I think it should be (B) i.e. -2
If x = 8
x - 1 = 7
x-(-2) = 8+ 2 = 10
8 x 7 x 10 is not divisible by 3
Integers, is there a better explanation for this?
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
Maciek
- Master | Next Rank: 500 Posts
- Posts: 164
- Joined: Sun Jul 18, 2010 5:26 am
- Thanked: 49 times
- Followed by:4 members
- GMAT Score:710
Hi!
Integer is divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
If the number is given as multiplication of factors, then any of them must be divisible my 3.
integer x(x-1)(x-k) is divisible by three if k has remainder 2 after dividing by 3.
a. -4
-4/3 = -2 remainder 2
b. -2
-2/3 = - 1 remainder 1
c. -1
-1/3 = -1 remainder 2
d. 2
2/3 = 0 remainder 2
e. 5
5/3 = 1 remainder 2
Hence, the answer is b
Hope it helps!
Best,
Maciek
Integer is divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
If the number is given as multiplication of factors, then any of them must be divisible my 3.
integer x(x-1)(x-k) is divisible by three if k has remainder 2 after dividing by 3.
a. -4
-4/3 = -2 remainder 2
b. -2
-2/3 = - 1 remainder 1
c. -1
-1/3 = -1 remainder 2
d. 2
2/3 = 0 remainder 2
e. 5
5/3 = 1 remainder 2
Hence, the answer is b
Hope it helps!
Best,
Maciek
"There is no greater wealth in a nation than that of being made up of learned citizens." Pope John Paul II
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
-
CompBanker
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Sat Jul 11, 2009 5:48 am
- Thanked: 1 times
- GMAT Score:760
This question is testing your knowledge of consecutive integers. If three consecutive integers are multiplied together, the result MUST be divisible by 3. (1*2*3, 2*3*4, 3*4*5, etc.). This is true because 3 divides into every third number (3,6,9,12, etc.).
For this problem:
x represents a number and (x - 1) represents 1 less than a number. In order for you to be SURE that the product is divisible by 3, the third number must represent either a consecutive integer or a consecutive integer +/- a multiple of 3.
Plugging in some numbers:
x = 11
(x-1) = 10
(x-?) = [The result is divisible by 3 as long as this number is +/- a multiple of 3 away from 9.]
So, the possible values of [?] in this case can be: -4: (x-(-4)=15); -1: (x-(-1)=12); 2: (x-2=9); 5: (x-5=6)
Notice that this pattern can go on forever. -4; -1; 2; 5; 8; 11; 14; 17; 20 are all viable numbers.
For this problem:
x represents a number and (x - 1) represents 1 less than a number. In order for you to be SURE that the product is divisible by 3, the third number must represent either a consecutive integer or a consecutive integer +/- a multiple of 3.
Plugging in some numbers:
x = 11
(x-1) = 10
(x-?) = [The result is divisible by 3 as long as this number is +/- a multiple of 3 away from 9.]
So, the possible values of [?] in this case can be: -4: (x-(-4)=15); -1: (x-(-1)=12); 2: (x-2=9); 5: (x-5=6)
Notice that this pattern can go on forever. -4; -1; 2; 5; 8; 11; 14; 17; 20 are all viable numbers.
CompBanker
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Our goal is to make each of the 3 factors -- x, (x-1), and (x-k) -- NOT divisible by 3.ru2008 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
This means that x cannot be a multiple of 3 and x-1 cannot be a multiple of 3.
Let x = 5. This works because x = 5 is not divisible by 3 and x-1=4 is not divisible by 3.
Now we just plug in the answer choices, which represent the value of k. We're looking for the answer choice that doesn't yield a multiple of 3.
A) If k = -4, x-k = 5 - (-4) = 9. 9 is a multiple of 3. Eliminate A.
B) If k = -2, x-k = 5 - (-2) = 7. 7 is not a multiple of 3. Success!
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
gig92
- Senior | Next Rank: 100 Posts
- Posts: 78
- Joined: Fri Jul 23, 2010 2:22 am
- Thanked: 2 times
- Followed by:1 members
The product of any three consecutive integers must be divisible by 3. In the question above, as it says, choose ANY integer as x (say 11) and then plug the values around:ru2008 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
e.g. if x = 11 -> 11(10)(11-k), we can plug each value one by one. Even if some values of k don't give the next consecutive integer, we have enough information base to check some mutiple of 3. The product is divisible by for any value of k EXCEPT -2 and it stands true for any integer value of x.
gig92
-
sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
ru2008 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 purposely taking x = 5 as reference, because the possible product
5 × 4 × (5 - k)
would have 5 × 4 as already indivisible by 3.
Hence, we only need to check with which choice for k, (5 - k) is not divisible by 3.
A. Gives 9, proceed
B. Gives 7, [spoiler]STOP
B[/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
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
Here's a 10 second solution, based on understanding of divisibility concepts (and an application of an old Sesame Street game, "one of these things is not like the others").ru2008 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
When we divide by 3, we "cycle" in 3s.
-4, -1, 2 and 5 are all in the same place in the 3 cycle (i.e. each one is a multiple of 3 apart from the others).
Accordingly, -2 MUST be the correct answer to the question.
Answer choices are your friends - pay attention to them and they'll help you out!
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
