Tricky math problem?

Question

In a class at a major university, three tests are given during the semester. At the beginning of the semester, there are x students in the class. Every student in the class takes the first test, and the average on the first test is 72%. After the first test, 20% of the students drop the class. Every student remaining in the class takes the second test, and the average on the second test is 75%. After the second test, 248 
students drop the class. Every student remaining in the class takes the third test, and the average on the third test is 76%. If the average of all of the students’ tests during the semester was 74%, then how many students were originally in the class?

david · Answer

first test, and the average on the first test is 72%. After the first test, 20% of the students drop the class. Every student remaining in the class takes the second test, and the average on the second test is 75%. After the second test, 248

students drop the class. Every student remaining in the class takes the third test, and the average on the third test is 76%. If the average of all of the students’ tests during the semester was 74%, then how many students were originally in the class? 
a = original no. students ... took test A
0.8a = number who took test B
0.8a - 248  = number who took test C (3rd test)

[0.72a + (0.8a)*.75 + (0.8a - 248)*.76] = 0.74a + (0.8a)*.74 + (0.8a - 248)*.74

-0.02a + (0.8a)*.01 + (0.8a - 248)*.02 = 0
  0.004a = 4.96
  a = 1240 <<<  answer

Morningfox · Answer

This is not "tricky". There are no special things you have to know, there are no double meanings of words, or anything like that.

If you start with 1240 students, then the total score for the first test is 72 * 1240 = 89280.
Then 20% drop the class, so that leaves 992 students.
Then for second test, the total score is 75*99 = 74400.
Then 248 students drop, that leaves 744.
For the third test, the total score is 76 * 744 = 56544
The total scores for all three tests add up to 89280 + 74400 + 56544 = 220224
The total number of tests taken is 1240 + 992 + 744 = 2976
The average score is 220224 / 2976 = 74, just like the problem said.
So it is correct that they started with 1240 students.

Captain Matticus, LandPiratesInc · Answer

x students take the first test
0.8 * x students take the 2nd test
0.8 * x - 248 students take the 3rd test

72 * x = cumulative score of first test
75 * 0.8 * x = cumulative score of 2nd test
76 * (0.8x - 248) = cumulative score of 3rd test

(72x + 75 * 0.8 * x + 76 * (0.8x - 248)) / (x + 0.8 * x + 0.8 * x - 248) = 74
192.8 * x - 76 * 248 = 74 * (2.6 * x - 248)
192.8 * x - 74 * 2.6 * x = 76 * 248 - 74 * 248
0.4 * x = (76 - 74) * 248
0.4 * x = 2 * 248
x = 2 * 248 / 0.4
x = 5 * 248
x = 5 * 2 * 124
x = 10 * 124
x = 1240

Originally, there were 1240 students in the class.

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Tricky math problem?

3 Answers