Question about a problem

StrugglingStudent

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Jul 13, 2021
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Hi, I'm stuck on a problem in my homework so I would be really grateful for any help! Here it is:

My friend and I took a maths test with 10 questions. Question 1 was worth 1 mark, question 2 was worth 2 marks, question 3 was worth 3 marks, and so on. Correct answers scored full marks and incorrect answers scored 0 marks. We both scored the same number of marks and correctly answered the same number of questions. However, we didn’t solve exactly the same set of questions as each other. What is the maximum score that I could have received for the test?

I am trying to create an equation but I got stuck when I realised that each question is worth a different amount of marks and I didn't know how many questions I got correct. Thank you so much!
 
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Dr.Peterson

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Nov 12, 2017
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12,170
Hi, I'm stuck on a problem in my homework so I would be really grateful for any help! Here it is:

My friend and I took a maths test with 10 questions. Question 1 was worth 1 mark, question 2 was worth 2 marks, question 3 was worth 3 marks, and so on. Correct answers scored full marks and incorrect answers scored 0 marks. We both scored the same number of marks and correctly answered the same number of questions. However, we didn’t solve exactly the same set of questions as each other. What is the maximum score that I could have received for the test?

I am trying to create an equation but I got stuck when I realised that each question is worth a different amount of marks and I didn't know how many questions I got correct. Thank you so much!
First, what course is this for, and what topics have you learned recently, that you can expect to use in solving this?

Second, I think it is more a matter of logical reasoning than of equations.

How can you answer the same number of questions and get the same score? An example would be if one gets #1 and #10, while the other gets #2 and #9 right, both totaling 11.

After some thinking about that, you might want to switch over to thinking about which questions each gets wrong. (Or you may not.)
 

pka

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Jan 29, 2005
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11,221
My friend and I took a maths test with 10 questions. Question 1 was worth 1 mark, question 2 was worth 2 marks, question 3 was worth 3 marks, and so on. Correct answers scored full marks and incorrect answers scored 0 marks. We both scored the same number of marks and correctly answered the same number of questions. However, we didn’t solve exactly the same set of questions as each other. What is the maximum score that I could have received for the test?
I am trying to create an equation but I got stuck when I realised that each question is worth a different amount of marks and I didn't know how many questions I got correct. Thank you so much!
It maybe that a computer program is what in needed here more so that an equation.
Here is the maximum(perfect score) [MATH]\sum\limits_{k = 1}^{10} k = \frac{{10 \cdot 11}}{2} = 55[/MATH].
If you miss questions [MATH]2,~6,~\&~9[/MATH] then [MATH]55-2-6-9=38[/MATH] is your score.
 
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