Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 135

If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
Updated on: 09 Jul 2013, 09:59
Question Stats:
67% (01:21) correct 33% (02:15) wrong based on 635 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by anilnandyala on 15 Dec 2010, 07:19.
Last edited by Bunuel on 09 Jul 2013, 09:59, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
15 Dec 2010, 07:52
anilnandyala 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
4 2 1 2 5 We have the product of 3 integers: (x1)x(xk). Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. Next, if k=2 then we'll have (x1)x(x+2)=(x1)x(x1+3) > which means that (x1) and (x+2) will have the same remainder upon division by 3. Thus for k=2 we won't be sure whether (x1)x(xk) is divisible by 3. Answer: B. 30 second approach: 4 out of 5 values of k from answer choices must guarantee divisibility of some expression by 3. Now, these 4 values of k in answer choices must have some pattern: if we get rid of 2 then 4, 1, 2, and 5 creating arithmetic progression with common difference of 3, so 2 is clearly doesn't belong to this pattern. Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 358
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross)  Class of 2014
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
15 Dec 2010, 07:41
There is probably an easier way, but I just used the picking numbers option for this. I chose x=2 2(1)(2k) then just plugged in the answer choices for K until one wasn't evenly divisible by 3. B gives you 8. 8/3 is not an integer. B is the answer.
_________________
Go Blue!
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 10 Nov 2010
Posts: 142

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
03 Jan 2011, 22:00
Hi bunuel, I don't understand the problem language, it says
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
how does it matter whats the value of K, i can choose x = 3 and the expression will always be divisible by 3.
Am i missing any minor yet important point?



Math Expert
Joined: 02 Sep 2009
Posts: 47983

If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
04 Jan 2011, 03:22
vjsharma25 wrote: Hi bunuel, I don't understand the problem language, it says
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
how does it matter whats the value of K, i can choose x = 3 and the expression will always be divisible by 3.
Am i missing any minor yet important point? Stem says: "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" The important word in the stem is "MUST", which means that we should guarantee the divisibility by 3 no matter the value of x (for ANY integer value of x), so you cannot arbitrary pick its value. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 10 Nov 2010
Posts: 142

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
04 Jan 2011, 08:46
OK. Now i get it.
Thanks Bunuel.



Intern
Joined: 11 Nov 2010
Posts: 5

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
04 Jan 2011, 09:41
To be divisible by 3, one of these sequences must be divisible by 3.
X(X1) (Xk)
Any 3 sequence number will always be divisible by 3. So X(X1) (x2) is divisible by 3.
K = 2, divisible by 3 K= 5, also a sequence ( parallel ) divisible by 3 K= 1, sequence is (X1) X (X+1) so divisible by 3 K= 4, also a sequence ( parallel ) divisible by 3 K=2, not a sequence, may not be divisible by 3
So Answer is (B)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
04 Jan 2011, 19:49
anilnandyala 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
4 2 1 2 5 I am providing the theoretical explanation below. Once you get it, you can solve such questions in a few seconds in future! Notice a few things about integers: 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16...... Every number is a multiple of 1 Every second number is a multiple of 2 Every third number is a multiple of 3 Every fourth number is a multiple of 4 and so on... So if I pick any 3 consecutive integers, one and only one of them will be a multiple of 3: e.g. I pick 4, 5, 6 (6 is a multiple of 3) or I pick 11, 12, 13 (12 is a multiple of 3) etc.. x(x  1)(x  k) will be evenly divisible by 3 if at least one of x, x  1 and x  k is a multiple of 3. We know from above, (x  2)(x  1)x will have a multiple of 3 in it. Also, (x1)x(x + 1) will have a multiple of 3 in it because they both are products of 3 consecutive integers. So k can be 2 or 1. Eliminate these options. Now let me write down consecutive integers around x: (x5), (x  4), (x  3), (x  2), (x  1), x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5) etc (x  2)(x  1)x will have a multiple of 3 in it. x could be the multiple of 3, (x  1) could be the multiple of 3 or (x  2) could be the multiple of 3, in which case (x  5) will also be a multiple of 3. So in any case, (x  5)(x  1)x will have a multiple of 3 in it. So k can be 5. Similarly, (x1)x(x + 1) will have a multiple of 3 in it. x could be the multiple of 3, (x  1) could be the multiple of 3 or (x + 1) could be the multiple of 3, in which case (x + 4) will also be a multiple of 3. So in any case, (x  1)x(x + 4) will have a multiple of 3 in it. So k can be 4. We cannot say whether (x1)x(x + 2) will have a multiple of 3 in it and hence if k = 2, we cannot say whether the product is evenly divisible by 3. Answer (B).
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 309

