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# N is a positive integer and N<10,000, how many prime

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Senior Manager
Joined: 07 Nov 2004
Posts: 459
Followers: 2

Kudos [?]: 25 [0], given: 0

N is a positive integer and N<10,000, how many prime [#permalink]  11 Jan 2005, 13:50
N is a positive integer and N<10,000, how many prime integers does N have?
1) N is a multiple of 30.
2) N is a multiple of 70.
Director
Joined: 03 Nov 2004
Posts: 867
Followers: 1

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

I will go with 'C'
From 1: N can be 30, 60, 90, ........210............300..........
From 2: N can be 70, 140, 210.......
Both put together we know that N can be 210, 420, 630...........
Based on this we can say that N can have 4 prime integers 2, 3, 5, & 7
Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 319 [0], given: 22

i think the Q has a typo it means Prime factors i guess

then i will go with C too
Senior Manager
Joined: 07 Nov 2004
Posts: 459
Followers: 2

Kudos [?]: 25 [0], given: 0

I will go with 'C'
From 1: N can be 30, 60, 90, ........210............300..........
From 2: N can be 70, 140, 210.......
Both put together we know that N can be 210, 420, 630...........
Based on this we can say that N can have 4 prime integers 2, 3, 5, & 7

there is not OA but I will choose E.

If 210 * 11 = 2310 < 10000 and are mutiple of 30 and 70, but have 5 prime integers.
VP
Joined: 25 Nov 2004
Posts: 1494
Followers: 6

Kudos [?]: 40 [0], given: 0

I will go with 'C'
From 1: N can be 30, 60, 90, ........210............300..........
From 2: N can be 70, 140, 210.......
Both put together we know that N can be 210, 420, 630...........
Based on this we can say that N can have 4 prime integers 2, 3, 5, & 7

Agree with rthothad. OA is C.
Intern
Joined: 06 Dec 2004
Posts: 20
Location: Lebanon
Followers: 0

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

hard one from real test [#permalink]  13 Jan 2005, 11:54
Can you please elaborate why you have picked C

For me E is the answer

As DLMD pointed the prime factor can be either 4 or 5

- Joe
hard one from real test   [#permalink] 13 Jan 2005, 11:54
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