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# On a test, students receive 3 points for each correct answer and are p

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Math Expert
Joined: 02 Sep 2009
Posts: 49892

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22 Apr 2015, 03:36
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15% (low)

Question Stats:

81% (02:07) correct 19% (02:33) wrong based on 123 sessions

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On a test, students receive 3 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?

A. -2
B. -1
C. 0
D. 1
E. 2

Kudos for a correct solution.

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Joined: 20 Apr 2015
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22 Apr 2015, 06:05
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Bunuel wrote:
On a test, students receive 3 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?

A. -2
B. -1
C. 0
D. 1
E. 2

Kudos for a correct solution.

In the worst score scenario, out of 3 questions marked as B, one is C, then the answers right are only 2 and wrong are 4, so minimum score is 2*3 - 4 = 6-4 = 2
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Joined: 21 May 2013
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22 Apr 2015, 10:10
1
Bunuel wrote:
On a test, students receive 3 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?

A. -2
B. -1
C. 0
D. 1
E. 2

Kudos for a correct solution.

For the minimum possible score, let us take the worst case scenario
Suppose, he gets all of the last 3 qs wrong whose correct answer options are B and one of the first 3 qs wrong whose correct option is C
In that case, he will get only 2 out of the first 3 qs right.
Therefore, minimum possible score=(3*2)-(4*1)=2
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Joined: 02 Sep 2009
Posts: 49892

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27 Apr 2015, 03:02
Bunuel wrote:
On a test, students receive 3 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?

A. -2
B. -1
C. 0
D. 1
E. 2

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Since 5 answers are B, the worst the student could do is answering C for three of the B answers, B for one of the Cs, and B for two of the Bs. That means that the student would get two correct (+6) and four incorrect (-4), so the minimum possible score is 2.
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14 Feb 2018, 17:02
Hi All,

This question really isn't about probability. Since the prompt as asking for the minimum score possible under a specific series of conditions, we want to try to maximize the number of wrong answers (out of 6 questions).

For the correct answers, we have 5 Bs and 1C
For the submitted answers, we have 3Bs and 3Cs

First, let's take the 3 Cs and put them all on 3 'correct Bs' --> that's 3 wrong answers.
Next, let's take 1 B and put it on the 1 'correct C' --> that's 1 wrong answer.
That leaves the final 2 Bs on the final 2 'correct Bs' --> that's 2 CORRECT answers.

Under the scoring system, each correct answer is worth 3 points and each incorrect answer is -1 point.

2(3) + 4(-1) = +2

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Re: On a test, students receive 3 points for each correct answer and are p &nbs [#permalink] 14 Feb 2018, 17:02
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