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If X, Y, and Z are integers, is X(Y + Z) an odd integer?

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Bunuel
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If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   04 Jan 2021, 21:00
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If X, Y, and Z are integers, is X(Y + Z) an odd integer?

(1) XYZ is an odd integer.
(2) X + Y + Z is an odd integer.
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D
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If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   04 Jan 2021, 21:23
Given: X,Y and Z are INTEGERS
Q: X(Y+Z) => ODD ?

(1) XYZ is an odd integer.
For this to be true, all three X,Y, and Z SHOULD be ODD.
\(X(Y+Z) => ODD (EVEN) = EVEN \) as Odd + Odd = Even

Statement 1 is sufficient

(2) X + Y + Z is an odd integer.

Case 1:
All three X,Y,Z are ODD
Eg: X = 1, Y = 3, Z = 5
X + Y + Z = 9 (ODD)

\(X(Y+Z) => ODD (EVEN) = EVEN \) as Odd + Odd = Even

Case 2:
Any 2 are EVEN and 1 is ODD
Either X, Y or Z is ODD, and the other 2 EVEN
If X is EVEN, Y or Z is EVEN, then \(X(Y+Z) = EVEN\) as anything multiplied by Even gives Even
If Y and Z are even, then \(X(Y+Z) => ODD(EVEN) = EVEN\)

Statement 2 is sufficient

Answer is D

Is my solution correct ?
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   04 Jan 2021, 22:51
Statement 1: Sufficient
xyz is odd
So x,y, and z all three are odd.
odd(odd+odd) = odd(even) = even
Hence x(y+z) will be even and we have a definite NO answer.
Statement 2: Sufficient
x +y+z = odd
Different combinations which will produce this outcome:
odd+odd+odd = odd
even+even+odd = odd
All other combination will give even:
Even +odd+odd = even
Even+Even+Even = Even

So if all three are odd than odd(odd+odd) = odd(even)=even
If two are even and one is odd than even(odd+even) or odd(even+even) = even
So x(y+z) will be even and we have a definite NO.

Answer D
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   06 Jan 2021, 06:55
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Bunuel wrote:
If X, Y, and Z are integers, is X(Y + Z) an odd integer?

(1) XYZ is an odd integer.
(2) X + Y + Z is an odd integer.



(1) This means all three integers are Odd. Odd+Odd=Even and Even*Odd=Even, So, X(Y + Z) is Even. The answer is No, Sufficient.

(2) This means all three integers are Odd. Odd+Odd+Odd=Odd, Odd+Odd=Even, and Even*Odd=Even, So, X(Y + Z) is Even. The answer is No, Sufficient.

The answer is D
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   13 Jan 2021, 02:32
Bunuel wrote:
If X, Y, and Z are integers, is X(Y + Z) an odd integer?

(1) XYZ is an odd integer.
(2) X + Y + Z is an odd integer.


Just want to know
if (5,-3,3)= No,(3,5,8)=yes

Anyone please explain
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If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   Updated on: 14 Jan 2021, 21:33
Bunuel wrote:
If X, Y, and Z are integers, is X(Y + Z) an odd integer?

(1) XYZ is an odd integer.
(2) X + Y + Z is an odd integer.



Statement 1 : If we consider -3,-3,3 as X,Y and Z respectively then, XYZ = 27 which is odd
So X(Y+Z) will be 0 which is not odd

if consider 3,3,3 then XYZ = 27
So X(Y+Z) will be 18 which is not odd

So 1st alone is sufficient.


Statement 2 : X + Y + Z = Odd

1. if X,Y,Z = 3,3,3 then X(Y+Z) = 18 not odd
2. if X,Y,Z = -3,-3,3 then X(Y+Z) = 0 not consider as ODD

So 2nd alone is sufficient

So D

Originally posted by HinalAmin24 on 13 Jan 2021, 10:57.
Last edited by HinalAmin24 on 14 Jan 2021, 21:33, edited 1 time in total.
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   13 Jan 2021, 15:36
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jrk23 wrote:
Bunuel wrote:
If X, Y, and Z are integers, is X(Y + Z) an odd integer?

(1) XYZ is an odd integer.
(2) X + Y + Z is an odd integer.


Just want to know
if (5,-3,3)= No,(3,5,8)=yes

Anyone please explain


Your first example is with the option given. But the second one contradicts.

3*5*8=120 Even
3+5+8=16 Even.

Thank you for asking.
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   13 Jul 2021, 08:38
target is X(Y + Z) an odd integer
where all x,y, z are integers
#1
XYZ is an odd integer.
possible when all are odd
so x*(y+z) will never be odd
sufficient
#2
X + Y + Z is an odd integer
possible when wither all three are odd or
either of two are even and other is odd
so
X(Y + Z) will never be odd
sufficient
option D

Bunuel wrote:
If X, Y, and Z are integers, is X(Y + Z) an odd integer?

(1) XYZ is an odd integer.
(2) X + Y + Z is an odd integer.
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink] New post   01 Oct 2023, 23:58
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Re: If X, Y, and Z are integers, is X(Y + Z) an odd integer? [#permalink]
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