Question

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

A
0
B
1
C
10
D
19

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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