If x and y are positive integers, is x% of y > y?

If the question did not mention that x and y were positive integers, this question would have been a bit more challenging than it is.

Breaking down the question stem, is x% of y > y, by taking y on to the LHS and maintaining the RHS as 0, we have,

Is x% of y – y > 0?

Factoring out y,
Is y(\(\frac{x}{100}\) – 1) > 0?

Since y is a positive integer (and hence already more than 0), the only way in which the above product can be greater than 0 is by having (\(\frac{x}{100}\) – 1) > 0.

Therefore, we can rephrase the question stem as,
Is \(\frac{x}{100}\) – 1 > 0??

Which can be simplified to,
Is\( \frac{x}{100}\) > 1?

And further to

Is x > 100?
Now, this is the question we are trying to answer.

From statement I alone, x > 99.

This means x is definitely not more than 100 because x could be equal to 100.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, x <101.

Since x is an integer, this means that x can be 100 or lesser; which then means that x is never greater than 100.
IS x > 100? NO, it is not.
Statement II alone is sufficient to answer the question with a NO. Answer options C and E can be eliminated.

The correct answer option is B.

Hope that helps!
Aravind B T