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

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

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11 Jan 2005, 13:50
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
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11 Jan 2005, 13:56
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
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11 Jan 2005, 14:16
i think the Q has a typo it means Prime factors i guess

then i will go with C too
Senior Manager
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11 Jan 2005, 14:50
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
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12 Jan 2005, 22:30
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
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hard one from real test [#permalink]

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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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