Question

В тесте было 20 вопросов. За каждый правильный ответ Вася получал 11 баллов. За каждый неправильный – минус 5. За отсутствие ответа отнимается 1 балл. Вася набрал 80 баллов. Сколько пропусков при таком результате могло оказаться у Васи?

Answer 1

Пусть х правильные ответы, у-за неправильные, z- пропуски. Х+у+Z=20 z=20-x-Y. По условию: 11х-5у-z= 80. Подставляем значени z. 11x-5y-20+x+y=80. 12x-4y=100. 3x-y=25 3х=25+у. (25+у кратно 3 и у принимает значения от 1 до 8) если у =2, х=9, а z=9. 11*9-5*2-9=80 все сходится. Если у=5, то x=10, а z=5. 11*10-5*5-5=80- все сходится. Если у=8, то х=11, а z=1. 11*11-5*8-1=80- сходится. Ответ: при таком результате у Вас могло оказаться 9, 5 или 1 пропуск.

Answer 2

Calculation of Skipped Questions

To determine the number of skipped questions, we need to analyze the scoring system and the total score obtained by Vasya.

According to the given information: - Each correct answer earns Vasya 11 points. - Each incorrect answer deducts 5 points. - Each unanswered question deducts 1 point.

Vasya obtained a total score of 80 points.

Let's assume that Vasya answered x questions correctly, y questions incorrectly, and z questions were left unanswered.

Based on this, we can set up the following equation to calculate the number of skipped questions:

11x - 5y - z = 80

To solve this equation, we need to find the values of x, y, and z that satisfy the equation and the given conditions.

Since there are multiple possible combinations of x, y, and z that can satisfy the equation, we need to find the values that also satisfy the conditions of the problem.

Let's analyze the possible scenarios:

1. If Vasya answered all 20 questions correctly (x = 20), the equation becomes: 11(20) - 5y - z = 80 220 - 5y - z = 80 -5y - z = -140

In this scenario, Vasya would have a negative score, which is not possible. Therefore, this scenario is not valid.

2. If Vasya answered all 20 questions incorrectly (y = 20), the equation becomes: 11x - 5(20) - z = 80 11x - 100 - z = 80 11x - z = 180

In this scenario, Vasya would have a positive score, but it is not possible to have a score of 80 with all incorrect answers. Therefore, this scenario is not valid.

3. If Vasya answered all 20 questions but left one unanswered (x = 19, z = 1), the equation becomes: 11(19) - 5y - 1 = 80 209 - 5y - 1 = 80 -5y = -130 y = 26

In this scenario, Vasya would have answered 19 questions correctly, left one unanswered, and answered 26 questions incorrectly. However, the number of incorrect answers cannot be greater than the total number of questions. Therefore, this scenario is not valid.

4. If Vasya answered all 20 questions but left two unanswered (x = 18, z = 2), the equation becomes: 11(18) - 5y - 2 = 80 198 - 5y - 2 = 80 -5y = -120 y = 24

In this scenario, Vasya would have answered 18 questions correctly, left two unanswered, and answered 24 questions incorrectly. This scenario satisfies the conditions of the problem, and Vasya's score would be 80 points.

Therefore, the number of skipped questions that could have been present for Vasya to obtain a score of 80 points is 2.