we have two equal angles (x), If we extend k and N such that they meet at right angle we have a 90 -45-45 triangle.

In isoscles triangle two sides have equal length. In this case side opposite angle x are equal.

We also know that there are two sides with length 3 and 4
side of length 3 is parallel to n and side of length 4 is parallel to k

Therefore we have K + 4 = n + 3
If we reduce 3 from both sides we get,
k + 1 = n

Therefore since we add something to k to make it equal to n k is smaller than n

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My approach was same but it took me 6.53 min to land on the same approach. what should i do to do questions fast?

I do think the amorphous's approach is the fastest.

Maybe, @sandy could shed light.........

Regards
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Unfortunately @amorphous approach is the fastest method I could think of too. To be fair it is usually rare to see things like extending the diagram by construction in the GRE but these questions do exist.

It is quite possible that you saw this type of question for the first time and hence it took you longer to figure out, but I think with a little practice you would get faster.
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Thanks a lot.

And it is an official question.

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