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by sanju09 » Wed Apr 15, 2009 3:18 am
What is the least possible value of n?

(1) The product of all the integers from 1 to n, inclusive, is a multiple of 990.

(2) n is a positive integer.



[spoiler]MBM to witness war of words between A and C. :roll: [/spoiler]
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by cubicle_bound_misfit » Wed Apr 15, 2009 6:02 am
IMO it is C. as least value of n which is a multiple of 11 can be determined from positive and negative both ways.
what is OA?
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by alexhard » Wed Apr 15, 2009 12:31 pm
I think (2) is useless. If n is negative, the product of all integers from 1 to n is 0, which isn't a multiple of 990, so A.
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by vittalgmat » Wed Apr 15, 2009 1:09 pm
As u mentioned, this is indeed tricky-- choose between A and C.

IMO A.
Product of integer from 1 to n (==> n!) is always a +ve number. This number is a multiple of 990 a +ve number. Then answer ends up as 11!.
coz 990 = 2 *3^2 *5 *11. The highest number is 11 and 11! includes 2, 3^2 and 5 as well.

Stmt 2: is N/S.

Can Ian/Stuart clarify pls.

thanks
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by cubicle_bound_misfit » Wed Apr 15, 2009 9:07 pm
yep I overlooked the fact that consecutive integers are between 1 and n hence for n negative it would become 0.

hence 2 is not needed.
my changed( following the footsteps of my country's politicians :-)) opinion it is A
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by sanju09 » Thu Apr 16, 2009 2:16 am
alexhard wrote:I think (2) is useless. If n is negative, the product of all integers from 1 to n is 0, which isn't a multiple of 990, so A.
Can't we say 0 the multiple of all integers? I'm only asking :)
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by mals24 » Thu Apr 16, 2009 11:27 am
sanju09 wrote: Can't we say 0 the multiple of all integers? I'm only asking :)
Well good question to ask.

0 is a multiple of all integers, but a factor of none.

Based on the above rule my vote goes for C.

St1: take n = -3
the number of all integers from 1 to -3 is 0, which is a multiple of 990

take n = 11
the number of all integers from 1 to 11 is a multiple of 990.

Insuff

St2: n is positive...Insuff

Combining 1+2
the least value of n is 11.

Just my 2 cents :)
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by scoobydooby » Thu Apr 16, 2009 11:43 am
thats convincing mals24.

so far i have been thinking: from 1 to n means we go rightwards from 1. didnt realize it could mean going backwards as well.

this question tests math and nuances of sc and critical reasoning :)
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by vittalgmat » Thu Apr 16, 2009 12:27 pm
mals24 wrote:
sanju09 wrote: Can't we say 0 the multiple of all integers? I'm only asking :)
Well good question to ask.

0 is a multiple of all integers, but a factor of none.

Based on the above rule my vote goes for C.

St1: take n = -3
the number of all integers from 1 to -3 is 0, which is a multiple of 990

take n = 11
the number of all integers from 1 to 11 is a multiple of 990.

Insuff

St2: n is positive...Insuff

Combining 1+2
the least value of n is 11.

Just my 2 cents :)
This is a good point. but from the GMAC perspective, when they say 1 to n, I think they mean numbers increasing from 1 and not decreasing from 1. Otherwise the phrase "1 to " in "1 to n" is meaningless, coz we can go either way from 1.

my 1 cent as well :)
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by mals24 » Thu Apr 16, 2009 12:45 pm
vittalgmat wrote: This is a good point. but from the GMAC perspective, when they say 1 to n, I think they mean numbers increasing from 1 and not decreasing from 1. Otherwise the phrase "1 to " in "1 to n" is meaningless, coz we can go either way from 1.

my 1 cent as well :)
Actually that point confused me as well, whether from 1 to n means increasing order or not. I guess we'll have to wait for Sanju or any of the GMAT experts to comment on this.

But I feel from 1 to n could include negative values of n as well. From 1 you could go left or right on the number line.

Just my 0.5 cents :)
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by vittalgmat » Thu Apr 16, 2009 12:54 pm
mals24 wrote:
vittalgmat wrote: This is a good point. but from the GMAC perspective, when they say 1 to n, I think they mean numbers increasing from 1 and not decreasing from 1. Otherwise the phrase "1 to " in "1 to n" is meaningless, coz we can go either way from 1.

my 1 cent as well :)
Actually that point confused me as well, whether from 1 to n means increasing order or not. I guess we'll have to wait for Sanju or any of the GMAT experts to comment on this.

But I feel from 1 to n could include negative values of n as well. From 1 you could go left or right on the number line.

Just my 0.5 cents :)
I will PM Ian/Stuart and get their Dollars
but for now my 0.25cents :)
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by Ian Stewart » Thu Apr 16, 2009 1:31 pm
On the GMAT, the phrase "from 1 to n" should be taken to mean "from 1 up to n". That said, the GMAT test will never be ambiguous on this point. To see how this would be worded on the real test, you can look at:

www.beatthegmat.com/ps-2-t15260.html

Notice that they begin the question by stating that n is a positive integer, so it is absolutely clear what the phrase "from 1 to n" means.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by sanju09 » Fri Apr 17, 2009 1:01 am
So, according to what Ian has quoted and mentioned, may we interpret the following, links?

If n is a +ve integer, '1 to n' is ascending or stand-still (for n = 1); if n is a -ve integer, '1 to n' is descending; and in the absense of any clues about n....?

For me, the phrase 'A to B' is a vector, isn't that so?
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