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Math Expert V
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If k, m, and p are integers, is k – m – p odd?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:32) correct 24% (01:22) wrong based on 48 sessions

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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 (not necessarily in that order).

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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Quote:
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.

Question: Is k - m - p = Odd?

For k - m - p to be ODD, either
Case 1) Two of them should be even and one must be odd OR
Case 2) All three of them should be odd

Statement 1: k and m are even and p is odd.

Case 1 applies hence answer to the question is YES

SUFFICIENT

Statement 2: k, m, and p are consecutive integers

i.e. either two of them are even and one of them is odd then k-m-p = ODD OR
two of them are Odd and one of them is even then k-m-p = EVEN

hence answer to the question is YES/NO

NOT SUFFICIENT

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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If k, m, and p are integers, is k – m – p odd?

(1) k and m are even and p is odd.
It will be -> Even - Even - Odd = 'Odd' always

Sufficient. A D / B C E

(2) k, m, and p are consecutive integers.
Let us take the examples starting with an odd (1, 2, 3)
Odd - Even - Odd = Even
Even - Odd - Even = Odd
Two different possibilities. Insufficient.

'A' is the winner

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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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.

i) Even - Even - Odd = Odd -> Sufficient

ii) k, m and p are consecutive => Since we are not given which of them are odd or even we can not determine
For eg. k=1, m = 2, p=3 => k-(m+p) = -4 = Even
k=2,m=3,p=4 => k-(m+p) = -5 = Odd
Not Sufficient

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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Quote:
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.

k,m,p=integers
cases: k-m-p=odd
o-o-o=e-o=odd
e-e-o=e-o=odd

(1) sufic
e-e-o=e-o=odd

(2) insufic
e-o-e=o-e=odd
o-e-o=o-o=even

Ans (A)
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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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If k, m, and p are integers, is k – m – p odd?

(1) k and m are even and p is odd.
e.g. k=4, m=2, p=1, then k – m – p = 1 (odd). Try various combinations and we will find that k – m – p is always odd here.
SUFFICIENT

(2) k, m, and p are consecutive integers (not necessarily in that order).
e.g. k=5, m=4, p=3, then k – m – p = -2 (even).
e.g. k=4, m=3, p=2, then k – m – p = -1 (odd).
NOT SUFFICIENT

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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Statement 1: given : k,m: even & p: odd

K-m-p = Even - Even - Odd = Odd ; sufficient

Statement 2: if p<m<k

case I: p is odd
k-m-p = Odd - Even -Odd = Even

case II: p is even
k-m-p = Even - Odd - Even = Odd

result will change with even / odd nature of first number. Not sufficient.

Ans: A
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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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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 (not necessarily in that order).

From statement (1), k and m are even and p is odd.
Even – Even – Odd = Even – Odd = Odd, Therefore, Sufficient.

From statement (2), when, k =1, m = 2, p = 3
Odd – Even – Odd = Odd – Odd –Even = Even – Even = Even

When, k = 2, m =3, p = 4
Even – Odd – Even = Even – Even –Odd = Even – Odd = Odd
Therefore, Insufficient.
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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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1
If k, m, and p are integers, is k – m – p odd?

(Statement1): k and m are even and p is odd.
—> Even —Even —Odd = Odd
Sufficient

(Statement2): k, m, and p are consecutive integers (not necessarily in that order).
—> k, m, p —Odd, Even, Odd
Odd —Even —Odd = Even (No)

—> k,m,p — Even, Odd, Even
Even —Odd —Even = Odd (Yes)
Insufficient

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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1
Only possible case is O-E-E

(1) k and m are even and p is odd...... SUFFICIENT
0-0-1=-1
-10-2+5=-7
8-2-3=3

Only possible result is odd

(2) k, m, and p are consecutive integers (not necessarily in that order).....

Below are the possible cases

O-E-O.....results in odd
E-O-E..... results in even

So INSUFFICIENT

OA:A

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Re: If k, m, and p are integers, is k – m – p odd?  [#permalink]

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#1
k and m are even and p is odd.
e-(e+o) ; e-o ; odd sufficient ( always)
#2
k, m, and p are consecutive integers (not necessarily in that order).
we can have k,m,p as o,e,o and e,o,e
for o,e,o ; o-(e+o) ; o-o ; even
for e,o,e; e-(o+e) ; e-o ; odd
insufficient
IMO A ; sufficient
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 (not necessarily in that order). Re: If k, m, and p are integers, is k – m – p odd?   [#permalink] 22 Feb 2020, 05:30

# If k, m, and p are integers, is k – m – p odd?  