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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Jun 01, 2011 1:58 am

X,Y,W and Z are all integers
X-Y-Z is even and 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 odd
e) Y must be even
OA later

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Source: Beat The GMAT — Data Sufficiency | Wed Jun 01, 2011 1:58 am

sameerballani: Legendary Member; Posts: 544; Joined: Mon Dec 27, 2010 8:10 amFollowed by: 2 members; Thanked: 45 times

by sameerballani » Wed Jun 01, 2011 2:05 am

OA: C ?

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sjmit4: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun Jan 10, 2010 4:52 am; GMAT Score:710

by sjmit4 » Wed Jun 01, 2011 2:08 am

cans wrote:X,Y,W and Z are all integers
X-Y-Z is even and 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 odd
e) Y must be even
OA later

Ans is C.
if X is even then Y and Z both are either odd or even.(First condition X-Y-Z is even)
and hence W should be odd (Second condition Y-Z-W is odd)

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Wed Jun 01, 2011 2:09 am

cans wrote:X,Y,W and Z are all integers
X-Y-Z is even and 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 odd
e) Y must be even
OA later

x-(y+z) is even; also x is even;
therefore y+z must be even because Even-Even=Even;
y+z will be even if y is even and z is even or if y is odd and z is odd,-----1)

Y-Z-W is odd; y-(z+w) is odd, from 1) we have that y,z both will either be even or odd,
y,z even
Even-(Even+odd)= Even-odd=odd,
ie w is odd for both y,z to be even,
when y,z are odd
odd-(odd+odd)= odd-even=odd;
ie w is odd for both y,z to be odd,
hence w must be odd, C

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Jun 01, 2011 2:19 am

OA C

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