Final answer:
The reference to the array grades is stored in the heap, while the primitive variable age is stored on the stack. The elements within the array grades can indeed be modified within the method.
Step-by-step explanation:
Among the given options, the true statement about how Java stores variables is that the reference to grades is stored in the heap. When a variable is declared as an array in Java, the actual object is stored in the heap memory, and the reference to this object is what the variable contains. This means that, while the variable grades is a reference variable and is stored on the stack, what it refers to - the array itself - resides in the heap.
In contrast, the variable age is a local variable of primitive type, which is stored on the stack. So, the statement 'the value of age is stored in the heap' is false because primitive types like int are stored on the stack unless they are part of an object.
Furthermore, it is possible to modify the elements of the array within the method, so the statement 'the elements in grades cannot be modified within the method' is incorrect. The array object that the reference points to is mutable and changes to its elements reflect on the original array unless the reference itself is made final.
Lastly, the statement 'the value of grades[2] is stored in the heap' is true in the sense that the array object is in the heap, but the wording is somewhat misleading as it seems to isolate the value of one element which does not have a separate storage classification from the rest of the array elements.