CAT 2017 Slot 1 — QA Question 13

${\left(\frac{a+3}{b}\right)}^2=9$ and ${\left(\frac{a-1}{b-1}\right)}^2=4$

⇒ $\frac{\mathrm{a}+3}{\mathrm{b}}=\pm 3$ and $\frac{\mathrm{a}-1}{\mathrm{b}-1}=\pm 2$

We get following cases:

Case 1(a): a + 3 = 3b and a - 1 = 2b - 2
⇒ a = 3 and b = 2 (Rejected)

Case 1(b): a + 3 = 3b and a - 1 = -2b + 2
⇒ b is not an integer (Rejected)

Case 2(a): a + 3 = -3b and a - 1 = 2b - 2
⇒ b is not an integer (Rejected)

Case 2(b): a + 3 = -3b and a - 1 = -2b + 2
⇒ a = 15 and b = -6
∴ (a/b)² = (15/-6)² = 25/4

Hence, option (d).