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21 Mar 2023, 23:49
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C
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Difficulty:
85%
(hard)
Question Stats:
38% (02:15) correct
62%
(02:25)
wrong
based on 39
sessions
History
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Not Attempted Yet
If m and n are positive integers greater than 1, is m + n odd?
(1) m is a divisor of 16
(2) The units digit of 12\(^m\) + 28\(^n\) is 6.
(1) m is a divisor of 16
(2) The units digit of 12\(^m\) + 28\(^n\) is 6.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
22 Mar 2023, 00:22
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ChandlerBong
Given: m and n are positive integers.
m + n = odd under the follwing two cases
Case 1: m is even ; n is odd
Case 2: m is odd ; n is even
Statement 1
(A) m is a divisor of 16
m is even. We don't know the even-odd nature of n. Hence this statement alone doesn't help us know the even odd nature of m + n.
Eliminate A and D.
Statement 2
(B) The units digit of 12\(^m\) + 28\(^n\) is 6
Cyclicity of 2 : 2, 4, 8 , 6
Cyclicity of 8 : 8, 4, 2 , 6
m = 2 ; n = 3 ⇒ m + n = odd
m = 3 ; n = 5 ⇒ m + n = even
Hence, the statement is not sufficient. We can eliminate B.
Combined
As m = even, m = 2 (or of form 2 + 4d) and n = 3 (or of form 3 + 4d).
In any case, m + n = odd.
Sufficient.
Option C
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