Notice that when the number of correct problems decreases by 1 (the number of incorrect problems increases by 1), the score is 9 less. The difference between possible scores is a multiple of 9.

Also, notice that possible scores are all 2 less than a multiple of 9.

You might notice a digits pattern for the possible scores — the sum of the digits for possible scores is 7 or when the sum is a two-digit number, add the digits again to
get 7.

Note: 196 is a possible score.

Using one of these pattern ideas, you can find possible scores close to 100. Scores of 97 and 106 are possible, but not 100. The closest possible score to 100 is 97.

Each incorrect problem makes the score 9 less and 11 x 9 = 99. So, to get a score of 151, there will be 11 problems incorrect and 39 (50 - 11 = 39) problems correct.