# Quantitative Aptitude – Algebra – Simple Equations – If a and b are integers

## Question

If a and b are integers of opposite signs such that (a + 3)^2 : b^2 = 9 : 1 and (a – 1)^2 : (b – 1)^2 = 4 : 1, then the ratio a^2 : b^2 is

A) 9:4 ‘
B) 81:4
C) 1: 4
D) 25: 4

Option (D)

## Solution

As per the question from CAT 2017 – Quantitative Aptitude – Algebra – Simple Equations,

We get 4 cases
CASE – 1
a+3 = 3b
a-1 = 2b-2

CASE – 2
a+3 = 3b
a-1 = 2b + 2

CASE – 3

a+3 = -3b
a-1 = 2b-2

CASE – 4
a+3 = -3b
a-1 = -2b+2

Subtracting the second equation from the first we get,
Case 1: 4 = b+2 => b = 2, a = 3 (Rejected as a and b should be of opposite sign)

Case 2: 4 = b-2 => b = 6, a = 15 (Rejected as a and b should be of opposite sign)

Case 3: 4 = -5b+2 => b = -2/5 (Rejected as both a and b are integers)

Case 4: 4 = -b-2 => b = -6, a = 15 (Accepted)

So, a^2/b^2 = (15/6)^2 = 25/4
Option (D)

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