There were 150 questions in an exam , where 1 mark was awarded for every correct answer and 1/3rd mark was deducted for every wrong answer. A certain number of students , whose total number of attempts were all different , got the same mark of 50 . Find the maximum number of such students possible .
(1)26
(2)24
(3)35
(4)25
(5)101
what does the meaning of "...A certain number of students , whose total number of attempts were all different ,,,"
did they attempted right or wrong questions ?
2007-06-22 18:56:20 · 4 answers · asked by calculus 1 in Science & Mathematics ➔ Mathematics
They attempted different number of correct and wrong answers.
2007-06-22 19:00:39 · answer #1 · answered by Anonymous · 0⤊ 0⤋
They could have attempted any number of right or wrong questions.
Lets say they attempted "x" correct and "y" incorrect.
so x - y/3 = 50
or 3x - y = 150
and x + y <=150, x and y both being non-negative integers (0 is possible, but obviously x being zero doesn't give us a desired result. although one result is possible when y=0, i.e. when x=50).
What you have to do now is find the number of possible solutions to this system of equations. Draw the graph of y = 3x - 150. Negative intercept, positive slope. Take only the first quadrant, as both x&y are positive. So we got the lower cut-off, which is where the line meets the x-axis: at (50,0). The upper cut-off can be obtained by the fact that x+y<=150. So the max value of this sum is 150. Then y=150-x. Hence both x and y turn out to be 75 on the line. So, x ranges from 50 to 75 and correspondingly y ranges from 0 to 75. For each x, there's a unique y, and for every integral x, y is also an integer (y=3x-150). So the maximum possibilities are the number of integral x lying between 50 and 75, inlcuding both, i.e. 26. Ok?
2007-06-23 02:12:38 · answer #2 · answered by sloth 3 · 0⤊ 0⤋
The phrase means that they attempted anything that would get them 50 points, such as 60 correct answers and 30 incorrect answers. Since this includes all correct answers between 50 (all correct, but no incorrect ones chosen) to 150 (75 correct, 75 wrong), there are 26 students.
2007-06-23 02:05:29 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋
between the marks gained from the correct answers and the ones deducted from the wrong ones, they got 50 marks.
2007-06-23 02:04:43 · answer #4 · answered by alexandra 3 · 0⤊ 0⤋