Answer:
Your friend's statement is incorrect.
Step-by-step explanation:
Let's denote the number of multiple-choice questions as x and the number of essay questions as y.
We know that:
1. The total number of questions is 36: x + y = 36
2. Each multiple-choice question is worth 2 points, and each essay question is worth 6 points.
3. The total number of points for the test is 100: 2x + 6y = 100
We can solve this system of equations to find the values of x and y.
From equation 1:
x = 36 - y
Substituting this expression for x into equation 3:
2(36 - y) + 6y = 100
72 - 2y + 6y = 100
4y = 28
y = 7
Substituting y = 7 into equation 1:
x = 36 - 7
x = 29
So, there are 29 multiple-choice questions and 7 essay questions on the test.
Now, regarding your friend's statement:
If the multiple-choice questions were worth 4 points each, the total number of points for the test would be 100 as given. However, this would change the total number of questions needed to achieve 100 points. Let's calculate:
4x + 6y = 100
4(36 - y) + 6y = 100
144 - 4y + 6y = 100
2y = 44
y = 22
So, with multiple-choice questions worth 4 points each, there would need to be 22 essay questions. But this contradicts the given total number of questions (36). Therefore, it's not possible for the multiple-choice questions to be worth 4 points each while still meeting the given conditions. Thus, your friend's statement is incorrect.