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
05 Jan 2011, 01:29
a. 4 b. 2 [2 more than A] c. 1 [3 more than A] d. 2 [6 more than A] e. 5 [9 more than A]
nice, so we do have a pattern ... 4 answers have a difference of a multiple of 3 except B ... 3, 6, 9 are all multiples of 3
so we can select B without solving much
_________________
press kudos, if you like the explanation, appreciate the effort or encourage people to respond.
Download the Ultimate SC Flashcards



Manager
Joined: 02 Oct 2010
Posts: 109

Re: x(x – 1)(x – k)
[#permalink]
Show Tags
07 Jan 2011, 23:49
Bunuel wrote: anilnandyala 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
4 2 1 2 5 We have the product of 3 integers: (x1)x(xk). Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. Next, if k=2 then we'll have (x1)x(x+2)=(x1)x(x1+3) > which means that (x1) and (x+2) will have the same remainder upon division by 3. Thus for k=2 we won't be sure whether (x1)x(xk) is divisible by 3. Answer: B. 30 second approach: 4 out of 5 values of k from answer choices must guarantee divisibility of some expression by 3. Now, these 4 values of k in answer choices must have some pattern: if we get rid of 2 then 4, 1, 2, and 5 creating arithmetic progression with common difference of 3, so 2 is clearly doesn't belong to this pattern. Hope it helps. Bunnel, The second approach is too good... Very helpful,...



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
07 Mar 2014, 04:52
Plugged in value of x = 8 It comes up 8 x 7 x (8k) Checking for each option available 4 >>> 8+4 = 12.. Divisible by 3 2 >>> 8+2 = 10.. Not divisible by 3 1 >>> 8+1 = 9 .. Divisible by 3 2 >>> 82 = 6 .. Divisible by 3 5 >>> 85 = 3 .. Divisible by 3 Answer = B
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Joined: 20 Dec 2013
Posts: 245
Location: India

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
08 Mar 2014, 05:51
Hats off to Bunuel for the 30 sec. Approach!Couldn't visualize that solution!
Posted from my mobile device



Director
Joined: 17 Dec 2012
Posts: 637
Location: India

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
02 Aug 2014, 01:42
anilnandyala 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 Since x(x1)(xk) is divisible by 3, take a case when x(x1) is not divisible by 3 and so (xk) has to be divisible by 3. Let us take x=8 and x1=7. Only for the second option we do not get xk divisible by 3.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
02 Sep 2014, 00:21
VeritasPrepKarishma wrote: I am providing the theoretical explanation below. Once you get it, you can solve such questions in a few seconds in future!
Notice a few things about integers: 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16......
Every number is a multiple of 1 Every second number is a multiple of 2 Every third number is a multiple of 3 Every fourth number is a multiple of 4 and so on...
So if I pick any 3 consecutive integers, one and only one of them will be a multiple of 3: e.g. I pick 4, 5, 6 (6 is a multiple of 3) or I pick 11, 12, 13 (12 is a multiple of 3) etc..
x(x  1)(x  k) will be evenly divisible by 3 if at least one of x, x  1 and x  k is a multiple of 3. We know from above, (x  2)(x  1)x will have a multiple of 3 in it. Also, (x1)x(x + 1) will have a multiple of 3 in it because they both are products of 3 consecutive integers. So k can be 2 or 1. Eliminate these options. Now let me write down consecutive integers around x:
(x5), (x  4), (x  3), (x  2), (x  1), x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5) etc
(x  2)(x  1)x will have a multiple of 3 in it. x could be the multiple of 3, (x  1) could be the multiple of 3 or (x  2) could be the multiple of 3, in which case (x  5) will also be a multiple of 3. So in any case, (x  5)(x  1)x will have a multiple of 3 in it. So k can be 5.
Similarly, (x1)x(x + 1) will have a multiple of 3 in it. x could be the multiple of 3, (x  1) could be the multiple of 3 or (x + 1) could be the multiple of 3, in which case (x + 4) will also be a multiple of 3. So in any case, (x  1)x(x + 4) will have a multiple of 3 in it. So k can be 4.
We cannot say whether (x1)x(x + 2) will have a multiple of 3 in it and hence if k = 2, we cannot say whether the product is evenly divisible by 3.
Answer (B). Quote: Plz Could you please explain how x5 will also be a multiple of 3. I couldnot understand that part. If (x  2) is a multiple of 3, (x  5), a number 3 places away from (x  5) will also be divisible by 3. Say (x  2) = 9 (a multiple of 3) then (x  5) = 6 (previous multiple of 3)
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 06 Aug 2013
Posts: 84

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
03 Oct 2014, 08:45
Bunuel wrote: anilnandyala 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
4 2 1 2 5 We have the product of 3 integers: (x1)x(xk). Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. Next, if k=2 then we'll have (x1)x(x+2)=(x1)x(x1+3) > which means that (x1) and (x+2) will have the same remainder upon division by 3. Thus for k=2 we won't be sure whether (x1)x(xk) is divisible by 3. Answer: B. 30 second approach: 4 out of 5 values of k from answer choices must guarantee divisibility of some expression by 3. Now, these 4 values of k in answer choices must have some pattern: if we get rid of 2 then 4, 1, 2, and 5 creating arithmetic progression with common difference of 3, so 2 is clearly doesn't belong to this pattern. Hope it helps. Hi Bunuel, does "evenly divisible" mean that the dividend on being divided by 3, leave a quotient that is even?? please correct me if i am wrong.



Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
03 Oct 2014, 08:49
arnabs wrote: Bunuel wrote: anilnandyala 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
4 2 1 2 5 We have the product of 3 integers: (x1)x(xk). Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. Next, if k=2 then we'll have (x1)x(x+2)=(x1)x(x1+3) > which means that (x1) and (x+2) will have the same remainder upon division by 3. Thus for k=2 we won't be sure whether (x1)x(xk) is divisible by 3. Answer: B. 30 second approach: 4 out of 5 values of k from answer choices must guarantee divisibility of some expression by 3. Now, these 4 values of k in answer choices must have some pattern: if we get rid of 2 then 4, 1, 2, and 5 creating arithmetic progression with common difference of 3, so 2 is clearly doesn't belong to this pattern. Hope it helps. Hi Bunuel, does "evenly divisible" mean that the dividend on being divided by 3, leave a quotient that is even?? please correct me if i am wrong. No, evenly divisible means divisible without remainder, so simply divisible.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Aug 2013
Posts: 84

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
03 Oct 2014, 08:56
Bunuel wrote: anilnandyala 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
4 2 1 2 5 We have the product of 3 integers: (x1)x(xk). Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. Next, if k=2 then we'll have (x1)x(x+2)=(x1)x(x1+3) > which means that (x1) and (x+2) will have the same remainder upon division by 3. Thus for k=2 we won't be sure whether (x1)x(xk) is divisible by 3. Answer: B. 30 second approach: 4 out of 5 values of k from answer choices must guarantee divisibility of some expression by 3. Now, these 4 values of k in answer choices must have some pattern: if we get rid of 2 then 4, 1, 2, and 5 creating arithmetic progression with common difference of 3, so 2 is clearly doesn't belong to this pattern. Hope it helps. I am sorry but i did not really get the solution. A little more elaboration would help Bunuel. My main concern here is, if x(x1)(xk) were to be evenly divisible, then plugging any value for x(lets say 3) should make it evenly divisible by 3.



Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
03 Oct 2014, 09:59
arnabs wrote: Bunuel wrote: anilnandyala 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
4 2 1 2 5 We have the product of 3 integers: (x1)x(xk). Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. Next, if k=2 then we'll have (x1)x(x+2)=(x1)x(x1+3) > which means that (x1) and (x+2) will have the same remainder upon division by 3. Thus for k=2 we won't be sure whether (x1)x(xk) is divisible by 3. Answer: B. 30 second approach: 4 out of 5 values of k from answer choices must guarantee divisibility of some expression by 3. Now, these 4 values of k in answer choices must have some pattern: if we get rid of 2 then 4, 1, 2, and 5 creating arithmetic progression with common difference of 3, so 2 is clearly doesn't belong to this pattern. Hope it helps. I am sorry but i did not really get the solution. A little more elaboration would help Bunuel. My main concern here is, if x(x1)(xk) were to be evenly divisible, then plugging any value for x(lets say 3) should make it evenly divisible by 3. Have you checked this: ifxisanintegerthenxx1xkmustbeevenlydivi106310.html#p846137 ?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Aug 2013
Posts: 84

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
03 Oct 2014, 11:17
Bunuel wrote: vjsharma25 wrote: Hi bunuel, I don't understand the problem language, it says
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
how does it matter whats the value of K, i can choose x = 3 and the expression will always be divisible by 3.
Am i missing any minor yet important point? Stem says: "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" The important word in the stem is "MUST", which means that we should guarantee the divisibility by 3 no matter the value of x (for ANY integer value of x), so you can not arbitrary pick its value. Hope it's clear. that was so helpful bunuel ,thank you so much!!!



Manager
Joined: 23 Sep 2015
Posts: 87
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38
GPA: 3.5

Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi
[#permalink]
Show Tags
26 Oct 2015, 16:34
if you draw out a quick number line on your paper and cover up the ones you select, the answers are either in a block of 3 connection, or apart by 3. This should help someone visualize the answer.




Re: If x is an integer, then x(x – 1)(x – k) must be evenly divi &nbs
[#permalink]
26 Oct 2015, 16:34



Go to page
1 2
Next
[ 27 posts ]



