Arithmetic and Geometric Progressions

You are here: Home  CAT Questionbank   CAT Quant  AP, GP  Question 8

Arithmetic Progression

    Sequence P is defined by pn = pn-1 + 3, p1 = 11, Sequence Q is defined as qn = qn-1 – 4, q3 = 103. If pk > qk+2, what is the smallest value k can take?
    1. 6
    2. 11
    3. 14
    4. 15

 

  • Correct Answer
    Choice D. 15

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

Detailed Solution

Sequence P is an A.P. with a = 11, and common difference 3.

So, Pk = 11 + (k – 1)3.

Sequence Q is an A.P. with third term 103 and common difference – 4.

t3 = a + 2d

103 = a + 2 (– 4) or a = 111

qk+2 = 111 + (k +1) (– 4)

qk + 2 = 111 – 4k – 4 = 107 – 4k

pk > qk + 2

11 + (k–1)3 > 107 – 4k

8 + 3k > 107 – 4k

7k > 99

k > 99/7

k has to be an integer, so smallest value k can take is 15.

Answer choice (d).

Correct Answer: 15



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Visit Piverb.com
Visit Wizako.com

More questions from Progressions

  1. Counting and Progressions
  2. Common Ratio
  3. Common Difference
  4. Sum up to 'n' Terms
  5. AP Puzzle
  6. GP Logical Puzzle
With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.