Slightly longer explanation:

Statement 1: If the average is $45, then the total cost per day is 4(45) = 180
With 4 people the cost is $120 + x + x + x
So, we get the equation 120 + 3x = 180 (clearly, we COULD solve this equation for x) --> sufficient


Statement 2:
The average cost for 2 people is (120+x)/2
The average cost for 4 people is (120+3x)/4
We know that the first average cost is $25 more than the second average, so we can create the equation (120+x)/2 = (120+3x)/4 + 25
(clearly, we COULD solve this equation for x) --> sufficient

Answer: D

IMO D.
A. If for each person the daly rate is 45$ than 45*4=280. 280-120=160 This is the additional payment that the 3 additional people in the room would have to pay. 160/3 is the rate that each of this 3 people would have to pay. Sufficient.
B. The room rate for 2 people = (120+X). The room rate for 4 people= (120+3*Y). In addition we know that X = 25+Y. So we have 2 integers and two equations. Sufficient.

Not clear with the second statement. Can anybody clear this please.

Total cost for the room renting; 120 + x*n

x - charge per additional person
n - number of additional people

Q: What is x?

1. (120 + x * 4)/4 = 45.
x can be found. Sufficient.

2. (120 + 2*x)/2 = (120+4x)/4 + 25
x can be found. Sufficient.

Ans; "D"

What's the equation for the second statement?

For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person.

What is the charge for each additional person?

(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.
Total cost for 4 person = 120 + 3x = 45*4 = 180
x = 60/3 = $20
SUFFICIENT

(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people.
\(\frac{120 + x}{2} - \frac{120 + 3x}{4} = 25\)
\(60 + \frac{x}{2} - 30 - \frac{3x}{4} = 25\)
\(5 = \frac{x}{4}\)
x = $20
SUFFICIENT

IMO C