SOLUTION

We are given:

• \(X\) and \(Y\) are non-zero integers.

We need to find:

• If \(\frac{X}{Y}\) is greater than \(\frac{5}{7}\) or not?

Let us analyze both the statements one by one.

Statement-1: \(X^3 >= 125\) and \(Y^2 <= 49\).

From \(X^3>=125\), we can write:

From \(Y^2 <= 49\), we can write:

For \(X=6\) and \(Y=7\), the value of \(\frac{X}{Y}\) is greater than \(\frac{5}{7}\).

However, for \(X=6\) and \(Y=-7\), the value of \(\frac{X}{Y}\) is less than \(\frac{5}{7}\).

Hence,

Statement 1 alone is not sufficient to answer the question.Statement-2 \(X*Y <= 0\).

Since \(X\) and \(Y\), both, are non-zero integers, \(X*Y\) can only be less than 0.

The product of \(X\) and \(Y\)is negative.

• Hence, we can say that \(X\) and \(Y\) are of different sign.

o Therefore, \(\frac{X}{Y}\) is also negative.

Hence, we can certainly say that \(\frac{X}{Y}\) is a negative value which is always less than \(\frac{5}{7}\).

Thus,

Statement 2 alone is sufficient to answer the question.Answer: B
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