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 63

Question:
Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals

Show Answer

Correct Answer: 12

Given, f(mn)=f(m)f(m)

Also, f(24)=54

$\Rightarrow $f(24) =2×3×3×3

$\Rightarrow $f(2×12)=f(2)f(12)=f(2)f(2×6)=f(2)f(2)f(6)=f(2)f(2)f(2×3)=f(2)f(2)f(2)f(3)=2×3×3×3

Given that f(1), f(2) and f(3) are all positive integers, by comparison, we get

f(2) = 3 and f(3)=2. And we can safely take f(1)=1

Now, f(18)=f(2)(9)=f(2)f(3×3)=f(2)f(3)f(3)=3×2×2=12


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