Men and women can be treated differently, so long as it serves an important state interest to do so. Is this statement true or false ?
The statement in this question is true. Laws that treat people differently on the basis of sex are subjected to what is called intermediate scrutiny. This is not as difficult to overcome as strict scrutiny, but harder to overcome than a rational basis test.
When laws treat people differently on the basis of race or national origin, the laws must pass strict scrutiny to be upheld by a court. The strict scrutiny test says that the law has to serve a “compelling state interest.” It also says that the law's provisions must be "necessary" to serve that interest. When the law treats people differently on the basis of sex, it has to pass intermediate scrutiny. In this test, the law has to serve an “important state interest.” The law's provisions must be "substantially related" to serving that interest. "Important state interest" is the exact phrasing that is used in your question. Therefore, this statement is true.