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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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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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27 Sep 2018, 19:59
2
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
insuff

(2) bc is odd
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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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

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

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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.

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

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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

Cheers,
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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