quite an interesting question on divisibility by 13

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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 Feb 10, 2010 8:51 am

All the digits of a 50 digit positive number are 4 except for the nth digit. If the number is divisible by 13 for some choice of that nth digit, then how many possible values can n have?

a) 17
b) 21
c) 24
d) 33
e) none

please try it yourself before asking me for solution .very good question indeed.

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Source: Beat The GMAT — Problem Solving | Wed Feb 10, 2010 8:51 am

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

by ajith » Wed Feb 10, 2010 10:04 am

shashank.ism wrote:All the digits of a 50 digit positive number are 4 except for the nth digit. If the number is divisible by 13 for some choice of that nth digit, then how many possible values can n have?

a) 17
b) 21
c) 24
d) 33
e) none

please try it yourself before asking me for solution .very good question indeed.

111111 is a multiple of 13
4444(48)times4x is not divisible by 13
4444(48)timesx4 is not divisible by 13

hmmmm I think I am in the right track but Nothing comes to my mind

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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 Feb 10, 2010 10:18 am

ajith wrote:
shashank.ism wrote:All the digits of a 50 digit positive number are 4 except for the nth digit. If the number is divisible by 13 for some choice of that nth digit, then how many possible values can n have?

a) 17
b) 21
c) 24
d) 33
e) none

please try it yourself before asking me for solution .very good question indeed.
111111 is a multiple of 13
4444(48)times4x is not divisible by 13
4444(48)timesx4 is not divisible by 13

hmmmm I think I am in the right track but Nothing comes to my mind

Just concentrate on divisiblity rule of 13. find the seed of divisiblity by 13 and try to solve it you will get it.

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