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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.
10 Oct 2009, 22:57
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yangsta8
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. 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...
10 Oct 2009, 23:31
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yangsta8
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. 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.
