abhirup1711 wrote:If a ≠b and |a-b| = b-a, which of the following statements must be true?
I. a < 0
II. a + b < 0
III. a < b
A) None
(B) I only
(C) III only
(D) I and II
(E) II and III
Can an expert please provide a simple explanation?
Be definition:
|a-b| is the DISTANCE between a and b.
|a-b| = b-a implies the following:
The DISTANCE between a and b is equal to the DIFFERENCE between b and a.
A DISTANCE must be greater than or equal to 0.
A DIFFERENCE can be negative, 0, or positive.
For the DISTANCE between two values to be equal to the DIFFERENCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
b-a ≥ 0
a ≤ b.
Here, it is given that a≠b, so a<b.
Thus, statement III must be true.
Eliminate any answer choice that does not include statement III (A, B and D).
The only difference between C and E is that the latter answer choice includes statement II.
Try to show that statement II does NOT have to be true.
If we plug a=2 and b=3 into |a-b| = b-a, we get:
|2-3| = 3-2
1 = 1.
Since it does not have to be true that a+b < 0, eliminate E.
The correct answer is
C.
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