Data Sufficiency

Is a-3b an even number?

1). b=3a+3
2). b-a is an odd number


Ans : C

Use the number properties :

e=even ; o=odd

e+e=e
e+o=o
o+o=e

Is the answer C ?? I got A

Sub 1) in the a-3b , you get -(8a+9) which is odd

Is a-3b even?

A. b=3a+3

a may be odd / even.

If a is odd, b = odd + odd = even. a-3b is odd. NO
If a is even, b = even + odd = odd. a-3b is odd. No

Sufficient.

B. b-a is odd

We have 2 possibilities,
i. odd-even = odd
then a-3b = even - odd = odd. NO

ii. even-odd = odd
then a-3b = odd - even = odd.NO

Sufficient.

Must be D

i also feel D is correct option..


1). b=3a+3
if a=2 then b=9
a-3b=-25

if a=3 then b=12
a-3b=-33

hence sufficient

2). b-a is an odd number
b=5,a=2
a-3b=-13
b=6,a=3
a-3b=-15

hence sufficient

1). b=3a+3
2). b-a is an odd number

interestingly, 2) can be derived from 1)

1) b=3a+3 or b-a = 2a + 3 , 2a is even so 2a + 3 has to be odd
so b-a is a odd no evident in statement 1) itself.

Everyone seems to be making a big assumption!

Do your proofs hold true if a and b are non-integers?

The point about non-integers just increased the difficulty of this problem by a lot.

What's the most efficient method of tackling this problem?

Picking numbers could take you years to solve this one.

Stuart Kovinsky wrote:Everyone seems to be making a big assumption!

Do your proofs hold true if a and b are non-integers?

Hello Stuart,

How can we test this for fractions?

Thanks