For any two points M, N on the number line representing numbers m, n the distance MN = | m - n|.
So, for three points, P, Q and R on the number line |p – q|, |q – r|, |r – p| are distances between three pairs of points on the number line.
In this case, we are trying to find maximum value of |a – b| + |b – c| – |c – a|. If b lies between a and c, the above value would be zero. So, b should not be between a and c.
The best case scenario would be if a, c were very close to each other and far from b. Let us try b = 24, a = 1, c = 2.
In this case |a – b| + |b – c| – |c – a| = 23 + 22 – 1 = 44. This is the maximum possible value.
We could also have b = 1, a = 24, c = 23,
|a – b| + |b – c| – |c – a| = 23 + 22 – 1 = 44.
Answer choice (a)
Correct Answer: 44
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