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Gmat prep problem- 2

Expert replies
Source: — Problem Solving |

by GMATGuruNY » Fri Nov 05, 2010 7:48 am
sugmomo wrote:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is multiple of 990, what is the least value of n?

A. 10
B. 11
C. 12
D. 13
E. 14
The product of all the integers 1 to n is n!. We need the smallest integer value of n such that n! will be divisible by 990.

990 = 10*99 = 2*5*9*11. Thus, n! must be divisible by 2, 5, 9 and 11.

If n=10, 10! will not be divisible by 11. Eliminate A.
If n=11, 11! will be divisible by 2, 5, 9, and 11. Thus, the smallest value of n that will work is n=11.

The correct answer is B.
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by sugmomo » Fri Nov 05, 2010 11:31 am
Thank you Guru :)


Thanks,
sugmomo
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by aftableo2006 » Sat Nov 06, 2010 12:58 am
sugmomo wrote:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is multiple of 990, what is the least value of n?

A. 10
B. 11
C. 12
D. 13
E. 14
the answer will be B
990=11*10*9 the product of all integers from i to n will be n! 11 has to be there in n! for its least value such that it is a multiple of 990 so the least value of n is 11
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