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Ballparking: Overview

Given that $$p=996$$, which of the following best approximates the value of $$\frac{p}{3p - 1}$$?
Incorrect. [[Snippet]] __Plug In__ $$p = 1{,}000$$ so that $$\frac{p}{(3p - 1)}$$ becomes >$$\displaystyle \frac{1{,}000}{(3{,}000 - 1)}$$ >$$\displaystyle = \frac{1{,}000 }{ 2{,}999}$$, which is not equal to $$\frac{1}{9}$$. Hence, eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$p = 1{,}000$$ so that $$\frac{p}{3p - 1}$$ becomes >$$\displaystyle \frac{1{,}000}{3{,}000 - 1} = \frac{1{,}000 }{ 2{,}999}$$, which is not equal to $$\frac{1}{8}$$. Hence, eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$p = 1{,}000$$ so that $$\frac{p}{3p - 1}$$ becomes >$$\displaystyle \frac{1{,}000}{3{,}000 - 1} = \frac{1{,}000 }{ 2{,}999}$$, which is not equal to $$\frac{1}{4}$$. Hence, eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$p = 1{,}000$$ so that $$\frac{p}{3p - 1}$$ becomes >$$\displaystyle \frac{1{,}000}{3{,}000 - 1} = \frac{1{,}000 }{ 2{,}999}$$, which is not equal to $$\frac{1}{6}$$. Hence, eliminate this answer choice.
Correct. [[Snippet]]
Incorrect. [[Snippet]] __Plug In__ $$p = 1{,}000$$ so that $$\frac{p}{3p - 1}$$ becomes >$$\displaystyle \frac{1{,}000}{3{,}000 - 1} = \frac{1{,}000 }{ 2{,}999}$$, which is not equal to $$\frac{1}{2}$$. Hence, eliminate this answer choice.
Did you use 1,000 instead of 996?
And why wouldn't you?
Oh, but there's a bunch of other stuff you can do if you are a masochistic person that seems much more enjoyable than trying to calculate $$\frac{996}{3(996)-1}$$. You are not a human calculator, and the GMAT does not test your ability to become one. Use approximations to cut through the hurdle of a long calculation, then aggressively __POE__ answers that are out of the __Ballpark__.
The number 1,000 is very close to 996 and gives you a number that's a pleasure to work with. >$$\displaystyle \frac{1{,}000}{3(1{,}000)-1}$$ Of course, for the sake of __Ballparking__ we can ignore the "1" in the denominator and get >$$\displaystyle \frac{1{,}000}{3{,}000} = \frac{1}{3}$$. By __Ballparking__, you get to a quick and painless estimation of the correct answer. In our case, all other answers are out of the __Ballpark__.
$$\frac{1}{8}$$
$$\frac{1}{6}$$
$$\frac{1}{4}$$
$$\frac{1}{3}$$
$$\frac{1}{2}$$
Yes, I did.
No, I did not.
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