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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: 453
N is a positive integer and N<10,000, how many prime [#permalink]

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11 Jan 2005, 14:50
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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: 853

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11 Jan 2005, 14:56
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: 612
Location: PA

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11 Jan 2005, 15:16
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: 453

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11 Jan 2005, 15:50
rthothad wrote:
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: 1483

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12 Jan 2005, 23:30
rthothad wrote:
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
hard one from real test [#permalink]

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13 Jan 2005, 12:54
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, 12:54
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N is a positive integer and N<10,000, how many prime

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