BTGmoderatorDC wrote:If k is an integer greater than 6, all of the following must be divisible by 3 EXCEPT

A. k(k + 3)(k - 1)
B. 3k^3
C. (k+1)(k+5)(k+6)
D. (k+2)(k-2)(k+3)
E. k(k+1)(k+2)

OA A

Source: GMAT Prep

Note that one among three consecutive integers must be divisible by 3. Let's see. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ...

So, one among k(k+1)(k+2) is divisible by 3. Thus, for example, if (k+1) is divisible by 3, (k+1+3) = (k+4) is divisible by 3.

Let's analyze each option one by one.

A. k(k + 3)(k-1): It can be written as (k-1)k(k + 3)

We see that the above are not three consecutive terms. If (k-1) and k are not divisible by 3, then (k+1) and (k+1+3) = (k+4) must be divisible. Since the third term (k+3) lies between (k+1) and (k+4), we are sure that k(k + 3)(k-1) is NOT necessarily divisible by 3. Correct answer.

Though we got the answer, let's analyze others, too.

B. 3k^3: Certainly divisible as 3k^3 has 3 as a factor.

C. (k+1)(k+5)(k+6):

"¢ Say (k+1) as well as (k+2) is not divisible by 3, then (k+3) and (k+3+3) = (k+6) are divisible by 3, so, (k+1)(k+5)(k+6) is disible by 3.
"¢ Say (k+1) is not divisible by 3 but (k+2) is divisible by 3, then (k+2+3) = (k+5) is divisible by 3, so, (k+1)(k+5)(k+6) is disible by 3.

D. (k+2)(k-2)(k+3): Let write it as (k-2)(k+2)(k+3)

"¢ Say (k-2) as well as (k-1) is not divisible by 3, then k and (k+3) are divisible by 3, so, (k+2)(k-2)(k+3) is divisible by 3.
"¢ Say (k-2) is not divisible by 3 but (k-1) is divisible by 3, then (k-1) and (k-1+3) = (k+2) are divisible by 3, so, (k+2)(k-2)(k+3) is divisible by 3.

E. k(k+1)(k+2): This is a product of three consecutive integers, certainly divisible by 3.

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Manhattan | GRE Prep Course Frankfurt | GRE Prep Bellevue | SAT Prep Course Orlando | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Hi All,

We're told that K is an integer GREATER than 6 and that all of the following MUST be divisible by 3 EXCEPT for one of them. We're asked to find which one. To start, the wording of this question implies that one of the answers might sometimes be divisible by 3.... but not always. Four of the answers will ALWAYS be divisible by 3, but one won't always be... Thus, we can answer this question by TESTing VALUES, but in a way that you might not be used to thinking about.

The smallest integer that K could be is 7, so we should start there.

Answer A: K(K + 3)(K - 1) = 7(10)(6)

We don't actually have to multiply those numbers together to know that it is divisible by 3. When dealing with the PRODUCT of a group of numbers, if ANY of the numbers is divisible by 3, then the overall product will ALSO be divisible by 3. When K=7, Answer A includes a "6" in its product - and since 6 is divisible by 3, that overall product will also be divisible by 3.

It's worth noting that as K increases by 1, each of those terms will also increase by 1. If we increase the K to 8, we end up with...

(8)(11)(7)

None of those numbers is divisible by 3, so the overall product will NOT be divisible by 3. Thus, we have the answer that we're looking for (it's sometimes divisible by 3, but not always).

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote:If k is an integer greater than 6, all of the following must be divisible by 3 EXCEPT

A. k(k + 3)(k - 1)
B. 3k^3
C. (k+1)(k+5)(k+6)
D. (k+2)(k-2)(k+3)
E. k(k+1)(k+2)

OA A

Source: GMAT Prep

FIrst, we can remove choices B and E from being the correct answer since both of those are divisible by 3 (3k^3 clearly has a factor of 3 and k(k+1)(k+2) is a product of 3 consecutive integers).

Now, let's examine the other choices by letting k = 7.

A) k(k + 3)(k - 1) = 7(10)(6) is divisible by 3.

C) (k+1)(k+5)(k+6) = 8(12)(13) is divisible by 3.

D) (k+2)(k-2)(k+3) = 9(5)(10) is divisible by 3.

We see that all these choices are divisible by 3 when k = 7. We need to change k to a different number, so let k = 8.

A) k(k + 3)(k - 1) = 8(11)(7) is NOT divisible by 3.

We see that we've found the correct choice. However, let's show the other two indeed are divisible by 3.

C) (k+1)(k+5)(k+6) = 9(13)(14) is divisible by 3.

D) (k+2)(k-2)(k+3) = 10(6)(11) is divisible by 3.

Answer: A