The distance from point X to point Y is 20 miles, and the distance from point X to point Z is 12 miles. If d is the distance, in miles, between points Y and Z, then the range of possible values for d is indicated by (big book p451, q 28)
(A) 8 <= d <= 20
(B) 8 <= d <= 32
(C) 12 <= d <= 20
(D) 12 <= d <= 32
(E) 20 <= d <= 32
Correct answer is B, but if we take d = 8 then triangle inequalities doesn’t hold i.e., a + b > c.
Put the three points on a line.
yeah I used a line and figured it out. You prob. misread and thought it was related to triangles.
I do concede your point, but here is a sounder reasoning, in my view.
It asks for “possible range” of values. If you just consider it line, you can only get extremes values i.e., 8, 32, to get other values in the range you have to consider the triangle cases.
But since it asks for "all possible values”, we have to consider both the triangle + line cases. This is why ETS have not mentioned in the question that weather points lies in 1-d or 2-d plane. If they wanted to just consider line, they would mention 1-d plane.