CAT 2025 Slot 1 QA Q1 Equations

Question 1 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

If \(a-6 b+6 c=4\) and \(6 a+3 b-3 c=50\), where \(a, b\) and \(c\) are real numbers, the value of \(2 a+3 b-3 c\) is

A
18
B
20
C
15
D
14

Answer: (A) 18 Equations MCQ

Solution

Let \(t = b - c\). The equations become \(a - 6t = 4\) and \(6a + 3t = 50\).
From the first, \(a = 4 + 6t\). Substituting: \(24 + 36t + 3t = 50 \Rightarrow t = \frac{2}{3}\), so \(a = 8\).
\(2a + 3b - 3c = 2a + 3t = 16 + 2 = 18\).

Shortcut. Only \(b - c\) ever appears, so treat it as a single variable.