What is the area of square ABCD?

Question

(1) The diagonal of square ABCD is  5\sqrt{2} 
(2) The perimeter of square ABCD is 20

Kudos for correct  solution .

Mo2men · Answer

Let the length of square= L

(1) The diagonal of square ABCD is  5\sqrt{2}

So L= 5........> Area =5*5=25

(2) The perimeter of square ABCD is 20..............> 4L=20...? L=5
Area= 25

Answer: D

shakticnb · Answer

Let the length of square= L

(1) The diagonal of square ABCD is 52√52

So L= 5........> Area =5*5=25

(2) The perimeter of square ABCD is 20..............> 4L=20...? L=5
Area= 25
WE KNOW THAT SQUARE FORMS 45, 45, 90 TRIANGLE , SO BASIC CONCEPT IS KNOWING ANY SINGLE SIDE WE CAN CALCULATE ALL OTHER SIDES..

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the area of square ABCD?

(1) The diagonal of square ABCD is 5 √2 
(2) The perimeter of square ABCD is 20

In the original condition, there is 1 variable(one side of square: x) for square, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. In fact, it is 99% that D is the answer.
For 1), from √2(x)=5√2, x=5, which is unique and sufficient.
For 2), from 4x=20, x=5, which is unique and sufficient.
Therefore, the answer is D.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

rhine29388 · Answer

Statement 1 gives the length of diagonal of square as 5  \sqrt{2} 
so side is 5 and area = side^2  = 25
So sufficient
Statement 2 gives the perimeter as 20
perimeter = 4 * side = 20 so side is 5 and area =  side^2  = 25
So sufficient
Correct Answer - D

msk0657 · Answer

Took 16 secs to solve..I think it's still more..

Stat 1:  a\sqrt{2} (Diagonal of a sqaure) =  5\sqrt{2} .
 a = 5.. Sufficient..

Stat 2: 4a = 20 , a = 5..Sufficient..

Option D is correct answer..

nailin16 · Answer

D
Statement 1 is sufficient 
Side is 7
So area would be 49
Statement 2 is sufficient as well
Side is 7 as diagonal is sideroot2
So area 49

Sent from my SM-G600FY using  GMAT Club Forum mobile app

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.

What is the area of square ABCD?

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

GMAT Data Sufficiency (DS) Questions

What is the area of square ABCD?

Prep Toolkit

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