Is (2a)(3b)/(2c)(3d) even?shrutib wrote:a, b, c and d are integers, is (2a·3b)/(2c·3d) even?
(1) a>c
(2) b=c+d
or
Is (a/c)*(b/d) even?
Statement(1):
a > c does not guarantee that a/c is an integer, not to mention that there is no information on b and d.
INSUFFICIENT.
Statement(2):
b = c + d
b/d = c/d + 1
No guarantee of b/d being an even integer, not to mention that there is no information on 'a'.
INSUFFICIENT.
Let's combine the statements.
a > c and b = c + d
Let's take c = 1, a = 2, d = 1, b = 1 + 1 = 2
(a/c)(b/d) = (2/1)(2/1) = 2. EVEN!
Let's take c = 1, a = 2, d = 2, b = 1 + 2 = 3
(a/c)(b/d) = (2/1)(3/2) = 3. ODD!
INSUFFICIENT.
When you plug-in values, you will also notice that for some values of a, b, c and d, (a/c)(b/d) might not even be an integer.
[spoiler](E)[/spoiler] is correct.
