Problem:
John scores on this year's . Had the old scoring system still been in effect, he would score only for the same answers. How many questions does he leave unanswered?
Answer Choices:
A.
B.
C.
D.
E. not uniquely determined
Solution:
Let be the number John gets correct, the number he gets wrong and the number he leaves unanswered. That his score under the old scoring system would have been 84 means
That his score under the new system is means
Since there are problems,
Solving these three simultaneous equations gives
OR
We have
Subtracting from , we obtain .
Note: the first sentence of this alternate solution shows that the old scoring system could have been described more simply as times the number correct + the number left unanswered. The second sentence shows that the difference between the new and old systems is that the new system gives you an extra point for each unanswered question.