Hi All,
This question is essentially just a 'clone' of the following one:
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For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is:
1. between 2 and 10
2. between 10 and 20
3. between 20 and 30
4. between 30 and 40
5. greater than 40
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It's based on the exact same principals; the main idea though is:
"The ONLY number that will divide into X and X+1 is 1."
In other words, NONE of the factors of X will be factors of X+1, EXCEPT for the number 1.
Here are some examples:
X = 2
X+1 = 3
Factors of 2: 1 and 2
Factors of 3: 1 and 3
ONLY the number 1 is a factor of both.
X = 9
X+1 = 10
Factors of 9: 1, 3 and 9
Factors of 10: 1, 2, 5 and 10
ONLY the number 1 is a factor of both.
Etc.
Knowing this....we can deduce....
1) 25! will have LOTS of different factors
2) NONE of those factors will divide into 25! + 1.
25! contains all of the primes from 2 through 23, inclusive, so NONE of those will be in 25! + 1. We don't even have to calculate which prime factor is smallest in 25! + 1; we know that it MUST be a prime greater than 23....and there's only one answer that fits.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Rich, can you please post this solution to that thread? Thank you!