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# For positive integer k, is the expression (k +

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Manager
Joined: 04 Jan 2008
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For positive integer k, is the expression (k + [#permalink]

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16 Sep 2008, 07:38
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For positive integer k, is the expression $$(k + 2)(k^2 + 4k + 3)$$ divisible by 4?

(1) k is divisible by 8.

(2) (k + 1)/3 is an odd integer.

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SVP
Joined: 05 Jul 2006
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16 Sep 2008, 07:55
dancinggeometry wrote:
For positive integer k, is the expression $$(k + 2)(k^2 + 4k + 3)$$ divisible by 4?

(1) k is divisible by 8.

(2) (k + 1)/3 is an odd integer.

from one:

(k+2) = even = 2(m+1) where m is devisible by 4..........a

(k^2 + 4k + 3) = even + even+ odd = odd..........b

thus from a & b

th expression boils down to

2*odd*odd thus we can deduct that k is not devisible by 4........ie: 1 is suff

from two

k+1 = odd and thus k is even could be ( check k = 0,2,4) we get multiple answers thus my answer is A

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Senior Manager
Joined: 31 Jul 2008
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16 Sep 2008, 17:21
A for me as well

2 statement only tells that K is even

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Director
Joined: 23 Sep 2007
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16 Sep 2008, 20:43
yezz wrote:
dancinggeometry wrote:
For positive integer k, is the expression $$(k + 2)(k^2 + 4k + 3)$$ divisible by 4?

(1) k is divisible by 8.

(2) (k + 1)/3 is an odd integer.

from one:

(k+2) = even = 2(m+1) where m is devisible by 4..........a

(k^2 + 4k + 3) = even + even+ odd = odd..........b

thus from a & b

th expression boils down to

2*odd*odd thus we can deduct that k is not devisible by 4........ie: 1 is suff

from two

k+1 = odd and thus k is even could be ( check k = 0,2,4) we get multiple answers thus my answer is A

Great solution/explanation, but you forgot that k is a positive integer.

D

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Intern
Joined: 21 Jun 2008
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16 Sep 2008, 23:30
(k+2)(k^2+4k+3) / 4 ***3 is the key...

1) Sufficient because with 8/k, k must be even. therefore, the equation is definitely NOT divisible by 4.

2) Sufficient. Work backwards with (k+1)/3=odd.

--> odd x 3 = odd.
--> k+1 = odd
--> k must be even.
--> if K is even, the equation is definitely NOT divisible by 4, so the final answer is D.

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SVP
Joined: 17 Jun 2008
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18 Sep 2008, 01:36
d2touge wrote:

2) Sufficient. Work backwards with (k+1)/3=odd.

--> odd x 3 = odd.
--> k+1 = odd
--> k must be even.
--> if K is even, the equation is definitely NOT divisible by 4, so the final answer is D.

Do not agree with this.

If (k+1)/3 = 1 then original expression will be 3*4*5 and will be divisible by 4.

But, if (k+1)/3 = 3 then original expression will be 9*10*11 and will not be divisible by 4.

Hence, stmt 2 is insufficient and answer should be A.

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SVP
Joined: 28 Dec 2005
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19 Sep 2008, 13:58
I agree with A as well ... from stat 2, the only thing I was able to derive was that k is even ...

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Re: Zumit DS 028   [#permalink] 19 Sep 2008, 13:58
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