It is currently 20 Nov 2017, 00:54

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z +

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 31 Aug 2009
Posts: 415

Kudos [?]: 357 [2], given: 20

Location: Sydney, Australia
For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + [#permalink]

### Show Tags

10 Oct 2009, 22:25
2
This post received
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

55% (01:41) correct 45% (01:54) wrong based on 131 sessions

### HideShow timer Statistics

For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + 3) divisible by 4?

(1) Z is divisible by 8.
(2) (Z+1)/3 is an odd integer.
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jan 2013, 04:11, edited 1 time in total.
Edited the question.

Kudos [?]: 357 [2], given: 20

SVP
Joined: 29 Aug 2007
Posts: 2471

Kudos [?]: 856 [1], given: 19

Re: Z divisible by 4 [#permalink]

### Show Tags

10 Oct 2009, 22:57
1
This post received
KUDOS
yangsta8 wrote:
For positive integer Z, is the expression (Z+2) (Z^2+4Z+3) divisible by 4?

1. Z is divisible by 8.
2. (Z+1)/3 is an odd integer.

Looking for an efficient way to solve this. I did it by picking numbers, however OA looks at evens and odds.

1. If Z is divisible by 8, z = 8k

= (Z+2) (Z^2+4Z+3)
= (8k+2) [(8k)^2 + 4(8k) + 3]
= (8k+2) [64k^2 + 32k + 3]

(8k+2) [64k^2 + 32k + 3] is not divisible by 4 as (8k+2) is only divisible by 2 and [64k^2 + 32k + 3] is an odd. Suff...

2. If (Z+1)/3 = an odd integer

Z+1 = 3(odd integer)
Z = 3(odd integer) - 1
Here Z is an even but it could be twice of an odd integer or an even integer. If z is twice the odd integer, (Z+2) (Z^2+4Z+3) is divisible by 4 otherwise not. NSF..

A...
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Kudos [?]: 856 [1], given: 19

Math Expert
Joined: 02 Sep 2009
Posts: 42259

Kudos [?]: 132744 [0], given: 12367

For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + [#permalink]

### Show Tags

10 Oct 2009, 23:31
yangsta8 wrote:
For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + 3) divisible by 4?
1. Z is divisible by 8.
2. (Z+1)/3 is an odd integer.

Looking for an efficient way to solve this. I did it by picking numbers, however OA looks at evens and odds.

For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + 3) divisible by 4?

$$(z + 2)(z^2 + 4z + 3)=(z+2)((z+2)^2-1)=(z+2)(z+3)(z+1)$$

Question: is $$(z+1)(z+2)(z+3)$$ divisible by 4?

(1) Z is divisible by 8 --> z=8k --> (8k+1)(8k+2)(8k+3) --> 2(8k+1)(4k+1)(8k+3) --> 3 odd integers (8k+1, 4k+1 and 8k+3)*2 --> not divisible by 4. SUFFICIENT

(2) (Z+1)/3 is an odd integer --> (z+1)/3=odd --> z=3*odd-1 --> z=3n-1 (n odd integer) --> 3n(3n+1)(3n+2) --> 3 odd integers (3, n and 3n+2) * 3n+1(even) --> 3n+1=odd+1=even, may or may not divisible by 4. NOT SUFFICIENT

Answer: A.
_________________

Kudos [?]: 132744 [0], given: 12367

Math Expert
Joined: 02 Sep 2009
Posts: 42259

Kudos [?]: 132744 [0], given: 12367

For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + [#permalink]

### Show Tags

11 Oct 2009, 09:56
This problem can be solved even easier I stated earlier:

Well we know that (Z + 2)(Z^2 + 4Z + 3) can be simplified=(z+1)(z+2)(z+3)

Q: is (z+1)(z+2)(z+3) divisible by 4?

This expression is divisible by 4 only in two cases:
I. z is odd (z+1 - even and z+3 also even, thus their multiplication is divisible by 4)
II. When z+2 is divisible by 4.

so let's check statements:

(1) z=8k --> z is not odd, z+2=8k+2 is not divisible by 4 --> expression is not divisible by 4. Sufficient

(2) z=3n-1 --> z is even, but not sure whether it's divisible by 4 or not. Not sufficient

Answer: A.
_________________

Kudos [?]: 132744 [0], given: 12367

Senior Manager
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 558 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + [#permalink]

### Show Tags

22 Jan 2013, 23:38
yangsta8 wrote:
For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + 3) divisible by 4?
1. Z is divisible by 8.
2. (Z+1)/3 is an odd integer.

This is my approach...

GIVEN:
(z+1)(z+2)(z+3) are consecutive integers...
We know that the multiple of 4 appears in this pattern: 1,2,3,(4),5,6,7,(8),9,10,11,(12),...
As you have noticed, after a multiple of 4, it will be followed by 3 non-multiple of 4...

1.
If z is a multiple of 4, then z+1,z+2,z+3 are all non-multiple of 4 based on the pattern above...
SUFFICIENT.
2.
Let z+1 = 3: (3)(4)(5) is divisible by 4
Let z+1 = 9: (9)(10)(11) is not divisible by 4
INSUFFICIENT.

Answer: A
_________________

Impossible is nothing to God.

Kudos [?]: 558 [0], given: 11

Non-Human User
Joined: 09 Sep 2013
Posts: 15637

Kudos [?]: 283 [0], given: 0

Re: For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + [#permalink]

### Show Tags

29 Jul 2014, 01:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15637

Kudos [?]: 283 [0], given: 0

Re: For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z + [#permalink]

### Show Tags

07 Jul 2017, 06:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Re: For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z +   [#permalink] 07 Jul 2017, 06:50
Display posts from previous: Sort by

# For positive integer Z, is the expression (Z + 2)(Z^2 + 4Z +

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.