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# wxy = 24 1.) wy is not divisible by 6 Let wy = 8 w = 1 ; y =

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wxy = 24 1.) wy is not divisible by 6 Let wy = 8 w = 1 ; y = [#permalink]

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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..
Senior Manager
Joined: 20 Mar 2008
Posts: 454
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Re: If w, x and y are different positive integers [#permalink]

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13 Sep 2009, 14:26
pejmanjohn wrote:
If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?

(1) wy is not divisible by 6.

(2) x is even.

Source: Magoosh.com

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!

Last edited by Jivana on 13 Sep 2009, 18:55, edited 1 time in total.
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Re: If w, x and y are different positive integers [#permalink]

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13 Sep 2009, 18:41
(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.
Re: If w, x and y are different positive integers   [#permalink] 13 Sep 2009, 18:41
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