Problem Solving

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) Z must be even.
(e) Z must be odd


DO u have a easy method to calculate this one without plugging Numbers???

OA :C

As X is even,Y and Z both needs to be simultaneously odd or even in order to make the expression X-Y-Z even.
For Y-Z-W to be odd,two cases are possible
Y Z W
E E O
O O O
In either case,W is odd.
Hence,option C.

gmatmachoman wrote: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) Z must be even.
(e) Z must be odd


DO u have a easy method to calculate this one without plugging Numbers???

Now,X is even.
That means -(Y+Z) is even.[X-(Y+Z) is even when X is even and Y+Z is even]
Hence,we have 2 cases.
Case 1:-Y even,Z even
Case 2:-Y odd,Z odd
Now, in any case Y-Z would be even only.[Even - Even =Even]
Hence,W has to be odd.
Hence,option C.

gmatmachoman wrote: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) Z must be even.
(e) Z must be odd


DO u have a easy method to calculate this one without plugging Numbers???

OA :C

X-Y-Z is even
Y-Z-W is odd

The sum ; X-2Z-W is odd

if X is even W is odd

gmatmachoman wrote: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) Z must be even.
(e) Z must be odd


DO u have a easy method to calculate this one without plugging Numbers???

OA :C

first remeber properties
even-even=even[8-6=2 for eg]
odd-odd=even[9-1=8]
even-odd=odd[8-3=5]

now in x-y-z=even----->{even-even-even or evn-odd-odd)
if y=odd---.z=odd
and if y=evn------->z=even

so for
y-z-w to be odd
if y=odd--->z=odd therfore z must be odd to get an odd value
and if y=evn------>w=evn--------->w must be odd to get an odd value

so in any case w is odd hence C

gmatmachoman wrote: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) Z must be even.
(e) Z must be odd


DO u have a easy method to calculate this one without plugging Numbers???

OA :C

(O+O=E, E+E=E, O+E = O , E+O = O)
X is even....X-Y-Z is also even --> Y+Z is even (E-E=E) so either both Y and Z is odd or both Y and Z is even (O+O=E, E+E=E)
Now since either both Y and Z is odd or both Y and Z is even (O+O=E, E+E=E)
--> Y-Z is also even.

Y-Z-W is odd --> now Y-Z is even and Y-Z-W is odd so W must be odd (O+E = O , E+O = O)
Hence W must be odd Ans C

The first expression is even and the second is odd,
the only difference between the expressions is that the first expression has X and the second has W.
So, if X is even W must be odd.