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Is a-3b an even number?

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Source: — Data Sufficiency |
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by chidcguy » Sat May 24, 2008 2:46 pm
Is the correct answer B?
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by netigen » Sat May 24, 2008 3:39 pm
OA is D
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by chidcguy » Sat May 24, 2008 5:51 pm
b-a is odd

For the difference to be odd one number should be odd and other even

So either b is odd or a is odd, but both of them are not odd and not even

b=8 a =3 b-a =5 is odd a-3b =3-24 = -21 Not even

b=5 a=8 b-a =-3 is odd a-3b = 8-15 = -7 Not even

b=5 a=0 b-a =5 is odd a-3b = -15 Not even

b=0 a=7 b-a =-7 is odd a-3b = 7 Not even

b=7 a=-4 b-a =11 is odd a-3b =-4-21 =-25 Not even

Looks like B or D is the answer

b=3a+3

Substitute b in a -3b=a-3(3a+3)= a-9a-9 = -8a-9

a =-2 -8a-9 = 7 Not even

a =-1 8-9 =-1 Not even

a = 0 0-9 = -9 Not even

a =1 -8-9 =-17 Not even

a=2 -16-9 = -25 Not even

We can definitively say that a-3b is Not even. we have sufficiency in both cases. Correct me if I went wrong with numbers some where.

Thanks for the good Questions
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by netigen » Sat May 24, 2008 11:43 pm
To solve for A convert it to b-a form

b=3a+3
b-a = 2a+3
or b-a = even+odd = odd

another approach:

b=3(a+1)
if a = even then b=3 x odd=odd
if a = odd then b = 3 x even = even

so one is even the other is odd
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