Predict the number and nature of bonds using Molecular Orbital Theory I found the following question in a high school chemistry problem book:

According to Molecular Orbital Theory which of the following is true:
(A) In $C_2$ molecule both the bonds are $\pi$ bonds.
(B) In $C_2^{2-}$ ion there is one $\sigma$ and one $\pi$ bond.

Both of these are true. But how can one know this using Molecular Orbital Theory?
P.S.: I don't know anything about Quantum Mechanics as I am a high school student. My textbooks only provide a result-oriented explanation. I would appreciate if the answers keep this in mind.
I presume you can draw the homonuclear diatomic MO diagram for these two species. 

As you probably already know, the s orbitals of the carbons form bonding and antibonding orbitals, both of which are filled. (The net effect of this is the “lone pairs” on each carbon.) 

The p orbitals for 2 pi bonds and a sigma bond. Due to s-p mixing, the pi bonds are lower in energy and are filled first, and these 2 bonds (with their 4 electrons) are the 2 bonds we see in C2. 

Add another 2 electrons to the system and you realise they fill the sigma bonding orbital, which means that the C2 2- anion has 2 pi bonds and a sigma bond (for a total bond order of 3). 

Hope this helped.