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A rectangular board measuring 9 inches by 11 inches is to be covered w

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Math Revolution GMAT Instructor
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A rectangular board measuring 9 inches by 11 inches is to be covered w  [#permalink]

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New post 22 May 2019, 02:10
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A
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C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (01:19) correct 39% (02:13) wrong based on 36 sessions

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[GMAT math practice question]

A rectangular board measuring 9 inches by 11 inches is to be covered with 2 inch by 3 inch rectangular tiles and 1-inch square tiles. What is the smallest number of tiles that can be used to cover the board?

A. 19
B. 20
C. 22
D. 24
E. 25

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Re: A rectangular board measuring 9 inches by 11 inches is to be covered w  [#permalink]

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New post 22 May 2019, 02:45
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MathRevolution wrote:
[GMAT math practice question]

A rectangular board measuring 9 inches by 11 inches is to be covered with 2 inch by 3 inch rectangular tiles and 1-inch square tiles. What is the smallest number of tiles that can be used to cover the board?

A. 19
B. 20
C. 22
D. 24
E. 25


toal area ; 9*11; 99
so we can use ; 16*2*3 ; 96
and 3 1*1 ; tiles
so total 16+3 ; 19
IMO A
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Re: A rectangular board measuring 9 inches by 11 inches is to be covered w  [#permalink]

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New post 22 May 2019, 02:56
Total area = 9 * 11 = 99 sq inches.

We have two types of tiles
1- measures 2 X 3 = 6 sq inches
2 - measures 1 X1 = 1 sq inches

No of type 1 tiles can be used = 99 / 6 = 16.
Remaining space => 99 - 96 = 3 sq inches.

We can use type 2 tiles for the remaining space -> 1 X 3 = 3 tiles

Total No tiles = 16 + 3 = 19.

IMO - A.

Thanks.
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Re: A rectangular board measuring 9 inches by 11 inches is to be covered w  [#permalink]

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New post 24 May 2019, 02:19
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Attachment:
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The smallest number of tiles will be obtained by using as many \(2\) inch by \(3\) inch rectangular tiles as possible since they are the larger tiles. As shown in the diagram above, \(16\) such tiles can be placed on the board, leaving three square inches to be covered with \(1\)-inch square tiles. The total number of tiles used is \(16 + 3 = 19.\)

Therefore, A is the answer.
Answer: A
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Re: A rectangular board measuring 9 inches by 11 inches is to be covered w   [#permalink] 24 May 2019, 02:19
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