Is a - 3b an even number?

Is a-3b an even number?


First note that we are not told that a and b are integers.


(1) \(b = 3a + 3\) --> \(a - 3b = -8a - 9\).

\(a = 1\) --> \(-8a - 9 = -17 = odd\).

\(a = \frac{3}{8}\) --> \(-8a - 9 = -12 = even\).

Not sufficient.


(2) \(b - a = odd\) --> \(a = b - odd\) --> \(a - 3b = b - odd - 3b = -2b - odd\)

\(b = odd\) --> \(a - 3b = -2b - odd = odd\)

\(b = \frac{3}{2}\) --> \(a - 3b = -2b - odd = even\)

Not sufficient.


(1)+(2) \(b=3a+3 and b=odd+a\) --> \(b=odd+a=3a+3\) --> \(odd=2a+3\) --> \(2a=even\) --> a is an integer --> b is an integer.

If a is even --> \(b=3a+3=odd\) and \(a-3b=even-odd=odd\);

If a is odd --> \(b=3a+3=even\) and \(a-3b=odd-even=odd\).

Sufficient.


Answer: C.
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for a -3b to equal even then a and b must be even or odd. One cannot be even and the other odd

Example:
if b = 3 to get an even a can be 11 but not 12
if b = 2 to get an even a must be even

1) b = 3a + 3
b = 3(a + 1)

if a = 2 then b = 9
if a = 3 then b = 12

none are both even or none are both odd so you can answer the question

2. b -a = odd

to get an odd b and a must be different



answer is D, each on its own that neither one will result in an even

Okay, having 2nd thoughts here because are not told that the numbers are integers. They can be fractions in which case the answer would be c

Debating between C and E. Testing decimals and C holds true a-3b is odd so I'll go with C.

if anyone did that in less than 2 mins; come on over and shovel some snow for me...!
you need a life and something to be busy with

[Except may be Bunuel; because he's already helping us]

Can a fraction be even?
Is 1\2 even or odd?

Isn't the question stem ambiguos

An even number is an integer that is "evenly divisible" by 2 i.e., divisible by 2 without remainder, an integer of the form n = 2k, where k is an integer.

An odd number is an integer that is not evenly divisible by 2, an integer of the form n = 2k + 1, where k is an integer.

As for the question: D can not be the answer, see the solution above two different answers possible for (1) and (2).
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I got the solution thanks, I ignored the fact that to get an integer results the input could be any kind of number

I went with option D, I completely ignored fraction values.

After going through the explanation I understand that it should be option C.

Think OA is wrong. Source? Any explanation given?
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sorry i typed it wrong .. i have edited the oa, it is C
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Please find detailed solution as attached

I fell for the oldest trick in the book :/

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