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What is the positive integer n? (1) For every integer m, the [#permalink]
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14 Dec 2008, 12:48
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This topic is locked. If you want to discuss this question please repost it in the respective forum. What is the positive integer n? (1) For every integer m, the product m (m + 1) (m + 2) ... (m + n) is divisible by 16 (2) n^2  9n + 20 = 0 Source: Gmat Club Forum Discussion.
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Re: DS: What is the positive integer n? [#permalink]
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14 Dec 2008, 12:53
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.



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Re: DS: What is the positive integer n? [#permalink]
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14 Dec 2008, 13:05
It is little more difficult than that.
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Re: DS: What is the positive integer n? [#permalink]
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14 Dec 2008, 13:30
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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
Statement 2 says n is 4 or 5  INSUFF
Together, only 5 will work, so SUFF.



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Re: DS: What is the positive integer n? [#permalink]
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15 Dec 2008, 05:41
I did not understand it all. Can someone explain the solution of twilight in layman's term?
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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.



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Re: DS: What is the positive integer n? [#permalink]
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15 Dec 2008, 23:36
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.



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Re: DS: What is the positive integer n? [#permalink]
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16 Dec 2008, 02:28
I Dont think we can conclude anything from statement 1. the sequence can be: 2,3,4,5,6 => 5 terms 8,9,10 => 3 terms
From statement 2 we get 4 or 5.
Then only when we apply statement 2 to 1 we get C. We CANNOT get 4 or 5 from statement 1. If anyone has any explaination please post.



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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.



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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) ??



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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.



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Re: DS: What is the positive integer n? [#permalink]
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16 Dec 2008, 19:03
Why can't m be a negative number and the product, which is equal to ZERO is still divisible by 16 ?



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Re: DS: What is the positive integer n? [#permalink]
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16 Dec 2008, 20:01
I will go with C..and N=5.
see for EVERY integer m..(m=0 is just one example, if m=1 then N=4 will not work).. you need a minimum of n=5 i.e 2^4 in the sequence..



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Re: DS: What is the positive integer n? [#permalink]
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18 Dec 2008, 04:11
LiveStronger wrote: Why can't m be a negative number and the product, which is equal to ZERO is still divisible by 16 ? m can be a negative integer or can even be zero. However, n = 5 is the number that will cover any value of m (whether positive, negative, zero, etc.)



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Re: DS: What is the positive integer n? [#permalink]
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18 Dec 2008, 04:11
LiveStronger wrote: Why can't m be a negative number and the product, which is equal to ZERO is still divisible by 16 ? m can be a negative integer or can even be zero. However, n = 5 is the number that will cover any value of m (whether positive, negative, zero, etc.)



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Re: DS: What is the positive integer n? [#permalink]
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18 Dec 2008, 05:15
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



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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. Therefore, C
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Re: DS: What is the positive integer n?
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