Re: Quant Shortcuts for CAT 2007
I don't think that it can be explained more beautifully as it has been done over there above.
See, purpose of this post is not to solve the question actually rather playing with the options.
In first question, it asks about the ratio of area of square after the punch to before the punch. Let it be x = (area of square remaining after punch)/(area of square).
We know that area of the square = 2² = 4, so area of square remaining after punch = 4x.
So area of square punched = 4 - 4x.
Now second question asks about the area of the round punch falling outside of square, let it be y.
It's obvious that if we add the two areas i.e. (4 - 4x) and y, we'll get the area of complete circle which is simply π.
Now you final job is only to check the options given as done beautifully in the article above.
I hope it is clear now.