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

Since the figure shows an option in which the shaded area does indeed look as if it is a square, the Alternative approach will try to find another option to draw the figure so that the shaded area is not a square.
Even if ABCD and EFGH are both identical squares, we can 'move' the upper square a bit to the left and create a rectangle (there are many more examples that will not give us a square, but all we need is one).
The correct answer is (E).

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#1
not sufficient
#2
same info as #1 not sufficient
from 1&2

intersection /cross over figure is not clear whether its at mid point or not.

IMO E

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.

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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.
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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 \(E.\)

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