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If a, b, and c are integers, is a + b + c even? (1) a + b is odd.

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If a, b, and c are integers, is a + b + c even? (1) a + b is odd. [#permalink] New post   29 May 2023, 01:30
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E

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If a, b, and c are integers, is a + b + c even?

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


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E
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Re: If a, b, and c are integers, is a + b + c even? (1) a + b is odd. [#permalink] New post   29 May 2023, 03:16
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Is a + b + c even?

(1) a + b is odd.

If c is odd, a+b+c=even (odd+odd= even).
If c is even, a+b+c=odd (odd+even= odd)
Statement I is insufficient.

(2) b + c is odd.
If a is odd, a+b+c=even (odd+odd= even).
If a is even, a+b+c=odd (odd+even= odd)
Statement II is insufficient.

Combining statement I and statement II: If b is odd, a and c are even.
a+b+c= odd

If b is even, a and c are odd.
a+b+c= even.
Both statements together are insufficient.

Option E is the answer

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Re: If a, b, and c are integers, is a + b + c even? (1) a + b is odd. [#permalink] New post   29 May 2023, 05:10
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(1) Only
Evidently insufficient.
(2) Only
Evidently insufficient.

(1)(2) Together
Adding (1) and (2), we get
a+2b+c is even.
So a +c is also even.

Consider two different scenarios.
(1) a = c = 1, and b = 2.
a+b+c is even
(2) a = c = 2, and b = 3
a+b+c is odd
Not sufficient.

The answer is (E).
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Re: If a, b, and c are integers, is a + b + c even? (1) a + b is odd. [#permalink] New post   29 May 2023, 08:12
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If a, b, and c are integers, is a + b + c even?
a+b+c is even under the following conditions (E+E+E) or (O+O+E)
(1) a + b is odd.
Implies a and b are of opposite nature. But we don't know anything about c.
Not sufficient
(2) b + c is odd.
Implies b and c are of opposite nature. But we don't know anything about a.
Not sufficient
Statement 1 n 2 together, we can have two scenarios - E + E + O = O (No, the sum is not Even)
or O + E + O = E (Yes, the sum is Even)
Not sufficient
Answer E
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gmatclubot
Re: If a, b, and c are integers, is a + b + c even? (1) a + b is odd. [#permalink]
29 May 2023, 08:12
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Bunuel
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