Bodhee Prep-Online CAT Coaching | Online CAT Preparation | CAT Online Courses

Get 30% OFF on CAT Crash Course. Code: LASTLAP. Course starts from 18th Sept Enroll Now

CAT 2019 Quant Question with Solution 21

Question:
For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals

Show Answer

Correct Answer: 10

Case 1: m is even.

Given, 8f(m + 1) - f(m) = 2

$\begin{align} & \Rightarrow 8\left( m+1+3 \right)-m\left( m+1 \right)=2 \\ & \Rightarrow 8m+32-{{m}^{2}}-m=2 \\ & \Rightarrow {{m}^{2}}-7m+30=0 \\ & \Rightarrow (m-10)(m+3)=0 \\ & \Rightarrow m=10\ or\ -3 \\ \end{align}$

As m is positive integer, the only possible value of m =10.

Case 2:

If m is odd, then we would not be getting positive solution.


CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2019 Slot-1


CAT 2019 Slot-2

CAT online Courses

CAT 2023 Mock Test Series

  • 400+ Topic Tests
  • 45 Sectional tests
  • 20 Mock Tests (Video Solutions)
  • Only at INR 2499

20% Discount Code: GET20

FREE CAT Prep Whatsapp Group

CAT 2023 Online Course at affordable price