BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Even Game

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
GMAT Score:710

Even Game

by gmatmachoman » Sun Feb 21, 2010 5:24 am
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
Last edited by gmatmachoman on Sun Feb 21, 2010 5:41 am, edited 1 time in total.
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 102
Joined: Sat Feb 20, 2010 5:38 am
Location: IIM Ahmedabad
Thanked: 10 times

by firdaus117 » Sun Feb 21, 2010 5:33 am
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.
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Sun Feb 21, 2010 5:40 am
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.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Sun Feb 21, 2010 6:12 am
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
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Sun Feb 21, 2010 6:35 am
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
Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Sun Feb 21, 2010 7:57 am
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
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
Senior | Next Rank: 100 Posts
Posts: 33
Joined: Thu Dec 20, 2018 2:09 am

by masoom j negi » Thu Dec 20, 2018 2:21 am
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.
Top
Post new topic Post Reply
• Page 1 of 1