One approach is to remember one key thing. Since its given that 7 is the mean, and 6 & 8 are on either sides of mean, therefore the other two numbers, namely x and y have to be equally spaced on either side of the mean.
The effect of +1 of 8 is equally compensated by the effect of -1 of 6. Hence for 7 to reman the mean of the set, the other numbers have to do so as well.

Statement 1) integer 3 is in the list A
3 is at a distance of 4 units from the mean on left hand side of number line. Therefore you are supposed to look for another number, but at the same distance on right hand side of the mean.
7+4=11 Hence the other number is 11.
Now we know the smallest and the largest of the set. So range can be easily found out.
Sufficient

Statement 2) The Largest term in A is greater than 3 times and less than 4 times the size of the smallest term.

One of the two numbers, the two that we don't know yet, have to be either side of the mean.
Let the smaller one be x and the larger one be y.
Since the set consists of positive numbers only, hence we have to check from 1 to 6.
3x<y<4x
Since only one number has to be on either side of the mean, hence the value of x comes out as 3 and y as 11.
The smallest and the largest are known. Hence sufficient.

+1D
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