Given: a ≠ –b
We have to whether (a – b)/(a + b) < 1.
Let's take each statement one by one.
(1) b^2 > a^2
Case 1: Say a = –2 and b = –3;
(a – b)/(a + b) < 1
(–2 + 3)/(–2 – 3) < 1
1/–5 < 1
–1/5 < 1. This is a valid inequality. The answer is yes.
Case 2: Say a = 2 and b = –3;
(a – b)/(a + b) < 1
(2 + 3)/(2 – 3) < 1
5/–1 < 1
–5 < 1. This is a valid inequality. The answer is yes.
Case 3: Say a = 2 and b = 3;
(a – b)/(a + b) < 1
(2 – 3)/(2 + 3) < 1
–1/5 < 1
–1/5 < 1. This is a valid inequality. The answer is yes.
Unique answer. Sufficient.
(2) a – b > 1
Case 1: Say a = –2 and b = –4;
(a – b)/(a + b) < 1
(–2 + 4)/(–2 – 4) < 1
2/–6 < 1
–1/3 < 1. This is a valid inequality. The answer is yes.
Case 2: Say a = 4 and b = 2;
(a – b)/(a + b) < 1
(4 – 2)/(4 + 2) < 1
2/6 < 1
1/3 < 1. This is NOT a valid inequality. The answer is no.
The correct answer: A
Hope this helps!
-Jay
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