Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Oct 2014, 10:43

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is an integer, then x(x 1)(x k) must be evenly

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 08 Jun 2007
Posts: 583
Followers: 2

Kudos [?]: 72 [0], given: 0

If x is an integer, then x(x 1)(x k) must be evenly [#permalink] New post 04 Jan 2008, 20:38
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A -4
B -2
C -1
D 2
E 5

Show work please.
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3573
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 367

Kudos [?]: 1853 [0], given: 359

GMAT ToolKit User Premium Member
Re: PS - equation divisible by 3. [#permalink] New post 04 Jan 2008, 21:56
Expert's post
B

Obviously, N=x(x – 1)(x – 2) is product of 3 consecutive integer and N is divided by 3.
So, k should be equal 3n+2:
-7,-4,-1,2,5,8

-2 is out.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
Followers: 18

Kudos [?]: 322 [0], given: 1

Premium Member
Re: PS - equation divisible by 3. [#permalink] New post 04 Jan 2008, 23:20
walker wrote:
B

Obviously, N=x(x – 1)(x – 2) is product of 3 consecutive integer and N is divided by 3.
So, k should be equal 3n+2:
-7,-4,-1,2,5,8

-2 is out.


this ps works for me, but wastes time. I see yr approach helpful, but I am not clear why k should be 3n+2. Maybe this is a basis, but I cannt get it. help Pls
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3573
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 367

Kudos [?]: 1853 [0], given: 359

GMAT ToolKit User Premium Member
Re: PS - equation divisible by 3. [#permalink] New post 05 Jan 2008, 01:26
Expert's post
Take a look at the integer line:

-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

we will use 3 colors to mark numbers.

-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

To catch number that is divisible by 3 we should have 3 different colors (numbers with different reminders)
we can substitute any number for a number with the same color (reminder).

1. at k=2: N=x(x – 1)(x – 2) - we have 3 numbers with different reminders.
2. Now we can go back or forward from number 2 by adding or subtracting 3.

Hope this help
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

VP
VP
avatar
Joined: 22 Nov 2007
Posts: 1102
Followers: 6

Kudos [?]: 135 [0], given: 0

Re: PS - equation divisible by 3. [#permalink] New post 05 Jan 2008, 03:11
ashkrs wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A -4
B -2
C -1
D 2
E 5

Show work please.


if we substitute x with 0 or 1 we always obtain 0, which is always evenly divisible by three (maybe the question should have excluded this 2 values for x).

let's try with x=2...the only value of k for which we don't have an even integer in the division is -2, therefore OA can be B
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3403
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 164 [0], given: 2

Re: PS - equation divisible by 3. [#permalink] New post 05 Jan 2008, 04:24
i was stuck between -2 and -4

lets see

if we have -4 then

if x=3 everything is divisible (no need to look at that)
if x=5 or 7, 2, 1 (i.e hint look at x=prime number)

you will quickly notice that -2 works..

B it is..
Manager
Manager
User avatar
Joined: 04 Jan 2008
Posts: 85
Followers: 1

Kudos [?]: 10 [0], given: 0

Re: PS - equation divisible by 3. [#permalink] New post 05 Jan 2008, 05:14
ANSWER IS -2.
Any one of 3 consecutive integers is divisible by 3.
so, we have x, x-1 and x-k, for them to be consecutive,
ie we have x-1, x and x-k,
so if x-k = x+1, then they are consecutive.
so, from above k=-1.
also remember that when you add multiples of 3 to a no. divisible by 3 it again gives multiple of 3, so try adding -3, 0, 3, and 6 to -1
you get all but -2
SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
Followers: 18

Kudos [?]: 322 [0], given: 1

Premium Member
Re: PS - equation divisible by 3. [#permalink] New post 05 Jan 2008, 18:00
walker wrote:
Take a look at the integer line:

-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

we will use 3 colors to mark numbers.

-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

To catch number that is divisible by 3 we should have 3 different colors (numbers with different reminders)
we can substitute any number for a number with the same color (reminder).

1. at k=2: N=x(x – 1)(x – 2) - we have 3 numbers with different reminders.
2. Now we can go back or forward from number 2 by adding or subtracting 3.

Hope this help

Hi walker,

you seems to think automatically "k should be equal to 3n+2" after you see problem, right? can you discribe that process of thinking? Thanks!
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3573
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 367

Kudos [?]: 1853 [0], given: 359

GMAT ToolKit User Premium Member
Re: PS - equation divisible by 3. [#permalink] New post 05 Jan 2008, 23:31
Expert's post
sondenso wrote:
walker wrote:
Take a look at the integer line:

-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

we will use 3 colors to mark numbers.

-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

To catch number that is divisible by 3 we should have 3 different colors (numbers with different reminders)
we can substitute any number for a number with the same color (reminder).

1. at k=2: N=x(x – 1)(x – 2) - we have 3 numbers with different reminders.
2. Now we can go back or forward from number 2 by adding or subtracting 3.

