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13 Sep 2009, 13:13
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wxy = 24
1.) wy is not divisible by 6
Let wy = 8
w = 1 ; y = 8 ; x = 3 => xy = 24
w = 2 ; y = 4 ; x = 3 => xy = 12
w = 8 , y = 1 ; x = 3 => xy = 3 not divisible by 6
Hence, insufficient..
2.) x is even , Let x = 2k
=> w2ky = 24
=> wky = 12
w = 1 ; k = 2 ; y = 6 => xy = 24
w = 1 ; k = 6 ; y = 2 => xy = 24
w = 2 ; k = 6 ; y = 1 => xy = 12
w = 2 ; k = 1 ; y = 6 => xy = 12
w = 6 ; k = 2 ; y = 1 => xy = 4
w = 6 ; k = 1 ; y = 2 => xy = 4
w = 1 ; k = 3 ; y = 4 => xy = 24
w = 1 ; k = 4 ; y = 3 => xy = 24
w = 3 ; k = 1 ; y = 4 => xy = 8
w = 3 ; k = 4 ; y = 1 => xy = 8
w = 4 ; k = 3 ; y = 1 => xy = 6
w = 4 ; k = 1 ; y = 3 => xy = 6
Hence, insufficient.
combiining both,
w = 1 ; k = 6 ; y = 2 => xy = 24
w = 2 ; k = 6 ; y = 1 => xy = 12
w = 1 ; k = 3 ; y = 4 => xy = 24
w = 1 ; k = 4 ; y = 3 => xy = 24
w = 3 ; k = 4 ; y = 1 => xy = 8
w = 4 ; k = 3 ; y = 1 => xy = 6
Insufficient..
Henc, answer is E
1.) wy is not divisible by 6
Let wy = 8
w = 1 ; y = 8 ; x = 3 => xy = 24
w = 2 ; y = 4 ; x = 3 => xy = 12
w = 8 , y = 1 ; x = 3 => xy = 3 not divisible by 6
Hence, insufficient..
2.) x is even , Let x = 2k
=> w2ky = 24
=> wky = 12
w = 1 ; k = 2 ; y = 6 => xy = 24
w = 1 ; k = 6 ; y = 2 => xy = 24
w = 2 ; k = 6 ; y = 1 => xy = 12
w = 2 ; k = 1 ; y = 6 => xy = 12
w = 6 ; k = 2 ; y = 1 => xy = 4
w = 6 ; k = 1 ; y = 2 => xy = 4
w = 1 ; k = 3 ; y = 4 => xy = 24
w = 1 ; k = 4 ; y = 3 => xy = 24
w = 3 ; k = 1 ; y = 4 => xy = 8
w = 3 ; k = 4 ; y = 1 => xy = 8
w = 4 ; k = 3 ; y = 1 => xy = 6
w = 4 ; k = 1 ; y = 3 => xy = 6
Hence, insufficient.
combiining both,
w = 1 ; k = 6 ; y = 2 => xy = 24
w = 2 ; k = 6 ; y = 1 => xy = 12
w = 1 ; k = 3 ; y = 4 => xy = 24
w = 1 ; k = 4 ; y = 3 => xy = 24
w = 3 ; k = 4 ; y = 1 => xy = 8
w = 4 ; k = 3 ; y = 1 => xy = 6
Insufficient..
Henc, answer is E
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pejmanjohn
St.1:
Case 1: wy = 2 or, w,y = 1,2 or 2,1
Case 2: wy = 4 or, w,y = 1,4 or 4,1
Case 3: wy = 8 or, w,y = 1,8 or 8,1 or 4,2 or 2,4
Case 4: wy = 3 or, w,y = 1,3 or 3,1
x = 12, 6, 3, 8 for case 1,2,3,4 respectively.
Insufficient.
St. 2:
x = 2,4,6,8,12
Insufficient.
Combined: For all values of x, xy will be divisible by 6 except when x= 8 & y=1.Insufficient.
Hence, E.
Edited: Missed case 4!
13 Sep 2009, 18:41
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(1) wy is not divisible by 6.
So, wy can be anything other than 6,12 or 24
Consider W= 8 , X= 3 and Y = 1 => xy = 3
Or W=1 Y =2 and X= 12 => XY = 24
So, not sufficient by itself.
(2) x is even.
Consider X = 2 , WY = 12 ; It can mean w= 12 and y =1 or it can also mean y=12 and w=1 ; so its not sufficient by itself.
Combined = >
X = (6,8,12)
WY = (4,3,2)
when X=6 , XY is obviously divisible by 6.
Lets consider X = 8 WY =3
W=3 and Y =1 => XY = 8
or W= 1 and Y=3 => XY= 24
So, combined is also not sufficient. Answer is E.
So, wy can be anything other than 6,12 or 24
Consider W= 8 , X= 3 and Y = 1 => xy = 3
Or W=1 Y =2 and X= 12 => XY = 24
So, not sufficient by itself.
(2) x is even.
Consider X = 2 , WY = 12 ; It can mean w= 12 and y =1 or it can also mean y=12 and w=1 ; so its not sufficient by itself.
Combined = >
X = (6,8,12)
WY = (4,3,2)
when X=6 , XY is obviously divisible by 6.
Lets consider X = 8 WY =3
W=3 and Y =1 => XY = 8
or W= 1 and Y=3 => XY= 24
So, combined is also not sufficient. Answer is E.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
