BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:13 am
If a, b & c are integers, is abc odd?
(1) ab is odd
(2) bc is odd
Answer:
C
Source: Empower GMAT
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
