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

Question

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

sashiim20 · Accepted Answer

(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)...

ScottTargetTestPrep · Answer

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

pushpitkc · Answer

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)

amanvermagmat · Answer

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

aurobindomahanty · Answer

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.

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=PXBdZoB4vCs

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=CSOputKYw9Y

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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?

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