BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

witness war

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

witness war

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]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 246
Joined: Mon May 19, 2008 7:34 am
Location: Texaco Gas Station
Thanked: 7 times

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?
Cubicle Bound Misfit
Top
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Thu Feb 12, 2009 7:40 am
Location: Sweden
GMAT Score:770

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.
Top
Legendary Member
Posts: 621
Joined: Wed Apr 09, 2008 7:13 pm
Thanked: 33 times
Followed by:4 members

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
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 246
Joined: Mon May 19, 2008 7:34 am
Location: Texaco Gas Station
Thanked: 7 times

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
Cubicle Bound Misfit
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

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 :)
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Legendary Member
Posts: 683
Joined: Tue Jul 22, 2008 1:58 pm
Location: Dubai
Thanked: 73 times
Followed by:2 members

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 :)
Top
Legendary Member
Posts: 1035
Joined: Wed Aug 27, 2008 10:56 pm
Thanked: 104 times
Followed by:1 members

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 :)
Top
Legendary Member
Posts: 621
Joined: Wed Apr 09, 2008 7:13 pm
Thanked: 33 times
Followed by:4 members

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 :)
Top
Legendary Member
Posts: 683
Joined: Tue Jul 22, 2008 1:58 pm
Location: Dubai
Thanked: 73 times
Followed by:2 members

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 :)
Top
Legendary Member
Posts: 621
Joined: Wed Apr 09, 2008 7:13 pm
Thanked: 33 times
Followed by:4 members

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 :)
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

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

ianstewartgmat.com
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

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?
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Post new topic Post Reply
• Page 1 of 1