Need Urgent Help. I have the percentage but not the number of test questions

[zorro94]

For reasons I cannot discuss, I urgently need to know if the grade I received was even possible (I suspect test tampering).
I know I scored a 74.38% on an exam which wrecked my career and devastated me a few years ago (I was told I missed the 75% cutoff by one question). Unfortunately, I do not have the number of test questions. I know the number of multiple choice questions was in the range of 100-220 (likely around the 130s). I believe they were all equally weighted (1pt).
Is such a percentage possible in the range of 100 to 200 test questions?

I think the test was out of 134 and here is why (please correct my faulty reasoning/I am not good at math):
74.38 x X =100
divided both sides by 74.38 = 134 (whole number)
I believe it was 134 questions thus making my score an impossibility (no exact numbers or score could have gotten that) if each question was weighted for 1pt.

In a nutshell, I need to know if it would be possible to score 74.38% on a test ranging from 100 to 200 questions and each weighted for one point.

Thanks so much!!!!

 

[Dr.Peterson]

For reasons I cannot discuss, I urgently need to know if the grade I received was even possible (I suspect test tampering).
I know I scored a 74.38% on an exam which wrecked my career and devastated me a few years ago (I was told I missed the 75% cutoff by one question). Unfortunately, I do not have the number of test questions. I know the number of multiple choice questions was in the range of 100-220 (likely around the 130s). I believe they were all equally weighted (1pt).
Is such a percentage possible in the range of 100 to 200 test questions?

I think the test was out of 134 and here is why (please correct my faulty reasoning/I am not good at math):
74.38 x X =100
divided both sides by 74.38 = 134 (whole number)
I believe it was 134 questions thus making my score an impossibility (no exact numbers or score could have gotten that) if each question was weighted for 1pt.

In a nutshell, I need to know if it would be possible to score 74.38% on a test ranging from 100 to 200 questions and each weighted for one point.

Thanks so much!!!!

You want to know whether any fraction x/n, where x is the number of correct answers and n is the total number of questions, can equal 74.38%, or 0.7438, when rounded to 4 decimal places.

I used a spreadsheet to find that

90/121 = 0.74380165289256198347107438016529​

119/160 = 0.74375​

151/203 = 0.74384236453201970443349753694581 (you said 220 in one place, 200 in others)​

So all of these are possible scores.

Your calculation of 134 is irrelevant. I don't know what you were thinking.

 

[zorro94]

You want to know whether any fraction x/n, where x is the number of correct answers and n is the total number of questions, can equal 74.38%, or 0.7438, when rounded to 4 decimal places.

I used a spreadsheet to find that

90/121 = 0.74380165289256198347107438016529​

119/160 = 0.74375​

151/203 = 0.74384236453201970443349753694581 (you said 220 in one place, 200 in others)​

So all of these are possible scores.

Your calculation of 134 is irrelevant. I don't know what you were thinking.

Thanks so much. I just didn't have the math skills to pull this off. This is great to know and really helps.