Length of interger

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Jinglander: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Jul 22, 2010 5:40 pm; Thanked: 1 times

by Jinglander » Sun Aug 08, 2010 2:12 pm

Ok we are told both x and y are posative and greater than 1. also x+3y<1000. what is the maximum number the sum of the lengths x and y can be

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Source: Beat The GMAT — Problem Solving | Sun Aug 08, 2010 2:12 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sun Aug 08, 2010 5:29 pm

Jinglander wrote:Ok we are told both x and y are posative and greater than 1. also x+3y<1000. what is the maximum number the sum of the lengths x and y can be

The length of a number is the maximum if it is made of prime nos.
So, let us put x = 2, then 2^9 = 512, which is the maximum power of 2 that we can take here as 2^10 = 1,024.

Next put y = 2^7 = 128, which gives 3y = 3*128 = 384

Then 512 + 384 = 896 < 1000
Therefore, maximum length = 9 + 7 = 16

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