Problem Solving

AdityaBir wrote: ↑

Sun Jan 26, 2020 12:23 am

\(if\ \ a\ \ne-b\ is\ \left(a-b\right)\div\left(b+a\right)\ <1\)
\(\left(1\right)\ b^{2\ }>\ a^2\)
\(\left(2\right)\ a\ -\ b\ >1\)

Correct answer : A

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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