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# Interger Pro (1)

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Intern
Joined: 09 Jan 2009
Posts: 23
Schools: SDSU
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Kudos [?]: 1 [0], given: 0

Interger Pro (1) [#permalink]  11 Feb 2009, 16:21
Someone helps me, thanks !
How positive integers less than 100 have exactly 4 odd factors but no even factors?
A. 13
B. 14
C. 15
D. 16
E. 17
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 576 [1] , given: 19

Re: Interger Pro (1) [#permalink]  11 Feb 2009, 19:03
1
KUDOS
baggio wrote:
Someone helps me, thanks !

How positive integers less than 100 have exactly 4 odd factors but no even factors?
A. 13
B. 14
C. 15
D. 16
E. 17

The only possible integers that have 4 odd integers as factors are:

The possible prime factors: 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

with 3, any of the above prime number is possible = 9 ways
with 5, any of the above prime number smaller than 19 is possible = 5 ways
with 7, any of the above prime number smaller than 13 is possible = 2 ways
with 11 and above, none.

got 16.

Definitely a good one.
Previously thought the question is wrong.
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Joined: 30 Nov 2008
Posts: 493
Schools: Fuqua
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Re: Interger Pro (1) [#permalink]  11 Feb 2009, 19:52
Intern
Joined: 09 Jan 2009
Posts: 23
Schools: SDSU
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Interger Pro (1) [#permalink]  11 Feb 2009, 21:46
GMAT TIGER wrote:
baggio wrote:
Someone helps me, thanks !

How positive integers less than 100 have exactly 4 odd factors but no even factors?
A. 13
B. 14
C. 15
D. 16
E. 17

The only possible integers that have 4 odd integers as factors are:

The possible prime factors: 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

with 3, any of the above prime number is possible = 9 ways
with 5, any of the above prime number smaller than 19 is possible = 5 ways
with 7, any of the above prime number smaller than 13 is possible = 2 ways
with 11 and above, none.

got 16.

Definitely a good one.
Previously thought the question is wrong.

According to your way, these found integers only have 2 odd factors but not 4 odd one. Not follow the requirement of this pro. Can u explain more detail 4 me ?
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 576 [0], given: 19

Re: Interger Pro (1) [#permalink]  12 Feb 2009, 05:08
baggio wrote:
GMAT TIGER wrote:
baggio wrote:
Someone helps me, thanks !

How positive integers less than 100 have exactly 4 odd factors but no even factors?
A. 13
B. 14
C. 15
D. 16
E. 17

The only possible integers that have 4 odd integers as factors are:

The possible prime factors: 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

with 3, any of the above prime number is possible = 9 ways
with 5, any of the above prime number smaller than 19 is possible = 5 ways
with 7, any of the above prime number smaller than 13 is possible = 2 ways
with 11 and above, none.

got 16.

Definitely a good one.
Previously thought the question is wrong.

According to your way, these found integers only have 2 odd factors but not 4 odd one. Not follow the requirement of this pro. Can u explain more detail 4 me ?

3x5 = 15 has four odd factors: 1, 3, 5 and 15.
3x7 = 21 has factors 1, 3, 7, and 21.
so on....
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Joined: 07 Nov 2007
Posts: 1824
Location: New York
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Kudos [?]: 564 [0], given: 5

Re: Interger Pro (1) [#permalink]  12 Feb 2009, 08:18
agreed .. good job GT
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Re: Interger Pro (1)   [#permalink] 12 Feb 2009, 08:18
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