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integers

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by aneesh.kg » Tue Jun 05, 2012 11:52 pm
shrutib wrote:a, b, c and d are integers, is (2a·3b)/(2c·3d) even?

(1) a>c

(2) b=c+d
Is (2a)(3b)/(2c)(3d) even?
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.
Aneesh Bangia
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by amit28it » Wed Jun 06, 2012 4:38 am
First of all its a very nice question and the solution provided by aneesh.kg is best, This time when I came up with the solution its not the same but the procedure followed was same and correct.
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