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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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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 do explain the answer

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.

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 do explain the answer

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.

Can someone explain please?

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.

From the rest of your solution, the answer should be D.

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)...

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 do explain the answer

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.

Can someone explain please?

thanks

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