GMAT Problem Solving - If d denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> ?

Question: If d denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> ?

1. 10
2. 12
3. 24
4. π*<12>
5. π*<24>

“If denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> ?” - is a topic of the GMAT Problem Solving of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Explanation - This question comes with only one solution,
To find which of the following options from below is equal to <4>*<6>, when d denotes the area of a circle with diameter d, let us follow the steps below-
It is given that,

Area of circle with diameter d
And
=\(\frac{π*d^2}{4}\)
<4>*<6> = \(\frac{π*4^2}{4}\) * \(\frac{π*6^2}{4}\)
=\(\frac{π^2*576}{16}\)
= \(\frac{π^2*144}{4}\)
= π* \(\frac{π*12^2}{4}\)
= π*<12>

As you can see that we get π*<12>, it is i equal to <4>*<6>, when d denotes the area of a circle with diameter d
The answer is D, which is π*<12>

Correct Answer: D

Approach Solution 2:

Given,

is the diameter of a circle.

We can first find the area of the circle

Solution,

We can find the area of the circle as follows:

We know that the area of a circle is given as = 

Where 

Now,

The diameter of a circle is always double the radius. If D is the diameter and r is the radius,

Substituting the value in 

Area of the circle = 

Now, if we take the equatiuon:

=\(\frac{π*d^2}{4}\)
<4>*<6> = \(\frac{π*4^2}{4}\) * \(\frac{π*6^2}{4}\)
=\(\frac{π^2*576}{16}\)
= \(\frac{π^2*144}{4}\)
= π* \(\frac{π*12^2}{4}\)
= π*<12>

We get π*<12>, is equal to <4>*<6>, when d denotes the area of a circle with diameter d

Correct Answer: D

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