age wrote:

tarek99 wrote:

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?

A. 10

B. 12

C. 14

D. 16

E. 18

please show the fastest way to solve this.

thanks

Well ..I think question should read as

3^k ....i.e, If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which

3^k is a factor of p?

Then C ..14 will be correct..

I agree. If C is the OA, then the questions should read as 3^k giving 14 as the answer.

Although if its not 3^k, then another interpretation of 3k could be 300 + k instead of 3*k, because 3*k makes the question silly. This means that when k=10, we get 310 and not 3*10 = 30

Thus proceeding with the "300 + k" assumption, we get:

P = 30!

Option A: 310

=> 310 = 2 * 5 * 31

=> 31 is a prime and is not present in 30!

Thus 310 is not a factor of P

=> A is Eliminated

Option B: 312

=> 312 = 2^3 * 3 * 13

Thus 312 is a factor of P

=> B is the correct answer !Option C: 314

=> 314 = 2 * 157

=> 157 is a prime and is not present in 30!

Thus 314 is not a factor of P

=> C is Eliminated

Option D: 316

=> 316 = 2^2 * 79

=> 79 is a prime and is not present in 30!

Thus 316 is not a factor of P

=> D is Eliminated

Option E: 318

=> 310 = 2 * 3 * 53

=> 53 is a prime and is not present in 30!

Thus 318 is not a factor of P

=> E is Eliminated

ANS: B

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