|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (02:21) correct
48%
(02:20)
wrong
based on 231
sessions
History
Date
Time
Result
Not Attempted Yet
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.
(1) Z is divisible by 8.
(2) (Z+1)/3 is an odd integer.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
10 Oct 2009, 22:57
Kudos
Bookmarks
yangsta8
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...
10 Oct 2009, 23:31
Kudos
Bookmarks
yangsta8
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.
