Question

Xzavier is competing in a math contest. The math test has 30 questions. The list shows the number of points that can be earned on each question.

Correct answer: +3 points
Incorrect answer: –4 points
No answer: –1 point
Xzavier answered 20 questions on the test. What is the minimum number of questions that Xzavier answered correctly if he earned a positive score?
A. 15
B. 12
C. 13
D. 14

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's calculate Xzavier's score if he answered 20 questions:

(3 x number of correct answers) - (4 x number of incorrect answers) - (1 x number of unanswered questions)

Let's represent the number of correct answers as C, the number of incorrect answers as I, and the number of unanswered questions as U.

So, C + I + U = number of questions answered
C + I = 20 because Xzavier answered 20 questions

Now, let's try each option:

A. If Xzavier answered 15 questions correctly, he would have answered 5 questions incorrectly. So, his score would be:
(3 x 15) - (4 x 5) - (1 x 10) = 45 - 20 - 10 = 15
Xzavier's score would not be positive.

B. If Xzavier answered 12 questions correctly, he would have answered 8 questions incorrectly. So, his score would be:
(3 x 12) - (4 x 8) - (1 x 10) = 36 - 32 - 10 = -6
Xzavier's score would not be positive.

C. If Xzavier answered 13 questions correctly, he would have answered 7 questions incorrectly. So, his score would be:
(3 x 13) - (4 x 7) - (1 x 10) = 39 - 28 - 10 = 1
Xzavier's score would be positive.

D. If Xzavier answered 14 questions correctly, he would have answered 6 questions incorrectly. So, his score would be:
(3 x 14) - (4 x 6) - (1 x 10) = 42 - 24 - 10 = 8
Xzavier's score would be positive.

Therefore, the minimum number of questions that Xzavier answered correctly if he earned a positive score is 13, so the answer is C.