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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) _________________

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

Hence, Answer is D _________________

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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

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.

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.

Answer: D
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