What is the area of square ABCD?

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

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..

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.

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

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..

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________