I have these two question which are confusing me because I do not understand how to determine the cash received if they do not give a beginning balance in the accounts that are changed.

Gomer has sales of $100,000, change in accounts receivable of $10,000, and change in accounts payable of $20,000. How much cash did Gomer receive from its customers?
A) $90,000
B) $100,000
C) $80,000
D) $110,000

Gomer has rent revenues of $80,000. It also has change in inventory of $(2,000), change in unearned rent of $7,000, and change in prepaid interest of $3,000. How much cash did Gomer receive from its renters?
A) $82,000
B) $73,000
C) $87,000
D) $77,000

A clue on how to proceed with the first one...

Let's call Beginning AR, Ending AR, Sales, and Customer Collections, B, E, S, and C, respectively. You'll agree that

E = B + S - C, no?

That equation can be rearranged to C = B - E + S. We don't know B or E (as you mention), but as it turns out, all we need to know is the change in AR (which we're given).

We're told that AR increased by 10K during the period. That means, of course, that Ending is 10K higher than Beginning. Thus, B - E = (negative) 10K. Regardless of what B and E happen to be, we know from the furnished info that B minus E must equal negative. 10K.

So in the above equation, the "B - E" part can be replaced by negative 10K.

In practice, though, you'll find a simpler, intuitive approach being used with questions of this type. Sales adds to AR, and Collections decreases AR. So if overall, AR managed to increase by 10K during the period, which was the greater---the 'additions to' AR (from Sales), or the 'deductions from' AR (from Collections)? You'll see that this intuitive answer squares with the analytical one derived above.

The second problem isn't identical, but some similar thinking will lead you to the answer.