2007 Cyprus MO/Lyceum/Problem 20

Problem

The mean value for 9 Math-tests that a student succeded was $10$ (in scale $0$ - $20$ ). If we put the grades of these tests in incresing order, then the maximum grade of the $5^{th}$ test is

$\mathrm{(A) \ } 15\qquad \mathrm{(B) \ } 16\qquad \mathrm{(C) \ } 17\qquad \mathrm{(D) \ } 18\qquad \mathrm{(E) \ } 19$

Solution

If the 5th test received a grade of $x$ , the minimum possible sum of the tests is $\displaystyle 0 + 0 + 0 + 0 + x + x + x + x + x + x = 6x$ . The average is $\frac{6}{9}x = \frac 23x \le 10$ , so $x \le 15 \Longrightarrow \mathrm{A}$ .

2007 Cyprus MO, Lyceum (Problems)
Preceded by Problem 19	Followed by Problem 21
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2007 Cyprus MO/Lyceum/Problem 20

Problem

Solution

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