Difference of the total scores after taking x+1 tests and x tests must equal 90.
=> 82(x+1) - 80 x = 90 => x =4

we know the formula of average is [SUM of tests/number of test = Average --> Sum of tests = (number of tests)(average)]
origianlly 80 was the average of X tests and this average increases to 82 when an other test with score 90 is done.

X = the unknown number of test taken when the average is 80
X+1 = the unknown number of test when one more test with socre 90 is taken
Sum of the tests = 80 (X number of test) + 90
Average increases to = 82
Number of tests = X+1

Putting this in the formula

80X + 90 = (82)(x+1)
80X +90 = 82X +82
90-82 = 82X- 80X
8 = 2X
X = 4

An alternate approach is to plug in the answers, which represent the value of x (the original number of tests).
The options for x are 2, 4, 8, 10 or 20.
When an ADDITIONAL test is included, the number of tests will be 3, 5, 9, 11, or 21.
Since the resulting average is 82, and sum = number * average, answer choice B seems the most likely: it is the only answer choice that will yield a multiple of 10 for the sum of all the scores when the additional test is included.
Sum of 5 tests with an average score of 82 = 5*82 = 410.

Answer choice B: 4
Sum of 4 tests with an average score of 80 = 4*80 = 320.
Sum of all 5 tests - sum of the first 4 tests = 410-320 = 90.
Success!
The score on the additional test is 90.

The correct answer is B.