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this is really confusing !!

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by desiguy » Tue Jul 22, 2008 4:42 am
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 !!
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by Canman » Tue Jul 22, 2008 5:06 am
Is this the entire problem copied correctly? Something doesn't look right.
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by pepeprepa » Tue Jul 22, 2008 5:13 am
Yeap,
n does not exist for "990=n!"
6!=720
7!=5040
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Re: this is really confusing !!

by parallel_chase » Tue Jul 22, 2008 5:19 am
desiguy wrote: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 !!
What I could gauge from the question is

n! =990

n (n-1)(n-2)......(n-k)

k=n-1

and n is a positive integer

answer has to be between 6 and 7

either there is something wrong with the question or in my understanding. Pls do let me know.
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error rectified.....please solve

by desiguy » Tue Jul 22, 2008 5:29 am
Spot - an error in problem -

reworded:
If n is a positive integer and the product of all the intergers from 1 to n, inclusive, is a multiple of 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 !!
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Re: error rectified.....please solve

by parallel_chase » Tue Jul 22, 2008 5:35 am
desiguy wrote:Spot - an error in problem -

reworded:
If n is a positive integer and the product of all the intergers from 1 to n, inclusive, is a multiple of 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 !!
Thanks for correcting the question.

Answer will always be 11

Reasoning

990= 9*11*10 = 3*3*11*2*5

From 1! - 10! everything contains all the prime factors of 990 but they dont contain 11 as a prime factor, therefore answer has to be 11! or n=11

Let me know if you still have any doubts.
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by newera » Tue Jul 22, 2008 5:45 am
start by looking at multiples of 990. those that jump out immediately are 11*90 and 10*99.

So you've now narrowed N down to 11 and 10.

start by looking at the greater number first. 11*10*9....already thats a possibility.

ok, lets consider 10. 10*9*8*7*6*5*4*3*2*1...will any of the number after 10 give you a product of 99? 99 is a multiple of 3,9,11, 99, 33, 30...those numbers under 10...the answer is no.

that was my reasoning. hope it helps.
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by newera » Tue Jul 22, 2008 5:48 am
start by looking at multiples of 990. those that jump out immediately are 11*90 and 10*99.

So you've now narrowed N down to 11 and 10.

start by looking at the greater number first. 11*10*9....already thats a possibility.

ok, lets consider 10. 10*9*8*7*6*5*4*3*2*1...will any of the number after 10 give you a product of 99? 99 is a multiple of 3,9,11, 99, 33, 30...those numbers under 10...the answer is no.

that was my reasoning. hope it helps.
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by desiguy » Tue Jul 22, 2008 6:42 am
not understood !!! i fail to understand the question itself. please simplify the question for me. thanks



newera wrote:start by looking at multiples of 990. those that jump out immediately are 11*90 and 10*99.

So you've now narrowed N down to 11 and 10.

start by looking at the greater number first. 11*10*9....already thats a possibility.

ok, lets consider 10. 10*9*8*7*6*5*4*3*2*1...will any of the number after 10 give you a product of 99? 99 is a multiple of 3,9,11, 99, 33, 30...those numbers under 10...the answer is no.

that was my reasoning. hope it helps.
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by newera » Tue Jul 22, 2008 6:50 am
ok, question basically says you have numbers 1 thru n. the product of any of these numbers should = 990.

so we can tackle this by asking, ok, what are some numbers that, when multiplied together, =990. we want the LOWEST value.

so when i looked 10*99 and 11*90, i looked at the two smallest numbers.

and then went from there.

if you pick 10, you look at numbers 1 thur 10. do any of them, when multiplied together =990? the answer is no. you can list out the numbers to help if you want. 10,9,8,7,6,5....1. if you pick 10, then you need 99. none of those numbers' products give you 99.

if you pick 11, you look at numbers 1 thru 11. do any of them, when multiplied together =990. YES. in fact, 11*10*9....perfect.

hope thats better.
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thats super ! thanks a lot.

by desiguy » Tue Jul 22, 2008 9:18 am
newera wrote:ok, question basically says you have numbers 1 thru n. the product of any of these numbers should = 990.

so we can tackle this by asking, ok, what are some numbers that, when multiplied together, =990. we want the LOWEST value.

so when i looked 10*99 and 11*90, i looked at the two smallest numbers.

and then went from there.

if you pick 10, you look at numbers 1 thur 10. do any of them, when multiplied together =990? the answer is no. you can list out the numbers to help if you want. 10,9,8,7,6,5....1. if you pick 10, then you need 99. none of those numbers' products give you 99.

if you pick 11, you look at numbers 1 thru 11. do any of them, when multiplied together =990. YES. in fact, 11*10*9....perfect.

hope thats better.
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