“Is that supposed to be his apartment?”
You're watching a movie about a guy who lives in New York. The character is a waiter at a restaurant, but the apartment he lives in is big and new-looking. You know that New York apartments are really expensive. You say this because don't believe that the character could afford such a nice apartment.
Is that supposed to be his apartment?
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Is (that/this) supposed to be (something)?
This phrase is used to criticize things. When you don't think something is good enough or realistic enough, you say "Is that supposed to be ___?" For example, if someone compliments your hair cut, but says it in a way that actually sounds rude, you can respond:
Is that supposed to be a compliment or something?
Or when someone tries to make a joke, but the joke offends you:
Is that supposed to be funny?
You can use "this" with the phrase as well as "that":
What, is this supposed to be a nice restaurant? If you ask me, it's way overpriced and not all that good.