What kind of good will be purchased even if the price rises?
There are at least two possible answers for this. The correct answer depends upon what you are studying at this point in your economics class.
One possible answer to this is that a good that is perceived as a necessity will be purchased even if its price rises. Let us imagine that there was a drug that you absolutely had to have in order to live. If the price of that good went up, you would presumably continue to purchase it as long as you had any ability to do so. You might even go out and steal to get the money to pay for it if the price got too high. If we need a particular good (if we perceive it as a necessity) we will continue to buy it even if its price rises. This is why the extent to which a good is a necessity is one of the major factors that determine how elastic its demand will be.
A second possible answer is to say that a good that is perceived as a luxury can be purchased even as its price rises. One technical term for such a good is a “Veblen good.” Veblen goods are goods for which quantity demanded rises as the price rises. This is because these goods are seen as luxurious status symbols. Part of their value is their price. People like them because they are expensive and exclusive. For such goods, quantity demanded will actually rise as the price goes up.
Thus, either of these two answers could be correct, depending on what aspect of economics you are currently studying.