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Solution


Q.

The arithmetic mean of five numbers is zero. They are distinct and non-zero numbers. Which of the following statements are true

 

(i) At least one of the numbers is positive.
(ii) The product of numbers is zero.
(iii) Maximum number of positive numbers is four.
(iv) At least one of the numbers is negative

 

Choose the correct option from the following:
1 (i) and (iii)   
2 (i) and (iv)   
3 (i), (iii) and (iv)   
4 (ii) and (iv)  

Ans.

(3)

The arithmetic mean of five numbers is zero implies that sum of the numbers is zero.

(i) At least one of the number is positive, this is true as the sum should be 0.
Sum of positive terms = sum of negative terms
so at least one number must be positive. (e.g. –1, –3, –5, 0, 9)

(ii) The sum being 0 does not imply that the product is also 0.
For example, 1, 1, 1, 1, –4

(iii) All five numbers can not be positive to give a sum zero, so maximum number
of positive numbers is four.

(iv) All five numbers can not be positive to give a sum zero, so at least one number
must be negative.

∴ (i), (iii) and (iv) are correct