Dear poster, don't imply all startups are equal.
If a startup asks you to solve math puzzles, it's possible that the work you will be doing heavily involves the creative use of math or information analysis. (This is more broadly valuable than many people recognize.)
Also, it's also possible that that particular startup doesn't know how to effectively interview.
It doesn't sensationalisticly mean all Startups (capitalization yours) don't know how to effectively interview.
Also, rather than focus on your ability to learn, I would humbly recommend you reconsider the basic nature of employment. An interview should be considered a two-way conversation. You're not selling yourself as a slave, you're entering into a mutually-beneficial, private, voluntary arrangement. Thus, even someone who goes into an interview willing to accept anything and everything they offer could be expected to ask simply, "And what exactly will I be doing?" But better yet, grill them about every nitty-gritty detail you can think of. Although some insecure interviewers may be taken aback (I'm guilty of asserting the interviewer was wrong on more than one occasion, both times still receiving an offer), I for one am impressed when a candidate demonstrates a sharp, critical and skeptical mind in this way.