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# If a and b are integers, is a + b + 3 an odd integer?

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If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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26 Jun 2017, 01:51
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If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.
[Reveal] Spoiler: OA

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If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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26 Jun 2017, 02:20
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Bunuel wrote:
If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

(1) $$ab$$ is an odd integer.

$$Odd * Odd = Odd$$

Therefore $$a$$ and $$b$$ should be Odd integers.

($$Odd + Odd = Even$$ ) and ($$Even + Odd = Odd$$)

$$a + b = Even$$

$$a + b + 3 = Even + 3$$ = Odd integer.

Hence I is Sufficient.

(2) $$a − b$$ is an even integer.

$$Odd - Odd = Even$$

$$Even - Even = Even.$$

Therefore $$a$$ and $$b$$ could both either be Even or both be Odd.

If $$a$$ and $$b$$ are Odd. ($$Odd + Odd = Even$$) and ($$Even + Odd = Odd$$)

$$a + b + 3 = Odd + Odd + 3 = Even + 3 = Odd$$ --------- True.

If $$a$$ and $$b$$ are Even. ($$Even + Even = Even$$) and ($$Even + Odd = Odd$$)

$$a + b + 3 = Even + Even + 3 = Even + 3 = Odd$$ ------- True.

Hence II is Sufficient. Answer (D)...

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If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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26 Jun 2017, 02:23
Given : a and b are integers
We need to find out if a + b + 3 is an odd integer

(1) ab is an odd integer.
This is possible only when both a and b are odd.
Hence sum of a and b will be even, making the sum(a + b + 3) an odd integer(Sufficient)
(2) a − b is an even integer.
This is possible when both a and b is even or odd.
In either case, the sum of a and b is even.
Thus, a+b+3 is odd(Sufficient) (Option D)
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Re: If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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26 Jun 2017, 02:32
If a and b are integers, is $$a + b + 3$$ an odd integer?

In order to find $$a + b + 3$$ is ODD, we need to find.

ODD + ODD + 3 = ODD

EVEN + EVEN + 3 = ODD

Which means, if we are able to confirm if a & b both are ODD or if a & b both are EVEN we should be able to answer the question.

(1) ab is an odd integer

ab = ODD

This means that a & b both are ODD

As per above this information should be sufficient to prove $$a + b + 3$$ is ODD as ODD + ODD + 3 = ODD

Hence, Eq. (1) =====> is SUFFICIENT

(2) a − b is an even integer

a - b is EVEN

This is only possible if

a & b are both ODD

a & b are both EVEN

As this is sufficient to answer the question $$a + b + 3$$ is ODD

Hence, Eq. (2) =====> is SUFFICIENT

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Re: If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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03 Jul 2017, 00:27
Given that a and b are both integers, so each of them must be either even or odd. a+b+3 will be odd when (a+b) is even.

Statement 1. product of a & b is odd, which is only possible when both a & b are odd. And if both a & b are odd, then (a+b) is even. So we know. Sufficient.

Statement 2. a-b is even, this will happen either when
both a & b are even, in which case (a+b) will also be even
or when both a & b are odd, in which case too (a+b) will be even.

a+b is even in any case, so we know. Sufficient.

Each statement alone is sufficient. Hence D answer

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Re: If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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03 Jul 2017, 22:49
Bunuel wrote:
If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

for a+b+3 to be odd a+b should be even

1) if ab is an odd integer then a and b are individually odd, so a+b= odd+odd=Even : sufficient .
2)a- b is an even integer, so a and b are both even or both odd. In either cases the sum a+b is even : sufficient.

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Re: If a and b are integers, is a + b + 3 an odd integer? [#permalink]

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17 Nov 2017, 11:31
Bunuel wrote:
If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

We need to determine whether a + b + 3 is odd, or in other words, whether a + b is even.

Statement One Alone:

ab is an odd integer.

Because ab is odd, we know that a and b must both be odd, and since odd + odd = even, a + b is even. Statement one alone is sufficient to answer the question.

Statement Two Alone:

a - b is an even integer.

Since a - b is even, a + b is also even. Statement two alone is sufficient.

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Re: If a and b are integers, is a + b + 3 an odd integer?   [#permalink] 17 Nov 2017, 11:31
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