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06 May 2020, 09:54
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (01:26) correct
26%
(01:31)
wrong
based on 133
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are integers and a - b = 6, then a + b CANNOT be
(A) 0
(B) less than 6
(C) greater than 6
(D) an even integer
(E) an odd integer
(A) 0
(B) less than 6
(C) greater than 6
(D) an even integer
(E) an odd integer
06 May 2020, 10:10
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Bunuel
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
---------------------
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
General Discussion
Archit3110
Major Poster
06 May 2020, 10:00
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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
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
Bunuel
