If a and b are integers and a - b = 6, then a + b CANNOT be

difference of two integers would be even only if both are either odd or even
so for a-b=6 ;
possible cases : 6,0 ; 0,-6 ; 8,2 ; 2,-4 ; 4,-2; 3,-3
we get all possible scenarios of a+b except an odd integer value ( a+b)
hence option E

Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN

APPROACH #1: Use odd/even properties
Given: a - b = 6
In other words: a - b = EVEN

From rule #1 and rule #3 , there are two possible cases:

case i: a and b are both ODD, in which case a + b = ODD + ODD = EVEN
case ii: a and b are both EVEN, in which case a + b = EVEN + EVEN = EVEN

In both possible cases, a + b is EVEN, which means a + b cannot be odd

Answer: E
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APPROACH #2: Eliminate for answer choices
Given: a - b = 6

So, it COULD be the case that a = 3 and b = -3, since 3 - (-3) = 6
If a = 3 and b = -3, then a + b = 3 + (-3) = 0
So, we can eliminate answer choices A, B and D

It COULD also be the case that a = 10 and b = 4, since 10 - 4 = 6
If a = 10 and b = 4, then a + b = 10 + 4 = 14
So, we can eliminate answer choice C

By the process of elimination, the correct answer is E

Cheers,
Brent
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\(A - B = 6.\) We must have either EVEN - EVEN = EVEN or ODD - ODD = EVEN. Then \(A + B\) has to be EVEN + EVEN = EVEN or ODD + ODD = EVEN.
Then \(A + B\) cannot be odd.

Ans: E
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