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The length of a certain rectangle is a multiple of 18, and the width

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Bunuel
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The length of a certain rectangle is a multiple of 18, and the width [#permalink] New post   13 Mar 2020, 07:57
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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
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Abhishek009
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Re: The length of a certain rectangle is a multiple of 18, and the width [#permalink] New post   13 Mar 2020, 10:12
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Bunuel wrote:
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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The length of a certain rectangle is a multiple of 18, and the width [#permalink] New post   Updated on: 13 Mar 2020, 10:47
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A) 60 = 2*30 = 2( 18+12)
C) 84 = 2*42 = 2( 18+12*2)
D) 96 = 2*48 = 2( 18*2 + 12)
E) 108 = 2*54 = 2( 18+ 12*3)

B) 72 = 2*36 cannot be the perimeter of the rectangle.

Answer (B)

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Originally posted by lacktutor on 13 Mar 2020, 08:05.
Last edited by lacktutor on 13 Mar 2020, 10:47, edited 1 time in total.
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Re: The length of a certain rectangle is a multiple of 18, and the width [#permalink] New post   13 Mar 2020, 08:15
OA is B
Length= 18x { 18,36,54...}
Width= 12y { 12,24,36,48...}
Perimeter= 2(l+w)
Put L= 18 and W= 12
2(18+12)=60
2(18+24)=84
2(36+12)=96
2(18+36)=108
2(36+24)=120
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Among all the options given only option B is not among the perimeter.
So OA is B

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Re: The length of a certain rectangle is a multiple of 18, and the width [#permalink] New post   13 Mar 2020, 11:10
Bunuel wrote:
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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Re: The length of a certain rectangle is a multiple of 18, and the width [#permalink] New post   17 Jan 2023, 17:39
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Re: The length of a certain rectangle is a multiple of 18, and the width [#permalink]
17 Jan 2023, 17:39
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