CAT 2025 Slot 1 · Quant · Question 1

CAT 2025 Slot 1 previous year question on Linear Equations, with the answer and a step-by-step solution.

Linear EquationsAlgebraMultiple choiceMedium
If a-6b+6c=4 and 6a+3b-3c=50, where a, b and c are real numbers, the value of 2a+3b-3c is
  1. A
    18
  2. B
    20
  3. C
    15
  4. D
    14
Pick an option, then check.
Answer & solution

Answer: Option A

Three unknowns and only two equations, so b and c cannot be found separately.

They never need to be: notice that b and c appear only through b-c.

Put u=b-c.

The equations become a-6u=4 and 6a+3u=50, and the target is 2a+3u.

From the first, a=4+6u.

Substituting: 6\left( 4+6u \right)+3u=50,

so 39u=26 and u=\frac{2}{3}.

Then a=4+6\cdot \frac{2}{3}=8, and 2a+3u=16+2=18.

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