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h is an integer greater than 1,is h a prime number? 1) each

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Manager
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h is an integer greater than 1,is h a prime number? 1) each [#permalink] New post 08 Aug 2004, 21:08
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A
B
C
D
E

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h is an integer greater than 1,is h a prime number?

1) each prime factor is greater than square root h
2) each prime factor is greater than h/2


Please explain.
Director
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 [#permalink] New post 08 Aug 2004, 22:30
D.

Don't know how to explain with theorems. I just substituted values:
N = 2, 5, 6, 13, 16, 24
Prime Factors = 2, 5, 2x3, 13, 2^4, 2^3 x 3
N/2 = 1, 2.5, 3, 6.5, 8, 12
Prime=Y, Y, N, Y, N, N
CEO
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 [#permalink] New post 09 Aug 2004, 20:17
afife

can you tell us the answer please.
Senior Manager
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Re: DS: Repost [#permalink] New post 09 Aug 2004, 23:11
I got D as the answer.
From the stem : h > 1 i.e., h can be [2, infinity]

I use => to state "it imples that"

(1)Each prime factor is sqrt(h) => the primefactors start with 2,3,5 etc.
=> h can be 2 or 3. The smallest primefactor is 2 and if we prove 'greater than' relation with it, the remaining numbers automatically are proved as for the relationship. Then 2 > sqrt(2) or sqrt(3). But, h cannot be 4. However, h be it 2 or 3 is prime and thus answers the question.

(2)Here also, h can be 2 or 3.
The smallest primefactor is 2 and if we prove 'greater than' relation with it, the remaining numbers automatically are proved as for the relationship.
B'cos 2 > 2/2 or 3/2. But, h cannot be 4.
However, h be it 2 or 3 is prime and thus answers the question.

So, it is D.

afife76 wrote:
h is an integer greater than 1,is h a prime number?

1) each prime factor is greater than square root h
2) each prime factor is greater than h/2


Please explain.

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Manager
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 [#permalink] New post 10 Aug 2004, 12:37
I do not have a OA for this question. It is from this forum's archive, posted by Stolyar.
  [#permalink] 10 Aug 2004, 12:37
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