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Question

The average of $$20$$ numbers is zero. Of them, at the most, how many may be greater than zero?


A
0
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B
1
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C
10
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D
19
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Solution

The correct option is D $$19$$
Let the $$20$$ numbers be $$a_1,a_2,...,a_{20}$$

Given that average of 20 numbers is zero.

Therefore, $$\dfrac{a_1+a_2+...+a_{20}}{20}=0$$

$$\implies {a_1+a_2+...+a_{20}}=0$$

$$\implies a_1+a_2+...+a_{19}=-a_{20}$$

Therefore, at the most $$19$$ numbers can be greater than zero.

Mathematics

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