**Concept: The question tests on the application of Number Properties.**

**Solution:**

**Statement I:** 130/4 = 32.5--> So sum of the middle 2 numbers should be 65 which is the sum of 32 and 33. The 4 numbers are 31 + 32 + 33 + 34 = 130**Statement II:** 130/5 = 26--> The middle number is 26 with the other 4 being 2 behind and 2 ahead of 26. The 5 numbers are 24 + 25 + 26 + 27 + 28 = 130**Statement III:** 130/6 = 21.67--> So sum of the middle 2 numbers should be 43.33 which then cannot have integers.**Option C**