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If a, b, and c are positive integers, is abc an even integer ?

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If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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New post 18 Jun 2015, 03:13
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If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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Stem asks if any of non-zero integers a, b and c is even?

(1) a + b is even.
Tells us that a and b are either both odd or both even (number properties). e.g. 3+3 = 6, 2+2 = 4. Not sufficient.

(2) b + c is odd.
If b + c is odd, then according to number theory one of them should be even and one should be odd. e.g. 3+2 = 5, 11+22=33.
Hence, at least one of them is even. Sufficient.

Answer
[Reveal] Spoiler:
B

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Re: If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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New post 18 Jun 2015, 07:46
Bunuel wrote:
If a, b, and c are positive integers, is abc an even integer ?

(1) a + b is even.
(2) b + c is odd.


Kudos for a correct solution.


Question : Is abc an even integer ?
Question Rephrased: Is any one of the Integers a, b, c an even integer ?

Statement 1: a + b is even.

i.e. either both a and b are even or both are odd

Hence, NOT SUFFICIENT

Statement 2: b + c is odd

i.e. One of b and c is even and other is odd

i.e. a*b*c will definitely have one Even Integers among them therefore resulting in product as an Even Integer

Hence, SUFFICIENT

Answer: Option
[Reveal] Spoiler:
B

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Re: If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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New post 18 Jun 2015, 08:00
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Bunuel wrote:
If a, b, and c are positive integers, is abc an even integer ?

(1) a + b is even.
(2) b + c is odd.


Kudos for a correct solution.


For abc to be even at least one of a,b,c should be even.

1) a and b can be both even or odd. Insufficient
2) either b is odd and c is even OR b is even and c is odd. Sufficient.

Hence B

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Re: If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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New post 18 Jun 2015, 23:54
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Bunuel wrote:
If a, b, and c are positive integers, is abc an even integer ?

(1) a + b is even.
(2) b + c is odd.


Kudos for a correct solution.


1: a+b is even -> even + even = even, but odd + odd = even. so a and b are the same sign, but that doesn't tell you if abc is even. Insufficient.
2: b+c is odd -> b and c have opposite signs. That means that one of them is even, so abc is even because even*anything = even. Sufficient.
Answer is B.

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Re: If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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New post 22 Jun 2015, 05:42
Bunuel wrote:
If a, b, and c are positive integers, is abc an even integer ?

(1) a + b is even.
(2) b + c is odd.


Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

We can test the odd/even scenarios using Scenario Charts. Statement (1) tells us that a + b is even, so a and b are either both odd or both even. INSUFFICIENT:
Attachment:
2015-06-22_1641.png
2015-06-22_1641.png [ 32.98 KiB | Viewed 1175 times ]

Statement (2) tells us that b + c is odd, so one of b and c is odd and the other is even. SUFFICIENT:
Attachment:
2015-06-22_1641_001.png
2015-06-22_1641_001.png [ 31.44 KiB | Viewed 1173 times ]

Since one of the two variables must be even, the product abc will always be even.

The correct answer is B.
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Re: If a, b, and c are positive integers, is abc an even integer ? [#permalink]

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New post 25 Sep 2017, 20:58
Bunuel wrote:
If a, b, and c are positive integers, is abc an even integer ?

(1) a + b is even.
(2) b + c is odd.


Kudos for a correct solution.


Three basic scenarios with addition

1.odd + odd = even
2.even + even = even
3.odd + even =odd

Scenarios with multiplication
1. odd x odd =odd
2. even x even =even
3. odd x even =even

Statement 1


Could be scenario 1 or 2- in which case the product could be odd or even

Statement 2

Only scenario 3 works

suff

B

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Re: If a, b, and c are positive integers, is abc an even integer ?   [#permalink] 25 Sep 2017, 20:58
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If a, b, and c are positive integers, is abc an even integer ?

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