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a,b,c are integers

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a,b,c are integers

by akhilsuhag » Wed Jul 02, 2014 6:54 am
If a, b, c and d are integers, is (2a·3b)/(2c·3d) even?

(1) a>c

(2) b=c+d

OA E
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by Brent@GMATPrepNow » Wed Jul 02, 2014 7:04 am
akhilsuhag 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

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by GMATGuruNY » Wed Jul 02, 2014 9:16 am
akhilsuhag wrote:If a, b, c and d are integers, is (2a·3b)/(2c·3d) even?

(1) a>c

(2) b=c+d

OA E
(2a*3b)/(2c*3d) = (6ab)/(6cd) = ab/cd.
Question rephrased: Is ab/cd an even integer?

Both statements are satisfied by a=2, b=3, c=1, and d=2.
In this case, ab/cd = (2*3)/(1*2) = 3, which is not even.

Both statements are satisfied by a=4, b=3, c=1 and d=2.
In this case, ab/cd = (4*3)/(1*2) = 6, which is even.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by [email protected] » Wed Jul 02, 2014 8:38 pm
Hi akhilsuhag,

DS questions that ask "is this result even?" or "is this result odd?" have a built-in Number Property shortcut that you might be able to take advantage of.

I'm a big fan of TESTing VALUES (as Brent and Mitch both did), but neither of them took advantage of this shortcut:

In this prompt, we're asked if AB/CD is even.

If that fraction equals ANY even number (e.g. -4, -2, 0, 2, 4, 6, etc.), then the answer to the question is YES.

If that fraction equals ANY odd number OR ANY NON-INTEGER, then the answer to the question is NO.

For example, in Fact 1, we know that A > C

If we TEST...
A = 2, B = 1, C = 1, D =1, then the answer is (2)(1)/(1)(1) = 2 and the answer is YES.
A = 3, B = 2, C = 2, D = 2, then the answer is (3)(2)/(2)(2) = 3/2 and the answer is NO.

Under these conditions, you don't have to work quite so hard to "find" a NO answer. ANYTHING not an even integer is a NO.

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