If P and Q are each circular regions, what is the radius of

SOLUTION

If P and Q are each circular regions, what is the radius of the larger of these regions?

(1) The area of P plus the area of Q is equal to \(90\pi\) --> \(\pi{R^2}+\pi{r^2}=90\pi\) --> \(R^2+r^2=90\). Not sufficient to get the value of R.

(2) The larger circular region has a radius that is 3 times the radius of the smaller circular region --> \(R=3r\). Not sufficient to get the value of R.

(1)+(2) \(R^2+r^2=90\) and \(R=3r\) --> \(10r^2=90\) --> \(r=3\) --> \(R=9\). Sufficient.

Answer: C.
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The radius of P and Q be R and r

Let the Area of P= \(\pi R^2\)
and Q = \(\pi r^2\)

Statement 1:

\(\pi R^2\) + \(\pi r^2\)= 90 \(\pi\).

On simplifying we will have \(R^2 + r^2\)= 90------- Not sufficient.

Statement 2:

Let Q be the larger region then,

r=3R------ Not sufficient.


Combining both, We can solve for the radius----- Sufficient


The answer is C.
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St1: The area of P plus the area of Q is equal to 90\pi

Not sufficient. We know nothing about the size (radius) of P and Q to make any sort of comparison.

St2: The larger circular region has a radius that is 3 times the radius of the smaller circular region.

Not sufficient. The smaller radius is not given.

St1 + St2: Sufficient.

Answer (C).

Let the area of the bigger circle is A and smaller is B
Statement 1) \(A^2 + B^2 = 90\)
Not Sufficient.

Statement 2) As actual values are not provided, we cannot determine the radius of the larger circle.

Combining the two statements
\(A^2 + B^2 = 90\)
And A = 3B
=> \(10B^2 = 90\)
Sufficient. - Option C)

First one is insufficient because 90pi can be sum of squared number? otherwise 9^2+3^2=90 is the only to get from integers.
please if there is other reasons of insufficiency of first one, tell me. thanks

Hi - the question does not say that R needs to be an integer. So we should not assume that.

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Kudos if the post helped

The process you used will definitely save you time while solving PS questions where we can use all sorts of assumptions to come at an answer because answer will always be one of the option and unique.

Butin DS question type never assume anything outside the information provided because it will lead you directly to a trap answer.

Statement 1 no where says the radii values are integer. So what you did is just one of the case where Radius= 3 but there are other cases with different radius values.

So answer is

There are 2 variables (a and b) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get a=b-6<0 and b<0. Since ab>0, the answer is no and the conditions are not sufficient. Thus, the correct answer is C.




l For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Originally misread the question as "which of the regions has a larger radius" and marked E ... we can't actually determine if P or Q is the larger region, but that could easily be a twist on this kind of question.

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