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GMAT Prep Question

by chaitanya.mehrotra » Sun Jul 03, 2011 9:05 am
If c and d are integers is c even ?

1) c(d+1) is even

2) (c+2)(d+4) is even

Looking for any short cut or easy method of solving this question. At the moment i solved it putting in numbers for diff even/odd combination .

OA C
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Jul 03, 2011 11:27 pm
chaitanya.mehrotra wrote:If c and d are integers is c even ?

1) c(d+1) is even
2) (c+2)(d+4) is even
Statement 1: c(d + 1) is even implies any one of the following three possible scenarios
  • 1. c is even, (d + 1) is odd --> c and d both even
    2. c is odd, (d + 1) is even --> c and d both odd
    3. c and (d + 1) both even --> c even, d odd
Not sufficient

Statement 2: (c + 2)(d + 4) is even implies any one of the following three possible scenarios
  • 1. (c + 2) is even, (d + 4) is odd --> c even, d odd
    2. (c + 2) is odd, (d + 4) is even --> c is odd, d even
    3. both (c + 2) and (d + 4) are even --> c and d both even
Not sufficient

1 & 2 Together: Only feasible scenarios are (c even, d odd) or (c and d both even). Hence, c is always even.

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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by magicalhat » Mon Jul 04, 2011 7:11 am
I would make a chart
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