saidov.mikhail wrote:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990. What is least possible value of n?
a) 10
b) 11
c) 12
d) 13
e) 14
990 = 9*10*11.
The product of all the integers from 1 to n, inclusive = n!.
We can plug in the answers for n.
Since the question stem asks for the LEAST POSSIBLE VALUE of n that is divisible by 9*10*11, start with the SMALLEST answer choice.
Answer choice A: n=10
10*9*8*7*6*5*4*3*2*1)/(
9*10*
11).
Only the values in blue cancel out.
11 cannot divide into 10!.
Eliminate A.
Answer choice B: n=11
(
11*10*9*8*7*6*5*4*3*2*1)/(
9*10*11).
Success!
All of the values in blue can divide into 11!.
The correct answer is
B.
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