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

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Manager
Joined: 15 Nov 2006
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h is an integer greater than 1,is h a prime number? 1) each [#permalink]

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17 Dec 2006, 21:54
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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

Solution:

(1) seems OK, if h is compound, it does not satisfy. For example 6, 3>sqrt6, but 2<sqrt6. If h=15, then 5>sqrt15, but 3<sqrt15. Only primes satisfy. If H=7. Prime factors are 1 and 7. (1) satisfies for 7 but not for 1.

(2) seems OK as well. If h is prime then it is OK. If h=15, then 3<15/2 and 5<15/2. (1) satisfies for 7 but not for 1.

thanks

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Manager
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18 Dec 2006, 02:41
Stmt 1) h > 1 and each prime factor greater than sq root h.
It means sq root of h should be between 1 and 2 so h can be either 2,3 both prime

Stmt 2) Each prime factor greater than h/2 means h should be in between 2 and 3 but as it is integer both are prime numbers.

So I think its .....D?

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Intern
Joined: 17 Dec 2006
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18 Dec 2006, 06:08
nitinneha 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

Solution:

(1) seems OK, if h is compound, it does not satisfy. For example 6, 3>sqrt6, but 2<sqrt6. If h=15, then 5>sqrt15, but 3<sqrt15. Only primes satisfy. If H=7. Prime factors are 1 and 7. (1) satisfies for 7 but not for 1.

(2) seems OK as well. If h is prime then it is OK. If h=15, then 3<15/2 and 5<15/2. (1) satisfies for 7 but not for 1.

thanks

I think you are getting wrong answer because you are assuming 1 as prime. 1 is not a prime number and hence it shouldnt be taken as a counter example here.

Hope this helps clarify

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Senior Manager
Joined: 04 Nov 2006
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19 Dec 2006, 00:08
Yes, D should be..

if each prime is greater than h/2..
2 is the least > 1 prime.. so h/2 will be the max value one can get dividing by prime.. if it has any prime factor, then this prime has to be less than h/2, unless it is divided by h only.. which makes h prime..

a similar argument can be made for root(h), due to each prime > root(h)...

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Senior Manager
Joined: 01 Oct 2006
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19 Dec 2006, 11:02
nitinneha 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

Solution:

(1) seems OK, if h is compound, it does not satisfy. For example 6, 3>sqrt6, but 2<sqrt6. If h=15, then 5>sqrt15, but 3<sqrt15. Only primes satisfy. If H=7. Prime factors are 1 and 7. (1) satisfies for 7 but not for 1.

(2) seems OK as well. If h is prime then it is OK. If h=15, then 3<15/2 and 5<15/2. (1) satisfies for 7 but not for 1.

thanks

Prime factor of which number..
or do u mean prime numbers?

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Re: DS   [#permalink] 19 Dec 2006, 11:02
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