The key to comparing these products is determining two things:
1. The sign of the product (which depends on the total count of negative factors).
2. The magnitude (the absolute value) of the product.

Quantity A: Product of integers from -87 to -36 inclusive
1. Count the Integers $\(\left(N_A\right)\)$ : The number of integers in this range is (Last - First) +1 .

$$
\(N_A=(-36)-(-87)+1=-36+87+1=51+1=52\)
$$


There are 52 negative integers.
2. Determine the Sign: Since the number of negative factors is even (52), the product is positive.

$$
\(\text { Quantity } A=(-87) \times(-86) \times \cdots \times(-37) \times(-36)>0\)
$$

3. Magnitude:
$\(\mid\)$ Quantity $\(\mathrm{A} \mid=87 \times 86 \times \cdots \times 37 \times 36\)$

Quantity B: Product of integers from -58 to -34 inclusive
1. Count the Integers $\(\left(N_B\right)\)$ :

$$
\(N_B=(-34)-(-58)+1=-34+58+1=24+1=25\)
$$


There are 25 negative integers.

2. Determine the Sign: Since the number of negative factors is odd (25), the product is negative.

$$
\(\text { Quantity } \mathrm{B}=(-58) \times(-57) \times \cdots \times(-35) \times(-34)<0\)
$$


Comparison
- Quantity A is Positive (Product of 52 negative numbers).
- Quantity B is Negative (Product of 25 negative numbers).

Any positive number is greater than any negative number.
Therefore, Quantity $A$ is greater than Quantity $B$.
The correct choice is Quantity A is greater.