Problem Solving

If n is the product of the integers from 1 to 70, inclusive, what is the greatest integer m for which 7^m is a factor of n/7^2?

(A) 2
(B) 7
(C) 9
(D) 11
(E) 14

OA: [spoiler]C: 9[/spoiler]
Source: Knewton

rahul.s wrote:If n is the product of the integers from 1 to 70, inclusive, what is the greatest integer m for which 7^m is a factor of n/7^2?

(A) 2
(B) 7
(C) 9
(D) 11
(E) 14

OA: [spoiler]C: 9[/spoiler]
Source: Knewton

n = 70!
n/7^2 = 70!/49
In 70 ! 7 comes in 7,14,21,28,35,42,49,56,63,70
Now we have excluded 49
Thus 7 occurs 9 times
Hence ,C should be the answer.

rahul.s wrote:If n is the product of the integers from 1 to 70, inclusive, what is the greatest integer m for which 7^m is a factor of n/7^2?

(A) 2
(B) 7
(C) 9
(D) 11
(E) 14

OA: [spoiler]C: 9[/spoiler]
Source: Knewton

If 7^m is a factor of n/7^2,

then 7^ (m + 2) is a factor of n

Need to know the greatest degree of 7 in 1 × 2 × 3 × ...69 × 70, is it 7^10? NOPE, do not forget 49, YEAH, it is 7^11. Hence, the greatest integer m for which 7^ (m + 2) is a factor of n, is 11 - 2 = [spoiler]9[/spoiler].

[spoiler]C[/spoiler]

A very easy question since it is written n/7^2
We can easily identify 49
Also,in the answer choices 8 should also be given to confuse the test-takers.
Then there could have been chances of ppl answering 10-2 =8 is the answer.
I am sure if sanju09 had framed the ques. it would have been something I had written above.
What-say??

rahul.s wrote:If n is the product of the integers from 1 to 70, inclusive, what is the greatest integer m for which 7^m is a factor of n/7^2?

(A) 2
(B) 7
(C) 9
(D) 11
(E) 14

OA: [spoiler]C: 9[/spoiler]
Source: Knewton

when 70! div by 7-------->10 is the quotient
10/7------>1 is the q

total 11 times 7

7^11/7^2=7^9-------> 9 is the ans