Data Sufficiency

VJesus12 wrote:Is quadrilateral a square?

(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.

The OA is the option C .

Experts, I would like your explanation. I don't know how can I show that the correct answer is C.

(1) Three angles of a quadrilateral are 90 degrees each.

Three angles of a quadrilateral are 90 degrees each is true for a rectangle as well as a square. Insufficient.

(2) 3 sides of a quadrilateral are equal in length.

Three angles of a quadrilateral are 90 degrees each is true for a trapezium as well as a square. Insufficient.

(1) and (2) combined

Combining the two statements, the quadrilateral can only be a square. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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VJesus12 wrote:Is quadrilateral a square?

(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.

Target question: Is quadrilateral a square?

Statement 1: Three angles of a quadrilateral are 90 degrees each.
ASIDE: This also means that ALL FOUR angles are 90 degrees each.
This means that EITHER the quadrilateral is a square OR the quadrilateral is a rectangle
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3 sides of a quadrilateral are equal in length.
There are many possible shapes that meet this condition.
For example, the quadrilateral could be is a square OR the quadrilateral could be a rhombus
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Combining the statements, we get 4 90-degree angles, and at least 3 sides the same length.
This LOCKS the shape into a definite SQUARE
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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