CAT 2026 Slot 1 Quant Q16: Algebra – Equations

MCQ · +3 / −1

Let $c$ and $k$ be positive integers such that $c^2 + ck + c = 40$ and $3k^2 + ck + k = 100$. What is the value of $\dfrac{c + 2k}{2}$?

Answer and solution

Correct answer: D

Solution

First equation: $c(c+k+1)=40$. Try $c=4$: $4(4+k+1)=40\Rightarrow k=5$. Check 2nd: $3(25)+4(5)+5=100$ ✓. $c+k=9$

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.