If the average height of three people with different heights is 68 inc

Since we're asked about the height of the shortest person, we'll look at the extremes of the range.
This is a Logical approach.

(1) If the tallest is 72, we'll try making the second tallest as tall as possible (so that the shortest will be as short as possible).
Then the second tallest is 71.
Since the tallest is 72-68=4 more than average and the second tallest is 71-68=3 more than average,
the shortest needs to balance them out by being 4+3=7 less than average, which is 68 - 7 = 61.
Then our answer is YES.
Sufficient.

(2) Again let's try looking at the extremes. First, say the heights are very different from each other.
Say our tallest is 90 or even 100. Then clearly the shortest must be much less than 60 (we won't bother calculating this!)
Now, let's look at the other extreme - where the heights are very close to each other.
If the tallest is 70, the middle is exactly average, then the shortest needs to be 'opposite' to 70, that is, at 66.
Insufficient.

(A) is our answer.

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