Deductions from the Given Information

The given information does not give us much to go on here. It just says that the probability both events $E$ and $F$ will occur is $0.42$. The good news is that, because we don't have much information, we can look at extreme cases. Before doing so, a quick review. If two events are independent (which, keep in mind, we don't that they are here), the probability that they both occur can be found by simply multiplying the two probabilities together. For example, if events $A$ and $B$ are independent and the probability of $A$ is $0.3$ and the probability of $B$ is $0.5$, the probability of $A$ and $B$ occurring is $(.3)(.5)=(.15)$. So now with that out of the way we can look at our extreme cases:

Extreme case 1: Events $E$ and $F$ are independent. The probability of $E$ is $1$ and the probability of $F$ is $0.42$.
Extreme case 2: Events $E$ and $F$ are independent. The probability of $E$ is $0.42$ and the probability of $F$ is $1$.

Notice that, in both cases, we're not violating the given information. The probability that both events $E$ and $F$ will occur is $0.42$ in both cases.

Solving the Problem

Much of the hard work has already been done in the deductions process. In the first case, Quantity A is $1$, which is larger than Quantity B's value of $0.58$. In the second case, Quantity A is $0.42$, which is less than Quantity B.

Thus, the answer is D, It cannot be determined.