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# A manufacturer is designing two rectangular game boards. Th

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A manufacturer is designing two rectangular game boards. Th [#permalink]  07 Jun 2017, 01:31
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A manufacturer is designing two rectangular game boards. The width of the smaller board is one-half the width of the larger board, and the length of the smaller board is one-sixth the length of the larger board. If the smaller board has area N, then what is the difference between the areas of the game boards, in terms of N ?

A) 3N

B) 9N

C) 11N

D) 12N

E) 18N
[Reveal] Spoiler: OA

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Re: A manufacturer is designing two rectangular game boards. Th [#permalink]  20 Sep 2017, 06:03
Keeping the width and length of the larger rectangular as X and Y, we have that the correspondent measures for the smaller rectangular are 1/2X and 1/6Y. Thus, since N is the area of the smaller rectangular, N = 1/2X*1/6Y = 1/12XY. The area of the larger rectangular, instead, is equal to XY. The difference is then equal to XY-1/12XY=11/12XY. Since N = 1/12XY, the difference in terms of N is 11N, i.e. 11*1/12 = 11/12. Then the answer is C!
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Re: A manufacturer is designing two rectangular game boards. Th [#permalink]  22 Sep 2017, 13:25
Carcass wrote:

A manufacturer is designing two rectangular game boards. The width of the smaller board is one-half the width of the larger board, and the length of the smaller board is one-sixth the length of the larger board. If the smaller board has area N, then what is the difference between the areas of the game boards, in terms of
N ?

A) 3N

B) 9N

C) 11N

D) 12N

E) 18N

For easy calculation at first consider-

Numerical value for wwidth and Length of the larger board and number is divisible

For larger board let us assume-

Length = 12

Width =4

therefore for smaller board

Length = $$\frac{1}{6}$$ *12 = 2

Width = $$\frac{1}{2}$$* 4 = 2 (Plz note every square can be rectangle but every rectangle cannot be square and these numbers assumed
still hold valid for the statement)

Therefore Area of Smaller Board= N = 4 and Area of Larger Board = 48

The difference between the areas= 48 -4 = 44

Now plug the value of N in the solution

Only option C satisfy

(Remember the we can put different value for Length and Breadth and the answer is remain the same, for easy calculation we take nos. that are divisible by 2 and 6)
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Re: A manufacturer is designing two rectangular game boards. Th   [#permalink] 22 Sep 2017, 13:25
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