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To include a penalty for guessing, the scoring formula for a 60- 1 que
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15 Aug 2021, 13:20
15 Aug 2021, 13:20
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To include a penalty for guessing, the scoring formula for a 60- 1 question, multiple-choice test is \(s = r-\frac{1}{4}w\), where s is the score on the test, r is the number of correct responses, and w is the number of incorrect responses. If a student answers all 60 questions, which of the following scores could be the student's score?
Indicate all such scores.
(A) —20
(B) —15
(C) —5
(D) 10
(E) 32
(F) 65
Indicate all such scores.
(A) —20
(B) —15
(C) —5
(D) 10
(E) 32
(F) 65
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Re: To include a penalty for guessing, the scoring formula for a 60- 1 que
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15 Aug 2021, 21:50
15 Aug 2021, 21:50
1
Carcass wrote:
To include a penalty for guessing, the scoring formula for a 60- 1 question, multiple-choice test is \(s = r-\frac{1}{4}w\), where s is the score on the test, r is the number of correct responses, and w is the number of incorrect responses. If a student answers all 60 questions, which of the following scores could be the student's score?
Indicate all such scores.
(A) —20
(B) —15
(C) —5
(D) 10
(E) 32
(F) 65
Indicate all such scores.
(A) —20
(B) —15
(C) —5
(D) 10
(E) 32
(F) 65
scoring formula for a 60- 1 question
means 1 mark questions?
Re: To include a penalty for guessing, the scoring formula for a 60- 1 que
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10 Sep 2021, 17:16
10 Sep 2021, 17:16
2
Carcass wrote:
To include a penalty for guessing, the scoring formula for a 60- 1 question, multiple-choice test is \(s = r-\frac{1}{4}w\), where s is the score on the test, r is the number of correct responses, and w is the number of incorrect responses. If a student answers all 60 questions, which of the following scores could be the student's score?
Indicate all such scores.
(A) —20
(B) —15
(C) —5
(D) 10
(E) 32
(F) 65
Indicate all such scores.
(A) —20
(B) —15
(C) —5
(D) 10
(E) 32
(F) 65
Nice question.
First, we can simplify the formula by noting that:
\(w + r = 60\)
So we can either solve for either \(w\) or \(r\) and then plug that into the scoring formula. The resulting formula will be more tractable, since we'll be dealing with two variables instead of 3. I did this solving for \(w\):
\(w = 60 - r\)
\(s = r-\frac{1}{4}(60-r)\)
Simplifying:
\(s = r - 15 + \frac{1}{4}r\)
\(s = \frac{5}{4}r - 15\)
\(s = 5(\frac{1}{4}r - 3)\)
From this, we know that the score must be a multiple of 5. So we can eliminate E.
Now consider the extreme case if \(r = 0\). In other words, this person gets no questions right.
That means we get \(s = -15\), which is our minimum. This eliminates A and gives us B as an answer choice.
Consider the other extreme case, where \(r = 60\). In other words, this person gets all the questions right.
This gives \(s = 60\), which is our maximum. Meaning we can eliminate F.
From here we can see that \(-15 < s < 60\), which gives us C and D as answer choices.
Therefore, altogether, the answers are B,C, and D.
