For an integer n, the function f(n) is defined as the product of all

Question

For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10

A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III

Bunuel · Accepted Answer

f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.

Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.

Answer: E.

Bunuel · Answer

chetan2u · Answer

F(n)=1*2*3*...n where n>10
So f(n)=1*2*3*....*10*..*n
Thus f(n) is product of all numbers till n and at least till 1
 f(n) and f(n)+1 are co-prime, as they are consecutive terms.

Therefore f(n)+1 will not have any common factor that f(n) has..
So all numbers till 10 will NOT be factors

E

US09 · Answer

f(n) can be expressed as n! hence n! + 1 will be a prime integer and none of the integers smaller than n can be a factor of the same. Hence, E.

chetan2u · Answer

Although the second part that none of the integers smaller than n can be a factor of n!+1 is correct..

But that n!+1 will be prime integer may not be correct every time..
Example 3!+1=6+1=7 yes..
4!+1=24+1=25....Not a prime 
5!+1=120+1=121=11^2... Again not aprime integer..

So the point is that n!+1 will not be a multiple of any prime number <n

ScottTargetTestPrep · Answer

Notice that f(n) = n!. Since two consecutive integers cannot share any of the same prime factors, f(n) and f(n) + 1 cannot share any of the same prime factors. Since f(n) is greater than 10!, and 10! has prime factors of 2, 3, 5, and 7, we see that 2, 3, and 2 x 5 = 10 cannot be primes of f(n) + 1.

Answer: E

ScottTargetTestPrep · Answer

We must remember that f(n) and f(n) + 1 WON’T SHARE ANY OF THE SAME PRIME FACTORS because they are consecutive integers.

So, since n is greater than 10, we see that f(n) will have prime factors of at least 2, 3, 5, and 7. Thus, 2, 3, and 10 won’t be factors of f(n) + 1.

Answer: E

chrtpmdr · Answer

Is this a applicable rule for other problems or just "made up" for this problem? 
Because if I try it wih 4! => 4*3*2*1 = 24 + 1 will result in 25 which is not a prime integer.

bumpbot · Answer

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For an integer n, the function f(n) is defined as the product of all

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