Is rectangle R a square? (1) At least one side of rectangle R has an

Question

Is rectangle R a square?

(1) At least one side of rectangle R has an integer length.

(2) The diagonals of rectangle R have integer lengths.

ATC93 · Answer

IMO the answer is E.

Knowing that one side is and integer and/or the diagonal is and integer is not enough.

Posted from my mobile device

firas92 · Answer

The statements are obviously not sufficient individually.

Combined, note that for a square the  diagonal=\sqrt{2}*side  and so if a square has integer sides, it cannot have integer diagonal and so the given rectangle is not a square

Answer is C

Posted from my mobile device

Niveditha28 · Answer

Bunuel  ,  chetan2u  - Can you please share your explanation

I choose Opt E. 
For example - Rectangle with diagonal 10 , one side as 9 and solving by pythogoras theorem - we get the third side as root 63. This is a valid example right?
It need not be an integer always.

chetan2u · Answer

Is rectangle R a square?

So we have to check whether sides are equal.

(1) At least one side of rectangle R has an integer length.
Sides could be 4 each, then a square. 
Sides could be 3,4,3,4, then a rectangle. 
Insufficient

(2) The diagonals of rectangle R have integer lengths.
If diagonal is 4, the sides could be  \frac{4}{\sqrt{2}} …Square
If diagonal is 5 and sides 3 and 4, then not a square. 
Insufficient

Combined 
The diagonal, say AC, and two sides, AB and BC, will make a right angled triangle. 
If R is a square the ratio of sides AB:BC:AC are  1:1:\sqrt{2} . 
 That is, in a square, both the diagonal and two equal sides will never be integer as DIAGONAL is  \sqrt{2}  times the side.  
Here, we have integer value for diagonal and a side, which will never be the case for a square. 
Thus R is not a square. 
Sufficient

C

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is rectangle R a square? (1) At least one side of rectangle R has an

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards