GMAT Prep problem

[Nerony]

If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
10
11
12
13
14

OA

SPOILER: B

Can anyone help to understand how we come to this answer?

[paul2432]

Originally Posted by Nerony

If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
10
11
12
13
14

OA

SPOILER: B

Can anyone help to understand how we come to this answer?

990 = 11 x 5 x 3 x 3 x 2. If a number is a multiple of 990, it must also be a multiple of 11, therefore n must be at least 11.

Paul

[zapped]

n should be a multiple of 9 and 11...therefore least should be 11. IMO B

[atombomb_blast]

If we split 990 = 11 * 90 ... so the least value is 11

[ashk29]

The question states that -the product is a multiple of 990 if its a multiple of 990 the we can write

product = 1*2*......*n = 990*k , where k is any integer

also 990 = 9*11*2*5 thus if the product is to be a multiple of 990 , it should be divisible by 990

product/990 = an integer = k

so in the product there should be 9,2,5,and 11 so we can say

the product ( minimum) = 1*2*3*....*8*9*10*11

hence the minimum value of n = 11

[Lock]

The easiest way to arrive at this result would, probably, be to break 990 into its factors and take the largest prime of this resultant series. Here, 990 is the product of three consequtive integers 9*10*11. So, the 'n' in this case, is the last digit, which is 11.

[riteshbindal]

Thanks all.

[kssshah]

i agree with Lock. That is the quickest way to solve this. Takes less than a minute.

[MBAchase]

IMO B