When this element was discovered, it exhibited luster and malleability, and it reacted very vigorously with water. This element is never found as a free element in nature and always exists in a compound. To which group does this element most likely belong?
a) alkali metals
b) halogens
c) noble gases
d) transition metals

The element described above definitely belonged to the alkali metals, the first group on the periodic table. They show the properties indicated in the text.

They are metals because only metals are lustrous and malleable. This eliminates the possibility of them being halogens and noble gases.
Only group 1 metals reacts vigorously with water to form alkali.
Alkali are aqueous solutions that are basic in nature.
The reactivity of group 1 metals is due to their one extra electrons in the outer most shell.
These electrons are easily and readily lost in order for such atoms to gain stability and replicate the nearest noble gases.
The most reactive metal belongs to this group elements.
This is why it is nearly impossible to find them occurring alone in free state.
Some of the elements in this group are Li, Na, K, Rb, Cs and Fr.
Transition metals have variable oxidation states and some can be found alone in nature.