OK, they kind of screwed up Chika's response on page 3. She doesn't just say "but I don't have the answer" while thinking "well, I don't know how". After thinking in the previous panel about how desperate her sister is, she continues with the thought "But I won't answer something like that", "won't" not "can't", and then verbally says "Eh--, but I don't know about that sort of thing!" While it leaves the question open as it always does, the manga makes it feel a lot more like she's just trying to torture her sister (which fits given her early-established jealousy) by playing dumb.
