MBApyq

Function defined by sum of terms

CAT 2007 Slot 1 · Quantitative Ability · Medium · Functions

This is a medium Quantitative Ability question from the CAT 2007 Slot 1 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2007 Slot 1 questionsMore Functions questionsAll CAT QA

A function f(x)f(x) satisfies f(1)=3600f(1) = 3600 and f(1)+f(2)+⋯+f(n)=n2f(n)f(1) + f(2) + \dots + f(n) = n^2 f(n), for all positive integers n>1n > 1. What is the value of f(9)f(9)?

  1. A.

    80

  2. B.

    240

  3. C.

    200

  4. D.

    100

  5. E.

    120

Answer

A

Explanation

Given f(1)+f(2)+⋯+f(n)=n2f(n)f(1) + f(2) + \dots + f(n) = n^2 f(n). For n=2n=2: f(1)+f(2)=4f(2)  ⟹  f(2)=f(1)3f(1) + f(2) = 4f(2) \implies f(2) = \frac{f(1)}{3}. By induction, f(n)=f(1)×22×32×⋯×(n−1)2(22−1)(32−1)…(n2−1)f(n) = f(1) \times \frac{2^2 \times 3^2 \times \dots \times (n-1)^2}{(2^2-1)(3^2-1)\dots (n^2-1)}. Simplifying terms yields f(9)=3600×29×10=80f(9) = 3600 \times \frac{2}{9 \times 10} = 80.

Related Functions questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace