problem on integers-how many m's and n's

[debarshi7]

What is the positive integer n?

(1) For every positive integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n2 - 9n + 20 = 0

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

[Amit]

I think its C.

on solving B we get n =4 or n=5,so still undecided.


for A take m=1.
So basically we have to check whether (n+1)! is divisible by 16.
Check to see if (4+1)!=120 or (5+1)!=720 is divisible by 16.As 720 is divisible n=5(unique now)....both statements needed
Testing with m=1 is sufficient .Consider m=2.Then we check if (n+2)! is divisible by 16 which is true for n=4 or n=5.
So m=1 is the case to test.
Note:if a number is divisible by n! it will always be divisible by (n+1)!,(n+2)!.....So max one needs to check is upto m=2

Experts:Do correct me if anything is wrong:P





:shock: :shock: :shock: :shock: [/quote]

[rfernandez]

debarshi7, is this problem from one of our strategy guides? Would you kindly post the book, chapter, and page number? Thanks.