How to solve this fraction within minute? (or trick)

Question

I want to solve this question within minute but bcz of fraction it take more than a minute. does any one know a trick to solve this type question.plz share thanks

Answer 1

Notice that answer (1) and (3) are equal. Notice also that, if you write the factors as non-mixed (improper) fractions, two numerators are even (and not divisible by 4), and only one denominator is even (and divisible by 4). Thus, if your answer is not (5), it must be (2), as the product is either a fraction without $1/4$ in it or an integer.

To find out whether it is (2) or (5), you have to be quick with numbers, I am afraid (not sure whether it took me less than a minute):

The numerators are $5*37+17=202$, $5*52-1=260-1=280-21=7*(40-3)=7*37$ and $7*11+1=78=6*13$. The second denominator is $52=4*13$, which leaves you with $202*6/4$ for the product term, which can still be done in the head.