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Does the integer K have a factor p such that 1 < p

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Director
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Does the integer K have a factor p such that 1 < p [#permalink] New post 24 Dec 2007, 16:16
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Does the integer K have a factor p such that 1 < p <k>= 4!

2. 13! + 2 <= k <= 13! + 13

Can someone explain the official answer? it is included in the picture.

I don't see how K necessary could have a factor of p according to statement 2.


13! = 6227020800

Lets say K = 13! + 4 = 6227020804

and p = 6227020803

p is not a factor of k

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Director
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 [#permalink] New post 24 Dec 2007, 17:31
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Rephrase the question: Does the integer K have a factor p such that 1 < p <k>4!

this tells us that K is greater than 4*3*2*1 or K>24

there are plenty of prime numbers and non-prime numbers that are greater than 24.

INSUFFICIENT


2. 13! + 2 <= k <= 13! + 13

this tells us that K is NOT a prime number. We know this because each of the numbers being added in there is a factor of 13!

Example:

13*12*11*10*9*8*7*6*5*4*3*2*1 + 2 is not prime because 2 is a factor
13*12*11*10*9*8*7*6*5*4*3*2*1 + 5 is not prime because 5 is a factor
13*12*11*10*9*8*7*6*5*4*3*2*1 + 13 is not prime because 13 is a factor

Here's the rule to remember:

for any number that has factor X, that number + X is still divisible by X

like 99 is divisible by 11 so 99+11 must be divisible by 11 as well. It's the same concept tested with huge numbers

13! is divisible by 2, 3, 4, 5...13 so 13! + 2, 3, 4, 5...13 must be divisible by any number between 2 and 13.

because of this Statement 2 tells us that K is NOT a prime number, answering the original question does K have a factor P between 1 and K. The answer is YES
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Re: DS from GMATPREP: Does the integer K have a factor p [#permalink] New post 25 Dec 2007, 23:43
gmatnub wrote:
Does the integer K have a factor p such that 1 < p <k>= 4!

2. 13! + 2 <= k <= 13! + 13

Can someone explain the official answer? it is included in the picture.

I don't see how K necessary could have a factor of p according to statement 2.


13! = 6227020800

Lets say K = 13! + 4 = 6227020804

and p = 6227020803

p is not a factor of k


bah fell for the 1 trap. forgot k could be prime.
Re: DS from GMATPREP: Does the integer K have a factor p   [#permalink] 25 Dec 2007, 23:43
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