CAT 2020 Slot 1 QA Q2 Functions & Graphs

Question 2 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

A
0
B
40
C
10
D
20

Answer: (D) 20 Functions & Graphs MCQ

Solution

\(f(5+x)=f(5-x)\) means the graph is symmetric about \(x=5\), so roots come in pairs \(5\pm k\).
Four distinct roots form two pairs, each summing to 10. Total \(= 20\).