Number Theory: Quiz Marks Averages
XAT 2011 · Quantitative Ability & Data Interpretation · Medium · Number Theory
Prof. Bee noticed something peculiar while entering the quiz marks of his five students into a spreadsheet. The spreadsheet was programmed to calculate the average after each score was entered. Prof. Bee entered the marks in a random order and noticed that after each mark was entered, the average was always an integer. In ascending order, the marks of the students were 71, 76, 80, 82 and 91. What were the fourth and fifth marks that Prof. Bee entered?
- A.
71 and 82
- B.
71 and 76
- C.
71 and 80
- D.
76 and 80
- E.
91 and 80
C
Explanation
For averages to be integers at every step, working backwards from total sum gives 3rd entered mark as 91, and 4th and 5th entered marks as 71 and 80.
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