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number properties - multiples of 990

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number properties - multiples of 990

by lind0923 » Fri Nov 28, 2008 11:20 am
Hi all,
Happy Friday! :D Can anyone explain the fastest way to solve this problem?

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 the least possible value of n?

A. 10
B. 11
C. 12
D. 13
E. 14

Answer: B. 11

Thanks!
Alicia
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Re: number properties - multiples of 990

by muzali » Fri Nov 28, 2008 7:42 pm
lind0923 wrote:Hi all,
Happy Friday! :D Can anyone explain the fastest way to solve this problem?

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 the least possible value of n?

A. 10
B. 11
C. 12
D. 13
E. 14

Answer: B. 11

Thanks!
Alicia
Fastest way is by recognizing that 990 = 11*10*9
So any factor of 990 will be 11*10*9*(x)
x can be any number like 8 or 8*7 or 8*7*6 till 8*7*6*5*..*2*1
so 11 is the least number satisfying the condition, hence the answer.
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