Data Sufficiency

BTGmoderatorDC wrote:If a, b & c are integers, is abc odd?

(1) ab is odd
(2) bc is odd

OA C

Source: EMPOWERgmat

For abc to be odd, each of a, b and c must be odd. Even if only one of then is even, abc is even.

Question rephrased: Is each of a, b and c odd?

(1) ab is odd.

c and be even or odd, making abc even or odd. Insufficient.

(2) bc is odd.

a and be even or odd, making abc even or odd. Insufficient.

(1) and (2) together

From (1), we have a and b are odd and from (2), we have b and c are odd, thus all are odd, making abc odd. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote:If a, b & c are integers, is abc odd?

(1) ab is odd
(2) bc is odd

Some important rules:
#1. (ODD)(ODD) = ODD
#2. (ODD)(EVEN) = EVEN
#3. (EVEN)(EVEN) = EVEN

Given: a, b & c are integers

Target question: Is abc odd?

Statement 1: ab is odd
This tells us that a and b are both odd. However, we have no information about c.
Consider these two cases that satisfy statement 1:
Case a: a = 1, b = 1 and c = 1. abc = (1)(1)(1) = 1, so the answer to the target question is YES, abc IS odd
Case b: a = 1, b = 1 and c = 2. abc = (1)(1)(2) = 2, so the answer to the target question is NO, abc is NOT odd
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: bc is odd
This tells us that b and c are both odd. However, we have no information about a.
Consider these two cases that satisfy statement 2:
Case a: a = 1, b = 1 and c = 1. abc = (1)(1)(1) = 1, so the answer to the target question is YES, abc IS odd
Case b: a = 2, b = 1 and c = 1. abc = (2)(1)(1) = 2, so the answer to the target question is NO, abc is NOT odd
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a and b are both odd
Statement 2 tells us that b and c are both odd
So, we can conclude that a, b, and c are ALL ODD
This means abc = (ODD)(ODD)(ODD) = ODD
So, the answer to the target question is YES, abc IS odd
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent