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WE:Education (Education)
m, n, and p are integers such that m + n + p is odd. Which of the
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09 Mar 2021, 02:20
09 Mar 2021, 02:20
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\(m, n,\) and \(p\) are integers such that \(m + n + p\) is odd.
Which of the following must be even?
A. \(m - n - p - 2\)
B. \(p - m - n - 3\)
C. \(n + p - 4 - m\)
D. \(p - 5 + m - n\)
E. \(6 - m - p + n\)
F. \(m + n - 7 - p\)
Which of the following must be even?
A. \(m - n - p - 2\)
B. \(p - m - n - 3\)
C. \(n + p - 4 - m\)
D. \(p - 5 + m - n\)
E. \(6 - m - p + n\)
F. \(m + n - 7 - p\)
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
m, n, and p are integers such that m + n + p is odd. Which of the
[#permalink]
09 Mar 2021, 23:16
09 Mar 2021, 23:16
KarunMendiratta wrote:
\(m, n,\) and \(p\) are integers such that \(m + n + p\) is odd.
Which of the following must be even?
A. \(m - n - p - 2\)
B. \(p - m - n - 3\)
C. \(n + p - 4 - m\)
D. \(p - 5 + m - n\)
E. \(6 - m - p + n\)
F. \(m + n - 7 - p\)
Which of the following must be even?
A. \(m - n - p - 2\)
B. \(p - m - n - 3\)
C. \(n + p - 4 - m\)
D. \(p - 5 + m - n\)
E. \(6 - m - p + n\)
F. \(m + n - 7 - p\)
OA Explanation:
\(m + n + p\) is odd
This means either we have 1 odd number or all 3 odd numbers
i.e. odd + even + even = odd
odd + odd + odd = odd
Which of the following must be even? - We are looking for option choices with either 0 even numbers or 2 even numbers or all 4 even numbers
A. \(m - n - p - 2\)
Case I: odd - even - even - even = odd
Case II: odd - odd - odd - even = odd
B. \(p - m - n - 3\)
Case I: odd - even - even - odd = even
Case II: odd - odd - odd - odd = even
C. \(n + p - 4 - m\)
Case I: odd + even - even - even = odd
Case II: odd + odd - even - odd = odd
D. \(p - 5 + m - n\)
Case I: odd - odd + even - even = even
Case II: odd - odd + odd - odd = even
E. \(6 - m - p + n\)
Case I: even - odd - even + even = odd
Case II: even - odd - odd + odd = odd
F. \(m + n - 7 - p\)
Case I: odd + even - odd - even = even
Case II: odd + odd - odd - odd = even
Hence, option B, D, and F
gmatclubot
m, n, and p are integers such that m + n + p is odd. Which of the [#permalink]
09 Mar 2021, 23:16
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