Hope this help

Hi walker,

you seems to think automatically "k should be equal to 3n+2" after you see problem, right? can you discribe that process of thinking? Thanks!


The problem took 15 sec for me and my way was exact as described above.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Director
User avatar
Joined: 08 Jun 2007
Posts: 583
Followers: 2

Kudos [?]: 72 [0], given: 0

Re: PS - equation divisible by 3. [#permalink] New post 06 Jan 2008, 11:07
ashkrs wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A -4
B -2
C -1
D 2
E 5

Show work please.


Well I got this question wrong because I did some calculations wrong and I thought my process was wrong . But I reworked again with same process and found B.

for x(x-1)(x-k) to be divisible by 3 , x + x-1 + x -k => 3x - ( k+1 ) should be divisible by 3
quickly substituting all values here

for -4 , 3x - ( -4 + 1 ) = 3x + 3 ->divisible by 3
for -2 , 3x - ( -2 + 1 ) = 3x - 1 not divisble by 3
for -1 , 3x - ( -1 + 1 ) = 3x ->divisible by 3
for 2 , 3x - ( 2 + 1 ) = 3x + 3 ->divisible by 3
for 5 , 3x - ( 5 + 1 ) = 3x - 6 ->divisible by 3

So B.
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 197 [0], given: 0

Re: PS - equation divisible by 3. [#permalink] New post 06 Jan 2008, 12:27
ashkrs wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A -4
B -2
C -1
D 2
E 5

Show work please.


picked 11 for x. 11(11-)(11-k) --> 11(10)(11--2) -2 is the only one that works.

I like walker's approach b/c picking numbers can get u into trouble...

B
SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
Followers: 18

Kudos [?]: 322 [0], given: 1

Premium Member
Re: PS - equation divisible by 3. [#permalink] New post 06 Jan 2008, 20:22
ashkrs wrote:
ashkrs wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A -4
B -2
C -1
D 2
E 5

Show work please.


Well I got this question wrong because I did some calculations wrong and I thought my process was wrong . But I reworked again with same process and found B.

for x(x-1)(x-k) to be divisible by 3 , x + x-1 + x -k => 3x - ( k+1 ) should be divisible by 3
quickly substituting all values here

for -4 , 3x - ( -4 + 1 ) = 3x + 3 ->divisible by 3
for -2 , 3x - ( -2 + 1 ) = 3x - 1 not divisble by 3
for -1 , 3x - ( -1 + 1 ) = 3x ->divisible by 3
for 2 , 3x - ( 2 + 1 ) = 3x + 3 ->divisible by 3
for 5 , 3x - ( 5 + 1 ) = 3x - 6 ->divisible by 3

So B.


ashkrs,

I like this approach,
I forgot the rule that the sum of the number that is divisible by 3 must evenly devide by 3. Thank you
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 19 Dec 2007
Posts: 87
Followers: 1

Kudos [?]: 20 [0], given: 0

Re: PS - equation divisible by 3. [#permalink] New post 08 Jan 2008, 05:32
ashkrs wrote:
ashkrs wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A -4
B -2
C -1
D 2
E 5

Show work please.


Well I got this question wrong because I did some calculations wrong and I thought my process was wrong . But I reworked again with same process and found B.

for x(x-1)(x-k) to be divisible by 3 , x + x-1 + x -k => 3x - ( k+1 ) should be divisible by 3
quickly substituting all values here

for -4 , 3x - ( -4 + 1 ) = 3x + 3 ->divisible by 3
for -2 , 3x - ( -2 + 1 ) = 3x - 1 not divisble by 3
for -1 , 3x - ( -1 + 1 ) = 3x ->divisible by 3
for 2 , 3x - ( 2 + 1 ) = 3x + 3 ->divisible by 3
for 5 , 3x - ( 5 + 1 ) = 3x - 6 ->divisible by 3

So B.


Hi, I went first with consecutive integers rule, which is also a good way to solve the problem..but this one is very nice. It is really: you are to have at least one factor which is divisible by three so the product of three different integers be divisible by three :-)
Thanks a lot for the idea
Re: PS - equation divisible by 3.   [#permalink] 08 Jan 2008, 05:32
    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic If x is an integer, then x(x - 1)(x - k) must be evenly dimitri92 12 22 May 2010, 04:15
Experts publish their posts in the topic If x is an integer, then x(x 1)(x k) must be evenly gmatnub 9 29 Jun 2008, 21:06
If x is an integer, then x(x 1)(x k) must be evenly shobuj 11 24 Apr 2008, 07:40
If x is an integer, then x(x 1)(x k) must be evenly ani 14 14 May 2007, 09:42
If x is an integer, then x(x 1)(x k) must be evenly sujayb 2 22 Nov 2006, 12:32
Display posts from previous: Sort by

If x is an integer, then x(x 1)(x k) must be evenly

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.