If X, Y, Z, and W are integers, X - Y - Z is even, Y - Z - W is odd an

Question

If X, Y, Z, and W are integers, X - Y - Z is even, Y - Z - W is odd and X is even, then which if the following must be true?

A. Y-Z must be odd.
B. W must be even.
C. W must be odd.
D. W must be even.
E. Z must be odd

X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true?
A. Y-Z must be odd.
B. W must be even.
C. W must be odd.
D. W must be even.
E. Z must be odd

Archit3110 · Answer

IMO C ; 
X-Y-Z ; even ; possible when e-e-e = even and e-o-o ; even
Y-Z-W; odd ; possible when ; e-e-o ; odd and o-o-o ; odd

A. Y-Z must be odd. ; NO
B. W must be even. ; NO
C. W must be odd; YES
D. W must be even; NO 
E. Z must be odd; NO

Bunuel  option B & D are same

Harsh9676 · Answer

IMO C

Givn that x is even

-Y-z should result be even and it's possible only if both y and z are of same even/odd nature

Case 1: Y is even and z is even

then Y-Z = even and w must be odd to make Y-Z-W odd.

Case 2: Y is odd and Z is odd

Then Y-Z = even and W must be odd to make Y-Z-W odd.

In both the cases, W is odd

Posted from my mobile device

anbknaga · Answer

Some basic math rules to make the problem easy :
a. Even + Even = Even
b. Odd + Odd = Even
c. Even + Odd = Odd
d. Odd + Even = Odd

Remember that in addition or subtraction of two numbers,  the output is EVEN only if both the numbers are even or if both the numbers are odd

Taking the given equation:
X - Y - Z is even. This equation can be re-written as:
X - (Y + Z) is even

Since we know that  x is even  and also from the basic math rules discussed above, for addition of two quantities to be even when one of the quantity is even, the other quantity must also be even.

so here, Y + Z must also be even. This means,
Y and Z are even  OR 
Y and Z are odd

Now lets move on to the other given equation:

Y - Z - W is odd

Since we have two possibilities of even/odd for Y and Z from the first equation, we will substitute both in this equation.

if both Y and Z are even, then in this equation,

Even(Y) - Even(Z) - W is odd.
Even - W is ODD.
Therefore from the basics,  W must be odd .

Now, if both Y and Z are odd, then in this equation,

Odd(Y) - Odd(Z) - W is Odd
Even - W is odd
Therefore  W must be odd

So from the given information it is true that  W MUST BE ODD .

The answer is  C

bumpbot · Answer

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If X, Y, Z, and W are integers, X - Y - Z is even, Y - Z - W is odd an

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If X, Y, Z, and W are integers, X - Y - Z is even, Y - Z - W is odd an

Prep Toolkit

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