: Master | Next Rank: 500 Posts; Posts: 202; Joined: Tue Sep 08, 2009 11:34 pm; Thanked: 15 times; GMAT Score:760

by cbenk121 » Sat Oct 03, 2009 7:29 pm

Break it down.

2 x 2 x 2 x 2.... * 5 x 5 x 5...

There's 9 2's, and 7 5's. So do this, by the commutive and associative laws.

(5x2)^7*2*2 = 10^7 * 4 = 10000000 * 4 = f(40000000) = 4.

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