As Shown Above, A Rectangle Is Divided Into Smaller Rectangles Of The GMAT Data Sufficiency

Question:

As shown above, a rectangle is divided into smaller rectangles of the same size and shape. What is the perimeter of the large rectangle?

(1) The length of the darkened path on the right is 36.
(2) The length of the darkened path on the left is 54.

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.

“As shown above, a rectangle is divided into smaller rectangles of the” - is a topic of the GMAT Quantitative reasoning section of GMAT. The GMAT Quant section includes 31 multiple-choice questions that need to be finished in 62 minutes.GMAT Data Sufficiency questions are followed by a problem statement that consists of two factual statements. This specific GMAT data sufficiency question evaluates the candidate’s mastery of solving calculative mathematical problems. The challenging portion of this type of question mainly comes from clever wording of the question that candidates overlook. GMAT data sufficiency contains 15 questions, two-fifths of the entire 31 GMAT quant questions.

Solutions and Explanation

Approach Solution : 1

The dimensions of a rectangle are length and width. However, we can infer from the graph that 2*Width = 1*Length. As a result, the width is the only variable needed to define the rectangle, and the length is equal to the width.

Statement 1:

We can count how many lengths and widths we must add up, but in the end, it will be a multiple of 36, so we can first solve for width before moving on to length. Sufficient.

Statement 2:

similar to above, that's enough.

Correct Answer: (D)

Approach Solution : 2

If we carefully observe, length = x, width = y, and x = 2y. Therefore, it is sufficient to find the perimeter of a large rectangle if we know x or y.

Large rectangle perimeter = 12x + 6y = 12x or 24y

1. Length of the path that is darkened on the right: 3x+6y =>6x =>6x= 36 =>x=6=>12x =>72, sufficient
2. Length of the left-hand darkened path: 4x+10y =9x= 54=> x=6=> 12x=>72, sufficient

Correct Answer: (D)

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