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A manufacturer is designing two rectangular game boards. The width of

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A manufacturer is designing two rectangular game boards. The width of  [#permalink]

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New post 12 Jul 2018, 05:04
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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

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Re: A manufacturer is designing two rectangular game boards. The width of  [#permalink]

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New post 12 Jul 2018, 05:13
Let's plug some noble integers:
Large board:
Width=4
Length = 6
Area of the large board 4*6=24

Small board
Width=4*0.5=2
Lenght=6*\(\frac{1}{6}\)=1

Area of the small board N=2*1=2

Difference between boards 24-2=22
Thus 22=11N (As N=2)

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Re: A manufacturer is designing two rectangular game boards. The width of  [#permalink]

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New post 12 Jul 2018, 06:24
Bunuel 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

Let the Length of the Larger board be 6 and width be 2 , So Area of the Large Board is 12

Again, Length of the Smaller board is 1 and width be 1, So Area of the Large Board is 1 = N

If N = 1, Difference of the areas will be (12- 1)N = 11N, Answer must be (C) 11N
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A manufacturer is designing two rectangular game boards. The width of  [#permalink]

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New post 12 Jul 2018, 06:49
Bunuel 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



It is mentioned in the question that Are of the smaller Rectangular is N. We can assume value for N. N must the the Multiple of LCM of 2 and 6 .

Smaller Rectangular :

Length = 6
width = 6

N = 36 ( Assumed )

Area of the Larger Rectangular:

Length = 36.................As per the question it is must be 6 times of the smaller board.

width = 12 .................As per the question it is must be 2 times of the smaller board.

Area : 432

So, Difference of the Area of the boards : 432 - 36 = 396.

Option C : 11 N = 11 *36 = 396. That meets our demand.

Thus option C is the best answer.
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Re: A manufacturer is designing two rectangular game boards. The width of  [#permalink]

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New post 12 Jul 2018, 09:10
Let L and W be the length and width of the smaller board. Its area will be WL (=N)

From the stem, we know that the length of the bigger board will be 6L, and its width 2W. Its area will then be 12WL, or 12N.

The difference between the two areas will be 12N - N = 11N.
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Re: A manufacturer is designing two rectangular game boards. The width of &nbs [#permalink] 12 Jul 2018, 09:10
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