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For nonnegative integers x , y , and m , what is the greatest value

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For nonnegative integers x , y , and m , what is the greatest value [#permalink] New post 23 Jan 2016, 01:08
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For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?

(1) y=x−1

(2) x is a prime number
[Reveal] Spoiler: OA

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For nonnegative integers x , y , and m , what is the greatest value [#permalink] New post 23 Jan 2016, 01:23
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shasadou wrote:
For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?

(1) y=x−1

(2) x is a prime number



Hi,
A Good Q..
the Q statement is "For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?"
What doe sthis mean..
It means the largest power of x that is there in y!..
formula is y/x + y/x^2.. and so on till the fraction y/x^z becomes less than 1..
x is a prime number or the biggest prime in any integer..

lets see the sentences..
(1) y=x−1
this means x^m in (x-1)!..
y/x + y/x^2.. and so on means (x-1)!/x..
if x is prime, answer is 0..
if not it will depend on x..
say x=6, so y=5..
check for 3s in 5! as 3 is the largest prime number in 6..
5/3=1 so m=1..
different answers
But we do not know if x is prime or what is the largest prime in the integer x..
insuff


(2) x is a prime number
since there is no corelation in y and x, we cannot answer ..
say y is 50 and prime is 5, then it is 50/5+50/25=12..
and say 4 and prime is 3then 4/3=1..
insuff..

combined .
we know that x is prime and y is x-1..
from this it becomes clear that y! or (x-1)! will not have x..
so power of x will be 0, or m=0..
suff
C
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Re: For nonnegative integers x , y , and m , what is the greatest value [#permalink] New post 23 Jan 2016, 13:21
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Aside: Whenever you see the word "non-negative," you should ask yourself "Why didn't they just say POSITIVE?"
The answer to this question is a big hint.
Non-negative is not the same as positive, since ZERO is a non-negative number and zero is not positive.
So, when you see the word "non-negative," be sure to consider the possibility that the number equals zero.

Cheers,
Brent
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Re: For nonnegative integers x , y , and m , what is the greatest value   [#permalink] 23 Jan 2016, 13:21
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For nonnegative integers x , y , and m , what is the greatest value

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