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 2020 Quant Question [Slot 2] with Solution 05

Question

Let the m-th and n-th terms of a geometric progression be \(\frac{3}{4}\) and 12 , respectively, where m<n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

  1. -2
  2. 2
  3. 6
  4. -4
Option: 1
Solution:

\({T_n} = 12\)

\({T_m} = 3/4\)

\(\frac{{{T_n}}}{{{T_m}}} = \frac{{a{r^{n - 1}}}}{{a{r^{m - 1}}}} = \frac{{12}}{{\frac{3}{4}}}\)

\({r^{n - m}} = 16 = {( \pm 2)^4} = {( \pm 4)^2}\)

To get the minimum value for \(r + n - m,r\) should be minimum.

\(\therefore r =  - 4\)

\(n - m = 2\)

\(\therefore \) Required answer =-2

CAT Online Course @ INR 12999 only

CAT 2020 Quant questions with Solutions

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