Can someone help me in this? Thanks in advance!

It is easy to check that lawyers doing corporate law are 21%. Those who are doing any type of litigation are x^2% + (x+1)%. Now, in order to find x, we can notice that x^2+(x+1)+x = 100%-21%-17%-22%-15% = 25%. Solving this equation we get that x = -6 and x = 4. Since x is a percentage it must be non-negative, thus x = 4. Then, we can substitute x^2=4^2=16 and x+1=4+1=5. Thus, the lawyers doing any type of litigation are 21% exactly as those doing corporate law. Answer C!

could you please help with the equation solving?

Given
civil ligitation = (x+1)%

criminal ligitation = \(x^2%\)

We are required to find out the total value of these ligitation, but here x are unknown. For that we have to find out x first.

In the circle the whole % will be equal to 100%

so we can add up all the individual group which will sum up to 100%

i.e we have x^2% +(x+1)% +15% + 22% +17% +x% +21% =100%
or x^2 +(x+1) +15 + 22 +17 +x +21 =100 (donot confuse with the percentage , for easy calculation i have removed percentage from both sides)

or x^2 + 2x = 100-1-15-22-17-21

or x^2 +2x = 24

or x^2 +2x-24 = 0

or (x-4)(x+6) =0

or x= 4 or x=-6

Since x cannot be negative we have taken x=4

now putting the vaules o f x we have

civil ligitation = (x+1)% = 5%

criminal ligitation = \(x^2%\) = 16%

Total = 5%+16% = 21%

and from the Diagram we know number of lawyers who practice corporate laws = 21%

so the option is C
_________________

Hi @IlCreator

How did you determine that he number of lawyers in the organization who
practice all types of litigation are only criminal and civil litigation ?

@Carcass

Please reply on my query.

The explanation above is perfect by @pranab01

both are the result (as per the graph above) the result of \(x^2 + (x + 1)\).

From this at the end of the day, we do know that our X is or 4 or -6 but a negative value is not possible. Hence, x = 4

Substitute 16 + (4 + 1) = 21

The two quantities are equal. Therefore, C is the best.

regards
_________________

As all the values are in percents. And percent means out of 100.
So, it must suggest that all types of law are practiced as 100%, meaning all 55,000 lawyers are participating.
Now, as it's given in Quantity B that 21% of all lawyers participates in Corporate Law.

IMPORTANT: YOU DON'T NEED TO WASTE YOUR TIME IN CALCULATING 21% OF 55,000. AS IT'S QUANTITATIVE COMPARISON TYPE OF GRE QUESTION, SO JUST THINK SMARTLY.

Now, we need to see whether all types of litigation {i.e \(x^2\)% and (x+1)%} greater than 21%, equals to 21% or less than 21%. For that purpose, we need to find value of x.

As we know, sum of all types of laws equals to 100% i.e:

17% + 21% + 15% + 22% + \(x^2\)% + (x+1)% + x% = 100%

75 + \(x^2\) + 2x + 1 = 100
\(x^2\) + 2x - 24 = 0
\(x^2\) + 6x - 4x - 24 = 0
x(x+6) -4(x+6) = 0
(x-4)(x+6) = 0
Either x = 4 or x = -6
As x cannot be negative, because the proportion of a law cannot be in negative. Thus,
x = 4

So, all litigation = Criminal Litigation + Civil Litigation
= \(x^2\) + (x+1)
= \(4^2\) + (4+1)
= 16 + 5
= 21%

As Quantity A also comes out to be 21%, so Choice C is correct.
_________________

C

is there anoter solution?

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