3. If k, m, and p are integers, is k – m – p odd?
(1) k and m are even and p is odd.
(2) k, m, and p are consecutive integers.
The answer seems to be A, but why is statement 2 not sufficient?
k – m – p odd?
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1) k and m are even and p is odd
k-m-p=>E-E-O=>E-O=>O
sufficient
2) k, m, and p are consecutive integers
k, m and p can be E, O, E or O, E, O
if E, O, E, k-m-p=>E-O-E=>E-O=O
if O, E, O, k-m-p=>O-O-E=>E-E>E
sometimes even, sometimes odd
not sufficient
hence, A
k-m-p=>E-E-O=>E-O=>O
sufficient
2) k, m, and p are consecutive integers
k, m and p can be E, O, E or O, E, O
if E, O, E, k-m-p=>E-O-E=>E-O=O
if O, E, O, k-m-p=>O-O-E=>E-E>E
sometimes even, sometimes odd
not sufficient
hence, A
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If we take any three consecutive integers, either two are even and one is odd, or one is even and two are odd; the two possibilities give contradicting results in our case, if statement (2) alone is considered, hence (2) is insufficient, and (1) is doubtlessly sufficient for an answer. My [spoiler]A[/spoiler].
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IMO A
Statement 1: even - even - odd is odd. Hence statement 1 is sufficient
Statement 2: what if two integers are odd try putting in 5,6 and 7 result would be even.
Also I try to put in -1,0,1 to check if the rule holds. In this case it does not. Hence statement 2 is insufficient
Statement 1: even - even - odd is odd. Hence statement 1 is sufficient
Statement 2: what if two integers are odd try putting in 5,6 and 7 result would be even.
Also I try to put in -1,0,1 to check if the rule holds. In this case it does not. Hence statement 2 is insufficient
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k - m - p = k - (m + p)crackgmat007 wrote:3. If k, m, and p are integers, is k � m � p odd?
(1) k and m are even and p is odd.
(2) k, m, and p are consecutive integers.
The answer seems to be A, but why is statement 2 not sufficient?
(1) m is even and p is odd.
So m + p is odd.
k is even.
So k - (m + p) is odd; SUFFICIENT.
(2) Since k, m and p are consecutive integers, let m = k + 1 and p = k + 2.
So m + p is 2k + 3.
k - (m + p) is k - (2k + 3) = -k - 3.
So the value of k - (m + p) depends on whether k is even or odd; NOT sufficient.
The correct answer is A.
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Target question: Is k - m - p odd?crackgmat007 wrote:3. If k, m, and p are integers, is k - m - p odd?
(1) k and m are even and p is odd.
(2) k, m, and p are consecutive integers.
The answer seems to be A, but why is statement 2 not sufficient?
To show why statement 2 is not sufficient, we can plug in some values for k, m and p that satisfy the given condition that k, m, and p are consecutive integers. Here are 2 possible cases:
case a: k=2, m=3, p=4, in which case k-m-p= -5 (so k-m-p is odd)
case b: k=1, m=2, p=3, in which case k-m-p= -4 (so k-m-p is not odd)
Since we get conflicting answers to the target question, statement 2 is NOT SUFFICIENT.
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I'm not sure about external sites, but you can use BTG's tagging feature to examine tons of other GMAT questions that test Integer Properties: https://www.beatthegmat.com/forums/tags/ ... ropertiesTRiXcare wrote:Analogues are available?
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