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

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If a, b & c are integers, is abc odd?  [#permalink]

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New post 27 Sep 2018, 07:50
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If a, b & c are integers, is abc odd?

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

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Re: If a, b & c are integers, is abc odd?  [#permalink]

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New post 27 Sep 2018, 19:59
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Abhi077 wrote:
If a, b & c are integers, is abc odd?

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


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
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Re: If a, b & c are integers, is abc odd?  [#permalink]

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New post 28 Sep 2018, 19:05
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:

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Re: If a, b & c are integers, is abc odd?  [#permalink]

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New post 02 Oct 2018, 20:00
Abhi077 wrote:
If a, b & c are integers, is abc odd?

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


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
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Re: If a, b & c are integers, is abc odd?  [#permalink]

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New post 17 Dec 2018, 07:42
Top Contributor
Abhi077 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

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Brent
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Re: If a, b & c are integers, is abc odd?   [#permalink] 17 Dec 2018, 07:42
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