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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 » Mon Feb 08, 2010 7:15 am

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

a) 31
b) 63
c) 75
d) 91
e) None of these

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 7:15 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 08, 2010 7:24 am

shashank.ism wrote:A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

a) 31
b) 63
c) 75
d) 91
e) None of these

Nice question, but base 2, 3 and 5 notation is out of scope for the GMAT.
You only need base 10.

Brent Hanneson - Creator of GMATPrepNow.com

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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 » Mon Feb 08, 2010 7:28 am

Brent Hanneson wrote:
Nice question, but base 2, 3 and 5 notation is out of scope for the GMAT.
You only need base 10.

Brent That is a good suggestion. So whether we should try the question with base 2,3,5 etc or leave it...

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 10:59 am

shashank.ism wrote:A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

a) 31
b) 63
c) 75
d) 91
e) None of these

Which base is 100 highlighted above is in? and to which base is answers are?

On a serious note

31 = 5^2+5+1 ; 3^3+3+1; 2^4+2^3+2^2+2+1

63 =2^5+ 2^4+2^3+2^2+2+1; 2*3^3+3^2; 2*5^2+2*5+3

75 = 3*5^2

91 = 2^6+2^4+2^3+2+1 ; 3^4+2^2+1; 3*5^2+3*5+1

As some of you can see, 91 satisfies all the conditions

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