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12 Oct 2021, 01:30
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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:
78% (02:07) correct
22%
(02:38)
wrong
based on 178
sessions
History
Date
Time
Result
Not Attempted Yet
If m and n are positive integers, is \(|m - n| + |2m - n| + |2n - m|\) divisible by 4 ?
(1) \(2m > n\)
(2) \(2n > m\)
(1) \(2m > n\)
(2) \(2n > m\)
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
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 10 Aug 2026
Posts: 3,095
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
12 Oct 2021, 04:34
Kudos
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|m - n| + |2m - n| + |2n - m|
1) 2m > n
Let m = n = 1
|m - n| + |2m - n| + |2n - m|
|1-1|+|2-1|+|2-1|
2 (2 is not divisible by 4)
Let M = 3 and N = 4
|m - n| + |2m - n| + |2n - m|
|3 - 4| + |2*3 - 4| + |2*4 - 3|
1+2+5
8 is divisible by 4
Not sufficient
2) 2N > M
Let m = n = 1
|m - n| + |2m - n| + |2n - m|
|1-1|+|2-1|+|2-1|
2 (2 is not divisible by 4)
Let M = 3 and N = 4
|m - n| + |2m - n| + |2n - m|
|3 - 4| + |2*3 - 4| + |2*4 - 3|
1+2+5
8 is divisible by 4
Not sufficient
Combining both,
Let M = 3 and N = 4
|m - n| + |2m - n| + |2n - m|
|3 - 4| + |2*3 - 4| + |2*4 - 3|
1+2+5
8 is divisible by 4
Let M = 3 and N = 2
|m - n| + |2m - n| + |2n - m|
|3 - 2| + |2*3 - 2| + |2*2 - 3|
1+4+1
6 is not divisible by 4
Answer is E
Posted from my mobile device
1) 2m > n
Let m = n = 1
|m - n| + |2m - n| + |2n - m|
|1-1|+|2-1|+|2-1|
2 (2 is not divisible by 4)
Let M = 3 and N = 4
|m - n| + |2m - n| + |2n - m|
|3 - 4| + |2*3 - 4| + |2*4 - 3|
1+2+5
8 is divisible by 4
Not sufficient
2) 2N > M
Let m = n = 1
|m - n| + |2m - n| + |2n - m|
|1-1|+|2-1|+|2-1|
2 (2 is not divisible by 4)
Let M = 3 and N = 4
|m - n| + |2m - n| + |2n - m|
|3 - 4| + |2*3 - 4| + |2*4 - 3|
1+2+5
8 is divisible by 4
Not sufficient
Combining both,
Let M = 3 and N = 4
|m - n| + |2m - n| + |2n - m|
|3 - 4| + |2*3 - 4| + |2*4 - 3|
1+2+5
8 is divisible by 4
Let M = 3 and N = 2
|m - n| + |2m - n| + |2n - m|
|3 - 2| + |2*3 - 2| + |2*2 - 3|
1+4+1
6 is not divisible by 4
Answer is E
Posted from my mobile device
05 Nov 2022, 09:07
Kudos
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Bunuel
The way I solved is - I can quickly see that each of the statements alone cannot be possibly sufficient. On combining both the statements I know that the second and third modulus are positive, but I still don't know whether the first one is positive or not. (since m>=n or m<=n). Either way, I get either 2m or 2n, which may or may not be divisible by 4, depending on whether m and n are even or not. So even both statements combined are not sufficient, and the answer is E.
