Question

Tim has to write two papers worth 50 points each. To pass, he must earn more than 45% of the total points. However, scoring 30% or less of the points on either paper, even if his total for both papers is above 45%, will result in him failing. Which graph represents the region in which Tim fails? (Assume that he scores x points on paper A and y points on paper B.)

Answer 1

Hi, and welcome to QuestionCove!

We can imagine a graph with the x-axis representing the score for paper1, and the y-axis representing the score for paper2, like in the drawing I attached. According to the question, each paper is worth 50 points, for a total of 100. Tim only needs 45 total points to pass, so we can say that x+y must be greater than or equal to 45, or x+y>=45. There is also the condition that if Tim scores less than 30% (or, 15 points) on either paper, he fails; so, x>15 and y>15 are two other conditions.
Plotting all of these conditions as lines, we can see the region in which Tim passes:
Specifically, the region where all three shades overlap represents the scores that Tim passes; the question asks which region Tim fails, which is the opposite