The average score of those students who passed a test was 65, the average score of those who did not pass was 35, and the overall average score was 53. What percentage of the students passed the test?

60%

Step-by-step explanation:

To find the total pass = 65 * number of student that passed, let it be be represented by P and number of students that failed F

Total pass = 65p

And total fail = 35F

For the total pass and failure will be 53 (P+F)

Equating to total pass and total fail

65P + 35F = 53 (P + F)

65P+35F = 53P + 53F

65P-53P = 53F-35F

12P=18F

2P = 3F

Hence there are 3 passing scores for every 2 failure scores, hence there are a multiple of 5 scores and the same multiple of 3 passing scores.

3/5 * 100 = 60%