Data Sufficiency

Kaustubhk wrote:In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS

What is the answer to this?

According to my analysis it has to be C.

Kindly comment.

Hi Kaustubhk,

The answer is A. Statement 1 alone is sufficient.

If two opposite sides are parallel and equal, the quadrilateral is a parallelogram.

Just to test it yourself. Put two equal sized pencils parallel to each other, and then move one of them keeping it parallel to the other. You would find that the quadrilaterals thus formed are all parallelograms.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Geometry Guide

-Jay
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Kaustubhk wrote:In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS

Target question: Is PQRS a parallelogram?

Given: Side PS is parallel to side QR

Statement 1: PS = QR
If side PS is parallel to side QR AND the 2 sides are equal length, then we will definitely get a parallelogram when we join the vertices.
Consider these examples of parallel sides of equal length.



When we connect the vertices, we get parallelograms.


Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Statement 2: PQ = RS
The following two quadrilaterals meet the given conditions:

Quadrilateral 1

In this case, PQRS IS a parallelogram

Quadrilateral 2

In this case, PQRS is NOT a parallelogram

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Answer: A

Cheers,
Brent

Kaustubhk wrote:Hi Brent,

It means that PS|| QR favours the statement A.

The other figures that we get after B are Rhombus and Trapezoid which are Quadrilateral and not parallelogram.

Thanks for the detailed explanation.

That's partially correct.
I just want to point out that a rhombus is a type of parallelogram.
Likewise, a square is a type of parallelogram
And a square is a type of rectangle.
etc.

For more on this, watch: https://www.gmatprepnow.com/module/gmat ... /video/874

Cheers,
Brent