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[Geometry]Manhattan Test question

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by Kaustubhk » Wed May 17, 2017 9:17 pm
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.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu May 18, 2017 11:02 am
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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by Kaustubhk » Fri May 19, 2017 1:01 am
Thanks Jay..

You are correct. The other set is not required to be parallel and equal. Just one pair of parallel and equal sides is enough.
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by Brent@GMATPrepNow » Fri May 19, 2017 4:55 am
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.
Image


When we connect the vertices, we get parallelograms.
Image

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
Image
In this case, PQRS IS a parallelogram

Quadrilateral 2
Image
In this case, PQRS is NOT a parallelogram

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


Answer: A

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Brent
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by Kaustubhk » Fri May 19, 2017 10:57 pm
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.
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by Brent@GMATPrepNow » Sat May 20, 2017 5:43 am
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

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Brent
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