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Bunuel
The length of a certain rectangle is a multiple of 18, and the width of the rectangle is a multiple of 12. Which of the following CANNOT be the perimeter of the rectangle?

(A) 60
(B) 72
(C) 84
(D) 96
(E) 108
Length = 18a ; Breadth = 12b

So, Perimeter must be 2 ( 18a + 12b) = 12(3a + 2b)

Now, check the options -

(A) 12(3a + 2b) = 60 ; So, 3a + 2b = 5 ; a = 1 , b = 1
(C) 12(3a + 2b) = 84 ; So, 3a + 2b = 7 ; a = 1 , b = 2
(D) 12(3a + 2b) = 96 ; So, 3a + 2b = 8 ; a = 2 , b = 2
(E) 12(3a + 2b) = 108 ; So, 3a + 2b = 9 ; a = 1 , b = 3

No such pair can be formed using option (B), hence answer must be (B)
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Bunuel
The length of a certain rectangle is a multiple of 18, and the width of the rectangle is a multiple of 12. Which of the following CANNOT be the perimeter of the rectangle?

(A) 60
(B) 72
(C) 84
(D) 96
(E) 108

the perimeter would be
12*(3x+2y)
least x=y=1 ; we get ; 60
and other options c,d,e are possible at x,y ; 2,2 ; 2,1 ; 1,3 ;
not possible is 72 ; i.e when 3x+2y= 6 as x,y cannot be 0
IMO B ; 72
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