How Many m and n's? -From your challenge series

[rhoeta]

04/03/06
Question
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

Its not clear to me in your OE why n =4 for 1) is not acceptable all the time. I tried a few +ve integers at it turns out the 4 works.

[StaceyKoprince]

When n=4, we have m(m + 1)(m + 2)(m + 3)(m + 4).

If m = 1, then we have 1*2*3*4*5, which has only three 2's as factors. 2*2*2 = 8, not 16. So this number is not divisible by 16.
If m = 2, then we have 2*3*4*5*6, which has four 2's as factors. 2*2*2*2 = 16. So this number is divisible by 16.

Trying numbers is often a very good technique, but when a question says something must be true for "every" value, you have to be careful - if you happen not to try the right numbers, you might miss the right answer.

[yousuf_azim]

What is the ans?

BR

Farid

[jnelson0612]

What is the ans?

BR

Farid

The answer should be C.

[matthewwhchu]

As from your explanation, 1) is not always true (for example, if m = 1). Therefore, could we conclude the answer should be E? Since 1) is not always true and 2) comes to either n = 4 or n = 5, which is not sufficient to have the result where n is.

[tim]

it's not correct to say that (1) is not always true. when the GMAT gives you a statement, you take it as always true, and accept whatever consequences flow from that. as shown in the example, (1) is not true when n=4 and m=1. what this means is that n cannot be 4 because it creates a situation that contradicts (1)..