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Question (11)

QN0030838

A 6 × 9 grid contains how many unit squares?

(A) 45
(B) 48
(C) 54
(D) 60

Correct Answer: C

Explanation:

Total unit squares = 6 × 9 = 54.

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Question (12)

QN0030839

How many 2 × 1 tiles are needed to tile a 6 × 9 grid completely?

(A) 24
(B) 27
(C) 30
(D) 54

Correct Answer: B

Explanation:

Number of tiles = 54 ÷ 2 = 27.

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Question (13)

QN0030840

Which of the following grids cannot be tiled using only 2 × 1 tiles?

(A) 2 × 9
(B) 5 × 8
(C) 7 × 7
(D) 6 × 5

Correct Answer: C

Explanation:

A 7 × 7 grid has 49 unit squares, an odd number.

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Question (14)

QN0030841

A 3 × 8 grid has a total area of

(A) 22 unit squares
(B) 24 unit squares
(C) 26 unit squares
(D) 28 unit squares

Correct Answer: B

Explanation:

Area = 3 × 8 = 24 unit squares.

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Question (15)

QN0030842

How many 2 × 1 tiles are required to tile a 3 × 8 grid completely?

(A) 10
(B) 11
(C) 12
(D) 24

Correct Answer: C

Explanation:

Total unit squares = 24. Therefore, 24 ÷ 2 = 12 tiles.

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Question (16)

QN0030843

A 5 × 4 grid contains how many unit squares?

(A) 18
(B) 20
(C) 22
(D) 24

Correct Answer: B

Explanation:

Total unit squares = 5 × 4 = 20.

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Question (17)

QN0030844

How many 2 × 1 tiles are needed to tile a 5 × 4 grid completely?

(A) 8
(B) 9
(C) 10
(D) 20

Correct Answer: C

Explanation:

Number of tiles = 20 ÷ 2 = 10.

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Question (18)

QN0030845

A 7 × 10 grid can be tiled using 2 × 1 tiles because

(A) both numbers are odd
(B) one dimension is even
(C) the grid is square
(D) diagonal placement is necessary

Correct Answer: B

Explanation:

A grid is tileable with 2 × 1 tiles if at least one dimension is even.

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Question (19)

QN0030846

A 9 × 9 grid contains

(A) 72 unit squares
(B) 79 unit squares
(C) 81 unit squares
(D) 90 unit squares

Correct Answer: C

Explanation:

Total unit squares = 9 × 9 = 81.

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Question (20)

QN0030847

Why is a 9 × 9 grid not completely tileable using 2 × 1 tiles?

(A) It has an odd number of rows.
(B) It has an odd number of columns.
(C) It contains an odd number of unit squares.
(D) It is too large.

Correct Answer: C

Explanation:

Since there are 81 unit squares, the total is odd and cannot be covered by 2 × 1 tiles.

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Question (11)

A 6 × 9 grid contains how many unit squares?

Explanation:

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Question (12)

How many 2 × 1 tiles are needed to tile a 6 × 9 grid completely?

Explanation:

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Question (13)

Which of the following grids cannot be tiled using only 2 × 1 tiles?

Explanation:

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Question (14)

A 3 × 8 grid has a total area of

Explanation:

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Question (15)

How many 2 × 1 tiles are required to tile a 3 × 8 grid completely?

Explanation:

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Question (16)

A 5 × 4 grid contains how many unit squares?

Explanation:

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Question (17)

How many 2 × 1 tiles are needed to tile a 5 × 4 grid completely?

Explanation:

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Question (18)

A 7 × 10 grid can be tiled using 2 × 1 tiles because

Explanation:

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Question (19)

A 9 × 9 grid contains

Explanation:

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Question (20)

Why is a 9 × 9 grid not completely tileable using 2 × 1 tiles?

Explanation:

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