The diagonal of a square can be found by the following formula : Squroot 2 * side
Since we already know the length = Squroot 2 * side = Squroo 2 * x
We can divide the square root and we have side = x. So the area is x^2

For Quantity B we know that the diameter is x, so the radii must be x/2 and for the area it is multiplied by pi.

Lets plug some values.
For x = 2.
QA = Area is equal to 4
QB= Area is 3,14
QA is greater than B.

Lets try x =36
QA = 36
QB = 9,42

But what is bizarre it that when I plug 1 B is greater

Can I ask you what is the right reasoning?

Here let us put statement 1

Area of the square = \(\frac{{diagonal^2}}{2}\)

or \((\sqrt{2}x)^2\) * \(\frac{1}{2}\)
or \(\frac{2x^2}{2}\)

From statement 2

Area of circle = \(\pi * r^2\)

or \(\frac{22}{7}\) * \((\frac{Diameter}{2})^2\)

or \(\frac{22x}{28}\)


From the two results statement 1 > statement 2 for any positive value of x
_________________

If you found this post useful, please let me know by pressing the Kudos Button


Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

@Emike56

You are right if \(x\) is the diameter then radius of circle is \(\frac{x}{2}\).

Area of the circle is \(\pi \times radius^2= \pi \times (\frac{x}{2})^2=\pi \times \frac{x^2}{2^2}= \pi \times \frac{x^2}{4}\).

Hope this explains the 4.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

The area of a square region with diagonal of length \(\sqrt{2} x\).
If the diagonal is \(x\sqrt{2}\), the sides are x as \(side^2+side^2=(x\sqrt{2})^2=2x^2=2side^2....side=x\)
so area = \(side^2=x^2=A\)

The area of a circular region with diameter of length x
so radius = x/2.
area = B = \(\pi*(\frac{x}{2})^2=\pi*\frac{x^2}{4}=\frac{22}{28}*x^2=\frac{11}{14}*A\).

Thus A is greater
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html