In the figure above, is the shaded region a square region? (1) ABCD a

Please comment on the flow of my thoughts,

Statement 1:
Not Sufficient - because there is no information about how much vertical line CD cuts into horizontal line EF
Not Sufficient - because there is no information about how much vertical line EH cuts into horizontal line AD

Statement 2:
EF = BC
Not Sufficient - because no information about the actual shape of quadrilateral is given

Combo:
Both squares are of the same dimension
Not Sufficient - because there is no information about how much vertical line CD cuts into horizontal line EF
Not Sufficient - because there is no information about how much vertical line EH cuts into horizontal line AD

The shaded region is square if information such as Vertical line CD bisects horizontal line EF and vertical line EH bisects horizontal line AD

All correct.
Note that for DS questions it is often much faster to try to SEE the answer then to formally analyze it.
When you do this, make sure that you know which parts of the drawings are 'fixed' and which can be 'played with'.

Solution

Steps 1 & 2: Understand Question and Draw Inferences
We are given:

• A shaded region

We need to find:

• Whether the shaded region is a square region or not.

For a region to be a square, its all the sides should be equal, and all the internal angles must be 900.

• So, we will check if all the sides are equal and all internal angles are 900.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1
“ABCD and EFGH are squares.”

From this information, we cannot say anything about the shaded region.

• It may or may not be a square.

Thus, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2
“BC = EF”

This information does not help us say anything about the shaded region.

• Thus, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

From statement 1:

• ABCD and EFGH are squares.

From statement 2:

• BC = EF

On combining both the statements, we can say that sides of square ABCD and EFGH are equal.
However, this does not ensure that shaded region is also a square.

Hence, we can find the answer even after combining both the statements together.

• Thus, the correct answer choice is option E.

In the figure above, is the shaded region a square region?

(1) ABCD and EFGH are squares.

We can't conclude that the shaded region is a square with this information. INSUFFICIENT.

(2) BC = EF

We can't conclude that the shaded region is a square with this information. INSUFFICIENT.

(1&2) We don't know if all the sides of the shaded region are equal. INSUFFICIENT.

Answer is E.

We need to know the size of the sides of the shaded region the comment on it.

(1) No information is given about the sides of the shaded region. Insufficient.

(2) No information is given about the sides of the shaded region. Insufficient.

Considering Both:
Still No information is given about the sides of the shaded region. Insufficient.

The answer is \(E.\)

Bunuel are questions like this now excluded from GMAT Focus? Thanks in advance!­

­
Such questions are no longer part of the DS syllabus. First, they require specific knowledge in geometry, which is no longer tested on the GMAT. Second, DS no longer includes pure math questions like these.

Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

• Word Problems
• Work Problems
• Distance Problems
• Mixture Problems
• Percent and Interest Problems
• Overlapping Sets Problems
• Statistics Problems
• Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.­