How to solve this PS. anyone pls help

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srini1988: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Jun 24, 2011 8:52 amFollowed by: 1 member

by srini1988 » Tue Aug 02, 2011 5:10 am

The "length of the integer" refers to the number of prime factors, not necessarily distinct, that x has(If x=60, the length of x would be 4 because 60=2*2*3*5). what is the greatest possible length of integer z if z<1080?

A.13
B.10
C. 9
D. 7
E. 6

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abhisays: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Sun Nov 29, 2009 7:11 pm; Location: Bangalore; Thanked: 4 times

by abhisays » Tue Aug 02, 2011 5:27 am

I think, 1024 which is < 1080 will have maximum length.

1024 = 2.2.2....10times..

so the maxium length would be 10.

so my answer is B

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Tue Aug 02, 2011 7:56 pm

That answer is correct. To expand a bit on the reasoning:

Your goal is to get the maximum length subject to the constraint z < 1080. To do this, use the smallest possible prime number (2) to build up the length. Multiply 2 by itself until the product is as close to 1080 as possible without going over. Since 2^10 = 1024, 10 is correct.

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naveen451: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat Jul 16, 2011 11:56 pmFollowed by: 1 member; Location: hyderabad; Thanked: 2 times

by naveen451 » Wed Aug 03, 2011 1:17 am

IMO B

2^10=1024

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Aug 03, 2011 4:43 am

srini1988 wrote:The "length of the integer" refers to the number of prime factors, not necessarily distinct, that x has(If x=60, the length of x would be 4 because 60=2*2*3*5). what is the greatest possible length of integer z if z<1080?

A.13
B.10
C. 9
D. 7
E. 6

Here we see that we have to find the greatest possible length if the integer z. So to increase the number we should first try to use smallest number possible prime number.
so lets start with (2)^10 = 1024 < 1080.
If we try any other combination like 3, 5 in it we will get smaller length.

Hence Correct Ans is B

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