CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

CAT Questions | Algebra | Geometric Progressions - Sum of all Terms

The question is about sum of all terms. Four terms are given in which some of them are in AP and some of them are in GP, we need to find out the sum of all the terms. 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. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 20: Find the sum of all the terms, If the first 3 terms among 4 positive 2-digit integers are in A.P and the last 3 terms are in G.P. Moreover the difference between the first and last term is 40.

  1. 108
  2. 172
  3. 124
  4. 196

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!

2IIM : Best Online CAT Coaching.

Best CAT Coaching in Chennai

CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: Make clear assumptions!

Let the numbers be x-a, x, x+a
∴ For last 3 terms to be in G.P:-
(x+a)2 = x(x-a+40)
x2+a2+2ax = x2-ax+40x
a2 = -3ax + 40x
=> x = \\frac{a^2}{(40-3a)}\\)
Now, since x is a positive integer, putting different integral value of a .
Only a = 12 gives a integer value of x = 36

(Note, a=b also give integral value x=b but then the first term becomes 0)
∴ x = 36, a = 12
∴ x – a = 24
x = 36
x+a = 48
x-a+40 = 64
∴ Sum of all the terms = 64+48+36+24 = 172
The terms are - 24,36,48,64

The question is "Find the sum of all the terms, If the first 3 terms among 4 positive 2-digit integers are in A.P and the last 3 terms are in G.P."

Hence the answer is "172"

Choice B is the correct answer.

CAT Online Preparation | CAT Algebra Videos On YouTube

Other useful sources for Algebra Questions | Arithmetic Progressions Geometric Progressions Sample Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now