das.ashmita wrote:If a and b are positive integers such that a < b, is b even?
(1) b/2 - a/2 is an integer.
(2) 3b/4 - a/2 is an integer.
Target question:
Is b even?
Statement 1: b/2 - a/2 is an integer
We can combine the fractions to get (b-a)/2 is an integer.
If (b-a)/2 is an integer, then b-a must be even.
So, statement 1 is really just telling us that b-a is even. There are several pairs of values that satisfy this condition. Here are two:
case a: a=3 and b=5, in which case
b is not even
case b: a=2 and b=6, in which case
b is even
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3b/4 - a/2 is an integer
We can combine the fractions to get (3b-2a)/4 is an integer.
If (3b-2a)/4 is an integer, then 3b-2a must be divisible by 4.
If 3b-2a is divisible by 4, then 3b-2a must be even
Well, we know that
2a will be even for all integer values of a
So, if 3b -
2a is even then 3b must also be even.
If 3b is even, then
b must be even
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
