Which one of the following is an example of a balanced chemical reaction? A) HCl + KMnO_4 = Cl_2 + MnO_2 + H_2O + KCl B) HCl + KMnO_4 = Cl_2 + MnO_2 + 2H_2O + KCl C) 2HCl + 2KMnO_4 = Cl_2 + MnO_2 + 2H_2O + 2KCl D) 6HCl + 2KMnO_4 = 2Cl_2 + 2MnO_2 + 4H_2O + 2KCl E) 8HCl + 2KMnO_4 = 3Cl_2 + 2MnO_2 + 4H_2O + 2KCl

Hello!
This is actually a math question.
For a chemical equation to be balanced, there must be an equal quantity of atoms of each type on both sides of an equation. Let's start from the first type of atoms involved here, H (hydrogen). It appears only in H Cl at the left (one atom for each molecule) and in H_2O at the right (two atoms for each molecule). Check:
A) 1*1 = 1*2 (false)B) 1*1 = 2*2 (false)C) 2*1 = 2*2 (false)D) 6*1 = 4*2 (false)E) 8*1 = 4*2 (true).
So the only equation which might be balanced is E. Check the remaining types of atoms: Cl, K, Mn, O.
Cl:  8*1 = 3*2 + 2*1 (true),K:    2*1 = 2*1 (true),Mn: 2*1 = 2*1 (true),O:     2*4 = 2*2 + 4*1 (true).
Great, E is a balanced equation and the only such. The answer is E.