x and y are two positive integers. Which number among x and y has more

Solution:

We are asked which positive integer x or y has more factors

Statement 1: x is a factor of y

If x is a factor of y then there might be cases where \(x = y\) and when \(x<y\)

For example, if y = 25 then x can also be 25 because 25 itself is also a factor of 25

Because of the case where \(x=y\), the number of factors of x will be equal to the number of factors of y

and because of the case where \(x<y\), the number of factors of x will be less than the number of factors of y

Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: \(x^3<y^2\)

This statement will not give us any information on the factors of x and y

Thus, statement 2 alone is also not sufficient

Combining:

From statement 1, we get that x is a factor of y

From statement 2, we have \(x^3<y^2\)

Since x is a factor of y, we can cancel the variables and say \(x<y\). This invalidates \(x=y\) case from statement 1

So, we can say that \(x<y\) and number of factors of x will be less than the number of factors of y

Hence the right answer is Option C