varun289 wrote:If a, b, c and d are integers, is (2a·3b)/(2c·3d) even?
(1) a>c
(2) b=c+d
Target question:
Is (2a·3b)/(2c·3d) even?
We can simplify this expression.
(2a·3b)/(2c·3d) = 6ab/6cd = ab/cd
Rephrased target question:
Is ab/cd even?
Statement 1: a>c
There are several sets of numbers that meet this condition. Here are two:
Case a: a=4, b=4, c=2 and d=2, in which case
ab/cd is even
Case b: a=3, b=4, c=2 and d=2, in which case
ab/cd is not even
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b=c+d
There are several sets of numbers that meet this condition. Here are two:
Case a: a=4, b=4, c=2 and d=2, in which case
ab/cd is even
Case b: a=3, b=4, c=2 and d=2, in which case
ab/cd is not even
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
There are still several sets of numbers that meet this condition. Here are two:
Case a: a=4, b=4, c=2 and d=2, in which case
ab/cd is even
Case b: a=3, b=4, c=2 and d=2, in which case
ab/cd is not even
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
