Practice test question

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Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Fri Mar 06, 2009 8:19 am

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

GMAX

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Source: Beat The GMAT — Problem Solving | Fri Mar 06, 2009 8:19 am

Mr2Bits: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Wed Jan 07, 2009 1:00 pm; Location: Tampa, FL; Thanked: 9 times; GMAT Score:630

by Mr2Bits » Fri Mar 06, 2009 8:24 am

11. Least prime number that is a multiple of 990.

Whats the OA?

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Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Fri Mar 06, 2009 9:03 am

OA is B. Can you explain how you got the answer?
thanks

GMAX

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bmlaud: Master | Next Rank: 500 Posts; Posts: 174; Joined: Thu Jan 08, 2009 12:04 am; Thanked: 5 times; GMAT Score:620

by bmlaud » Fri Mar 06, 2009 9:08 am

990 has 4 prime factors 2,3,5,11
the minimum no. that n can take should be 11.

"Great works are performed not by strength but by perseverance."

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Fri Mar 06, 2009 10:22 am

n*(n-1)*(n-2)*.......1 =n!
=>n!=990k (k an integer)
=>n!=9*2*5*11 (for the smallest n, lets take k=1)

if n=10, 10!=10*9*8..1 (we cant get 990, which has a 11)
so the least value of n could be 11, so that 11! would give the 11 we need to make a 990 atleast.

n=11

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Mr2Bits: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Wed Jan 07, 2009 1:00 pm; Location: Tampa, FL; Thanked: 9 times; GMAT Score:630

by Mr2Bits » Fri Mar 06, 2009 10:23 am

Baldini wrote:OA is B. Can you explain how you got the answer?
thanks

When you see the following : product of all the integers from 1 to n

Think PRIME numbers. Of the numbers listed, 11 is the smallest prime number that is a multiple of 990

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