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# If c and d are integers, is c even? a. c(d+1) is even b.

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Manager
Joined: 31 Jul 2006
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If c and d are integers, is c even? a. c(d+1) is even b. [#permalink]

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11 Oct 2008, 01:28
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If c and d are integers, is c even?
a. c(d+1) is even
b. (c+2)(d+2) is even

Kudos [?]: 93 [0], given: 0

Manager
Joined: 07 Jan 2008
Posts: 87

Kudos [?]: 248 [0], given: 1

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11 Oct 2008, 05:44
Ans is E.

(a) when d is odd, c can be even or odd
(b) when (c+2) is even, c is even. when (d+2) is even, c can be odd or even.

both together doesn't give any info. So E.

Kudos [?]: 248 [0], given: 1

SVP
Joined: 05 Jul 2006
Posts: 1750

Kudos [?]: 430 [0], given: 49

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12 Oct 2008, 14:28
If c and d are integers, is c even?
a. c(d+1) is even
b. (c+2)(d+2) is even

from a

even*odd(d is even) or odd *even thus(d is odd) or both even ( c even d is odd)

from 2

odd *even ( c is odd, d is even) or even*odd ( c is even, d is odd) or even * even thus both are even

both together

E

Kudos [?]: 430 [0], given: 49

Senior Manager
Joined: 21 Apr 2008
Posts: 269

Kudos [?]: 165 [0], given: 0

Location: Motortown

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12 Oct 2008, 14:33
Clearly E

I will go with the explanations above

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SVP
Joined: 17 Jun 2008
Posts: 1535

Kudos [?]: 279 [0], given: 0

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12 Oct 2008, 23:11
C for me.

from 1: c can be even and d can be odd / even or
c and d will be odd.

From 2: c and d can be even, c can be even and d can be odd/even, c is odd and d is even.

Combining the two,

c is even and d can be odd/even. Hence, sufficient.

Kudos [?]: 279 [0], given: 0

Intern
Joined: 02 Oct 2008
Posts: 16

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

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13 Oct 2008, 00:26
C.

A) C ODD and D even -- not possible
B) C ODD and D EVEN -- not possible

So combining the two,
C has to be even and D can be odd/even.
Amazing what time pressure does to our thinking.

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Senior Manager
Joined: 21 Apr 2008
Posts: 269

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Location: Motortown

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13 Oct 2008, 04:59

I think I was
Unlike guttal07, may be I need to be under time pressure to solve the problem properly

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Current Student
Joined: 28 Dec 2004
Posts: 3351

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Location: New York City
Schools: Wharton'11 HBS'12

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13 Oct 2008, 16:14
If c and d are integers, is c even?
a. c(d+1) is even
b. (c+2)(d+2) is ev

1) cd+c=even, well we dont anything here c could be even.. or odd,
2) again same thing cd+2c+2d+4=even

together

cd+c=even, ok..even+c+2d=even

we know that 2d is even, even+c=even, which means C has to be even

C it is

Kudos [?]: 319 [0], given: 2

Re: Even numbers DS   [#permalink] 13 Oct 2008, 16:14
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