It is of course possible that the examiner is being really devious….
All gust load calculations questions have previously been concerned with vertical gusts. This is why my earlier explanation considered only the vertical gust scenario.
But it is possible that this new question is concerned with horizontal gusts.
If so the solution takes the following form.
Horizontal gusts will not change angle of attack or CL, but they will change the dynamic pressure and lift. Because the angle of attack remains constant the wing will not stall.
At 2Vs the gust caused load factor to double.
This means that V squared increased by a factor of 1.41 from 2Vs to 2.82Vs.
So the gust speed was 0.82 Vs
At 1.3 Vs adding 0.82 gives a new speed of 2.12 Vs
New load factor = New V squared / Old V squared
So new load factor = 2.12 squared / 1.3 squared = 2.66
So the new load factor is 2.66
If this was the examiner’s intention then it really was a devious question because most candidates, being familiar with previous questions would have assumed that it was a vertical gust.
Hmmmmmmm.......The examiner -Instructor arms race moves on