CAT Exam Model Paper 2 with solutions for free online practice

Question : 67 of 100

Marks: +1, -0

Section III Quantitative Aptitude

A teacher gave sum to his class to find the average of n numbers viz. 1, 2, 3, 4, 5, 6,... etc. But when the teacher checked the solution, he has found that during the calculation a students just missed a number for the addition thus his average of the n numbers was 15. The value of n is

30
26
31
not unique

Validate

Solution:

(d) Let there be n number and he missed a number k, then theaverage (which he has calculated =

{ ( { n ( n + 1 ) }/ { 2 } - k ) }/ { n } = 15

⇒ n

^2

− 29n = 2k
⇒ n(n − 29) = 2k
Thus at n = 29 or n < 29, the expression is invalid since the value of k is neither zero nor negative, which is actually a natural number. So for the least possible valued of n = 30
k = 15
and for n = 31, k = 31
Again for n > 31, k is beyond the range i.e., greater than n. Since k can not be greater than n. Hence there are only two values of k.
So, there is no unique value of n.

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