A 2 min read

OGQR 2020: Question No. 211

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

1. ABCD and EFGH are squares.
2. BC = EF

Source	OGQR 2020
Type	Data Sufficiency
Topic	Geometry
Sub-Topic	Polygons
Difficulty	Medium

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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