last day queries !! thanks

desiguy · Posted: Tue Jul 22, 2008 4:09 am Post subject: last day queries !! thanks

If n is a positive integer and the product of all the intergers from 1 to n, inclusive is 990, what is the least possible value of n ?

choice:
10 or 11

Ans: is 11.

My answer is 10 because if the integers are say (1 and 10), it meets the criteria above !!

VP_Tatiana · Posted: Tue Jul 22, 2008 12:43 pm Post subject:

I'm not sure I understand the question correctly.

The product of all the numbers from 1 to 6 inclusive is 720, and the product of all the numbers from 1 to 7 inclusive is 5040. So, it does not seem that there exists an n such that the product of the numbers from 1 to n equals 990.

Is there an "answer does not exist" answer choice?

Tatiana

parallel_chase · Posted: Tue Jul 22, 2008 1:40 pm Post subject:

DUDE you have made the same mistake while re posting the question.

Here is the actual question.

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 ?

If I take you answer which is 10

Then, what the question stem means is 10! is a multiple of 990.

10! = 10*9*8*7*6*5*4*3*2*1=3628800

990 = 9*10*11

I'll rephrase the question for you.

Is 3628800 a multiple of 990?

The answer is no if n = 10, simply because n! which is 10! does not have 11

Now lets look at 11

11! = 11*10*9*8*7*6*5*4*3*2*1
990 =9*10*11

In this case answer is yes 11! is a multiple of 990.

In the test all you have to do is look at the prime factors.

if x is a multiple of y, then x should have all the prime factors of y, but it is not necessary for y to have all the prime factors of x.

I hope this clears everything. Let me know if you still have any doubts.

All the Best.

gmatutor · Posted: Tue Jul 22, 2008 5:10 pm Post subject: Prime factor

Prime factor 990.

990 = 2 X 5 X 3^2 X 11

Since the largest prime factor of 990 is 11, choose 11 it must be the least possible value for n.

egybs · Posted: Tue Jul 22, 2008 8:33 pm Post subject: Re: Prime factor

gmatutor · Posted: Wed Jul 23, 2008 2:09 pm Post subject:

Absolutely!

Forgive my imprecise language.

egybs · Posted: Wed Jul 23, 2008 2:11 pm Post subject:

You're forgiven! Wink