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Question 46
The average of a non-decreasing sequence of N numbers $$a_{1},a_{2}, ... , a_{N}$$ is 300. If $$a_1$$, is replaced by $$6a_{1}$$ , the new average becomes 400. Then, the number of possible values of $$a_{1 }$$, is
Correct Answer: 14
Solution
$$a_1+a_2+.....+a_N=300N$$
$$6a_1+a_2+.....+a_N=400N$$
$$5a_1=100N$$
$$a_1=20N$$
As the given sequence of numbers is non-decreasing sequence, N can take values from 2 to 15.
N is not equal to 1, if N = 1, then average of N numbers is 300 wouldn't satisfy.
Therefore, N can take values from 2 to 15, i.e. 14 values.
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