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

Question

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

chetan2u · Answer

for abc is odd, each of them should be ODD...

(1) ab is odd
nothing about C
insuff

(2) bc is odd
nothing about a
insuff

combined
ab*bc is odd, so all 3 integers are odd
suff

EMPOWERgmatRichC · Answer

Hi All,

We're told that A, B and C are INTEGERS. We're asked if (A)(B)(C) is ODD. This is a YES/NO question and can be solved with Number Properties and TESTing VALUES.

1) (A)(B) is ODD

Since A and B are both integers, the only way the product of those two numbers to be odd is if BOTH A and B are ODD. However, we don't know whether C is odd or even. 
IF... 
A=1, B=1, C=1, then (A)(B)(C) = 1 and the answer to the question is YES 
A=1, B=1, C=2, then (A)(B)(C) = 2 and the answer to the question is NO 
Fact 1 is INSUFFICIENT

2) (B)(C) is ODD

Since B and C are both integers, the only way the product of those two numbers to be odd is if BOTH B and C are ODD. However, we don't know whether A is odd or even. 
IF... 
A=1, B=1, C=1, then (A)(B)(C) = 1 and the answer to the question is YES 
A=2, B=1, C=1, then (A)(B)(C) = 2 and the answer to the question is NO 
Fact 2 is INSUFFICIENT

Combined, we know... 
A and B are ODD 
B and C are ODD 
Thus, (A)(B)(C) will ALWYS be ODD and the answer to the question is ALWAYS YES. 
Combined, SUFFICIENT

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

We need to determine whether abc is odd.

Statement One Alone:

ab is odd

Since ab is odd, we know that both a and b are odd. However, without knowing anything about c we cannot answer the question. Statement one alone is not sufficient.

Statement Two Alone:

bc is odd

Since ab is odd, we know that both b and c are odd. However, without knowing anything about a we cannot answer the question. Statement two alone is not sufficient.

Statements One and Two Together:

Using the information from both statements we see that a, b, and c must all be odd, so the product of a, b, and c is odd.

Answer: C

BrentGMATPrepNow · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards