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Re: DS: What is the positive integer n? [#permalink]

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14 Dec 2008, 13:30

1

This post received KUDOS

C for me.

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

In a sequence of consequetive numbers, every other number will be even, and every fourth number will be a multiple of 4, so the minimum numbers you need for the products to be divisible by 16 (2^4) would be 5 (if the first is even) or 6 (if the first is odd).Since the statement is true for every integer m, (irrespective of odd or even), the minimum is 6 => minimum n = 5. But n could also be any number greater than 5 for the above to hold true, hence (1) in itself is INSUFF

Re: DS: What is the positive integer n? [#permalink]

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15 Dec 2008, 06:15

statement 1 you clearly cant estimate without somewhere to start, so go to statement 2.. factoring easily you get n=4 or n=5..not suff

go back to statement 1 and plug 4 and 5 in for N. it says any integer will work, so if you just use 1 you get (5*4*3*2*1) = not divs by 16, and (6*5*4*3*2*1)=720= 16*45...so 1 and 2 together are suff.

Re: DS: What is the positive integer n? [#permalink]

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16 Dec 2008, 04:51

ritula wrote:

scthakur, can u pls explain hw did u get n=4 or 5 in stmt1?

scthakur wrote:

I will go with E.

From stmt1: n = 4 or 5 (depending upon whether m is even or odd). From stmt2: n = 4 or 5.

Every third even integer is divisible by 4. Hence, if m is an odd integer then, m+1, m+3 and m+5 will be even and one of them will also be divisible by 4. But this means, n = 5.

However, if m is even then, m, m+2 and m+4 will be even and one of them will be divisible by 4. Hence, n = 4.

Re: DS: What is the positive integer n? [#permalink]

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16 Dec 2008, 05:10

Hi scthakur,

I think you mean one in every three consecutive even integers is a multiple of 4 ( and not every third even integer is a multiple of four ).

My point is why do we take 4 terms min..8,9,10 are also consecutive and also satisfy the condition!! is it because the question says m ( m+1) (m+2)...(m+n) ??

Re: DS: What is the positive integer n? [#permalink]

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16 Dec 2008, 05:24

Economist wrote:

Hi scthakur,

I think you mean one in every three consecutive even integers is a multiple of 4 ( and not every third even integer is a multiple of four ).

My point is why do we take 4 terms min..8,9,10 are also consecutive and also satisfy the condition!! is it because the question says m ( m+1) (m+2)...(m+n) ??

You are right with your example. I took the worst case. If we start with smallest even integer, a minimum of four consecutive even integers will be required for the product of these to be divisible by 16. Same goes for starting integer as odd integer too.

Else, 15*16 is divisible by 16 and n = 1. 16 is divisible by 16 and n = 0, etc.

Re: DS: What is the positive integer n? [#permalink]

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18 Dec 2008, 12:38

LiveStronger wrote:

scthakur:

I am still confused how about when m= -1 and n= 3, m (m + 1) (m + 2) ... (m + n) is still divisible by 16

Thats a case for some value of m not for all values of m.

If m = 0, n could even be 1 but 1 doesnot work for all m. Similarly, n = 3 or 4 also donot work for all values of m. If n = 5, no matter the integer value of m, m (m + 1) (m + 2) ... (m + n) is divisible by 16.