Sometimes the only way to tackle a question is trial and error, even though is time consuming.
However, amorphous above provided a pretty fast and elegant solution to you
Quote:
take \(y = 10\) and for consecutive integers take some small numbers such as \(1, 2, 3 or 2, 3, 4 or 3, 4, 5\)
doing so will invalidate all of the options from A to D because non of the final result will be an integer
Leaving the only E for ans
To speed up, even more, the process you could think about two things:
- first off: when a question asks you "which of the following" start always from the bottom of the answer choices. More often than not the correct answer is from the bottom-up:
- secondly: the numerator of the fraction is 3 consecutive integers.
if x is even = 2 AND y= 0, which means that \(5^0 = 1\) then you do have
\(\frac{2*3*4}{2*3*1}\)
2 and 3 cancel out and you do have \(\frac{4}{1} = 4\).
Now, the question has only one correct answer and it is also a must be true question. As such, E must be the correct answer without bothering you to check the others.
Hope now is clear to you.
Regards