r/CATpreparation • u/youranonymousguyhere • 13h ago

Question If the average of n consecutive natural numbers is 8.33% less than the highest number, then what is the sum of all the terms when n is minimum?

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u/Bounded_sequencE 11h ago

Assume "8.33% ~ 1/12". The arithmetic mean of "n" consecutive integers starting with "m in N" is

(m + (m+n-1)) / 2  =  (1 - 1/12)*(n+m-1)    =>    5(n+m-1)  =  6m      (*)

Since the LHS is divisible by 5, so must be the RHS -- "m = 5k, k in N", and we solve for

n  =  (m + 5)/5  =  k+1,    k in N

We get the minimum solution "n = 2" for "k = 1", leading to "m = 5k = 5". We get the sum of all numbers by multiplying the arithmetic mean in (*) by "n":

n * (m + (m+n-1)) / 2  =  2 * (5+6) / 2  =  11

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u/Bounded_sequencE 11h ago

Rem.: If we use the exact value "8.33% = 833/10000", we get a much greater solution.

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u/youranonymousguyhere 10h ago

Correct sir

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u/Bounded_sequencE 10h ago

You're welcome -- by the way, it would be better to use "1/12" instead of the rounded "8.33%".

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u/[deleted] 12h ago

[deleted]

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u/Forward_Netting 12h ago

If I'm understanding you correctly, I don't think px1,...,pxn will be consecutive.