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If j and k are positive integers, is j divisible by 6?

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If j and k are positive integers, is j divisible by 6?  [#permalink]

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New post 18 Jun 2015, 03:22
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Question Stats:

78% (01:06) correct 22% (01:12) wrong based on 167 sessions

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Re: If j and k are positive integers, is j divisible by 6?  [#permalink]

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New post 18 Jun 2015, 04:47
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Bunuel wrote:
If j and k are positive integers, is j divisible by 6?

(1) j = (k + 1)(k + 2)(k + 3)
(2) k is an even integer.


Kudos for a correct solution.

(1) j = (k + 1)(k + 2)(k + 3)

At least one of three (k + 1), (k + 2), (k + 3) is even (If k even, k+2 is even; If k is odd, k+ 1 and k+3 are even) => j is divisible by 2.
Moreover, one of tree (k + 1), (k + 2), (k + 3) is divisible by 3. For example, 3, 4, 5 or 4, 5, or 7, 8, 9 ...Or among three consecutive integers, one integer will be divisible by 3.

=> j is divisible by 6 => SUFFICIENT
integer
(2) k is an even integer.
INSUFFICIENT

Answer: A
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Re: If j and k are positive integers, is j divisible by 6?  [#permalink]

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New post 18 Jun 2015, 08:38
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Bunuel wrote:
If j and k are positive integers, is j divisible by 6?

(1) j = (k + 1)(k + 2)(k + 3)
(2) k is an even integer.

Kudos for a correct solution.


Question : Is j divisible by 6?

CONCEPT-1: A number will be divisible by 6 when the Number is divisible by 2 as well as by 3 [Because 6 = 2 x 3]

CONCEPT-2: Product of any Three consecutive Integers always includes one of the Numbers a Multiple of 3 and an Even Number i.e. a Multiple of 2 therefore Product of three consecutive Integers is always divisible by 6


Statement 1: j = (k + 1)(k + 2)(k + 3)

Since, k is a positive Integer therefore j is a Product of 3 consecutive positive integers and hence will be a multiple of 6 [CONCEPT-2]

Hence, SUFFICIENT

Statement 2: k is an even integer

relation between k and j is unknown to infer any information about j

Hence, NOT SUFFICIENT

Answer: Option
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Re: If j and k are positive integers, is j divisible by 6?  [#permalink]

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New post 18 Jun 2015, 23:04
1
Bunuel wrote:
If j and k are positive integers, is j divisible by 6?

(1) j = (k + 1)(k + 2)(k + 3)
(2) k is an even integer.


Kudos for a correct solution.


1: j is the product of 3 consecutive integers, therefore, j is divisible by 3 and 2 and therefore 6. Sufficient.
2: Tells nothing about J. Insufficient.
Answer is A.
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Re: If j and k are positive integers, is j divisible by 6?  [#permalink]

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New post 22 Jun 2015, 05:33
Bunuel wrote:
If j and k are positive integers, is j divisible by 6?

(1) j = (k + 1)(k + 2)(k + 3)
(2) k is an even integer.


Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

In order to determine whether j is divisible by 6, we need to know whether j is divisible by 2 (even) and also divisible by 3.

Statement (1) is SUFFICIENT: k + 1, k + 2, and k + 3 are 3 consecutive integers. The product of 3 consecutive integers will always be divisible by 3, because one of the 3 integers must be a multiple of 3.

Additionally, at least one of those integers must be even (it's possible that two of them are even), so the product will be even.

Statement (2) is INSUFFICIENT: knowing that k is even tells us nothing about j.

You might Spot One Statement Adding Nothing here. Knowing that k is even adds no information to Statement (1), because the product (k + 1)(k + 2)(k + 3) is going to be even for any value of k. Therefore, C can be eliminated.

You might also Judge by Appearance on this problem. We need to know whether j is divisible by 2 and 3, and since Statement (1) tells us that j is the product of 3 consecutive integers, it seems as though this statement is likely to be sufficient.

You could also use Discrete Number Listing to test numbers for k and prove to yourself that j must be divisible by 6.

The correct answer is A.
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Re: If j and k are positive integers, is j divisible by 6?  [#permalink]

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New post 17 Jul 2017, 17:02
Bunuel wrote:
If j and k are positive integers, is j divisible by 6?

(1) j = (k + 1)(k + 2)(k + 3)
(2) k is an even integer.


Kudos for a correct solution.


Statement 1

The product of 3 consecutive integers is always a multiple of 3; moreover, one of the numbers is even so so it it must be divisible by 2 and thus a product of 6.

A
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Re: If j and k are positive integers, is j divisible by 6?   [#permalink] 17 Jul 2017, 17:02
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If j and k are positive integers, is j divisible by 6?

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