I think this Q has already been discussed earlier. I hope you have searched for it before posting.
Average is 61..find the max and min values possible, you will get the answer
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Hi,
Let's say smallest is X then,
{X+(6X+7)}/2 = 61

7X = 122 - 7

X = 115/7

Now, pls suggest what am I doing wrong?

Thanks,

Here is what I did for this one-->

Smallest value = a(let)
Largest value => 6a+7


Now the smallest value of the set must be less than the mean and the largest value must be greater than the mean.

Hence a>61
and 6a+7>61 ==> a>9

At a=61 => Largest value => 6a+7= 373

Hence the range of the set would be (9,373)

Only 9 elements are in the range.

Hence C.

NOTE --> THIS QUESTION is a part of the MOCK SERIES --> https://gmatclub.com/forum/stonecold-s- ... l#p1676182
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Given average \(61\) and \(max\) = \(min * 6 + 7\), so set must have alteast two different integers (meaning it is not a set of all same integers)

in a set of different integers, min value can't be equal to average, so \(min\) < \(61\) => \(max\) < \(61 * 6 + 7\), so \(max\) < \(373\)
similarly, max value can't be equal to average, so \(max\) > \(61\) => \(61\) < \(max\) < \(373\)

now we found, \(max\) > \(61\)=> \(min * 6 + 7\) > \(61\) => \(min\) > \(9\).

all the elements in the set must be between \(9 < S < 373\), only 9 integers of the given falls within the range => Answer (C)