gmat prep prime numbers

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vinviper1: Master | Next Rank: 500 Posts; Posts: 222; Joined: Tue Mar 25, 2008 3:52 pm; Thanked: 2 times

by vinviper1 » Sun Jun 08, 2008 6:44 pm

Wouldn’t the smallest prime factor be 2 here? Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Jun 08, 2008 6:44 pm

VerbalAttack: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Mon May 26, 2008 9:34 pm; Thanked: 3 times

by VerbalAttack » Mon Jun 09, 2008 1:07 am

Hi vinviper1,

h(100) = 2*4*...*100 ==> (1*2) * (2*2) * (3*2)...(50*2)

From the above breakdown, every prime number under 50 (<= 49) is a factor of h(100).

Now h(100)+1 will have none of the prime numbers under 50 (<=49) as a factor.

Think about this, 3 is a factor 6, 3 is not a factor of 6+1 or 6+2. Need to wait for 6+3 for the next multiple.
5 is a factor 10, 5 is not a factor of 10+1, 10+2, 10+3 or 10+4. Need to wait for 10+5 for the next multiple.

If N is a multiple of prime factor F, N+F is the next multiple of F.

So we are left with prime factors greater than 49.

Cheers

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gmatinjuly: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue May 27, 2008 6:03 am; Thanked: 5 times

by gmatinjuly » Mon Jun 09, 2008 3:46 am

Awesome reply Verbal Attack ...

Yeah it makes sense.....

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vinviper1: Master | Next Rank: 500 Posts; Posts: 222; Joined: Tue Mar 25, 2008 3:52 pm; Thanked: 2 times

by vinviper1 » Mon Jun 09, 2008 7:36 pm

I second that! Cheers mate!

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manu217: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sat Jun 07, 2008 11:09 am

by manu217 » Thu Jun 12, 2008 8:29 am

Hello VerbalAttack, could you please explain your reply?
The question states p is 'smallest prime factor', how did you get greater than 49?

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