For every positive integer n, the function h(n) is defined t

imane81 wrote:Thank you for your input on this one

For every positive integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. Between 2 and 10
B.Between 10 and 20
C.Between 20 and 30
D.Between 30 and 40
E. Greater than 40

komal wrote:

imane81 wrote:Thank you for your input on this one

For every positive integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. Between 2 and 10
B.Between 10 and 20
C.Between 20 and 30
D.Between 30 and 40
E. Greater than 40

source : testmagic
h(100)= 2*4*6............100
h(100)+1=2*4*6............100 +1
2(1*2*3.......50)+1

so when h(100)+1 is divided by any of the nos between 2 and 50 will leave a remainder 1.

2*50!+1 will not be divisible by any no <50

answer E

imane81 wrote:Thank you for your input on this one

For every positive integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. Between 2 and 10
B.Between 10 and 20
C.Between 20 and 30
D.Between 30 and 40
E. Greater than 40

harsh.champ wrote:

komal wrote:

imane81 wrote:Thank you for your input on this one

For every positive integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. Between 2 and 10
B.Between 10 and 20
C.Between 20 and 30
D.Between 30 and 40
E. Greater than 40

source : testmagic
h(100)= 2*4*6............100
h(100)+1=2*4*6............100 +1
2(1*2*3.......50)+1

so when h(100)+1 is divided by any of the nos between 2 and 50 will leave a remainder 1.

2*50!+1 will not be divisible by any no <50

answer E

Hey komal,
I didn't get this :-2*50!+1 will not be divisible by any no <50
Even if we take 50 or 51 how can we confidently say that 2*50!+1 will be divisible by it.The remainder 1 will be there then also.
Kindly clarify.