What is the Perimeter of a Square Chessboard, If a Chessboard is made GMAT Data Sufficiency

Question: What is the perimeter of a square chessboard, if a chessboard is made of 8 rows of 8 equal squares?

1. The sum of the perimeters of all 64 squares on the board is 320 units
2. The perimeter of a single square is 5 units

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“What is the perimeter of a square chessboard, if a chessboard is made of 8 rows of 8 equal squares?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer: D
Solution and Explanation:
Approach Solution (1):

(1) The sum of the perimeter of all 64 squares on the board is 320 units.

Let the perimeter of the larger square be 4A and smaller square be 4a

Now n*4a = 320

a = 320/46 * 4 = 5/4

A = 8*5/4 = 10

Perimeter of the larger square = 40

Sufficient

(2) The perimeter of a single square is 5 units

4a = 5

a = 5/4

Sufficient

Correct Option: D

Approach Solution (2):

We have a restricted figure with pre defined square. We only need to know the side of square to know about the perimeter

(1) We can easily deduce side of square from this info

Sufficient

(2) We know the side of the square from this info

Sufficient

Correct Option: D

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