# CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

###### CAT Questions | Algebra | Progressions - Geometric Progressions

The question is about CAT Geometric Progressions. A question on possible values. We need to find out the possible values of 'n' which is related to the common ratio of a GP. 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 1: Second term of a GP is 1000 and the common ratio is r = $$frac{1}{n}\\$ where n is a natural number. Pn is the product of n terms of this GP. P6 > P5 and P6 > P7, what is the sum of all possible values of n? 1. 4 2. 9 3. 5 4. 13 ## 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 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Progressions: This question is almost a puzzle. You have to carefully consider the implications for the common ratio, and then extrapolate to the Product of n terms. Common ratio is positive, and one of the terms is positive => All terms are positive P6 = P5 * t6 => If P6 > P5, t6 > 1 P7 = P6 * t7 => If P6 > P7, t7 < 1 t6 = t2 * r4 = 1000r4; t7 = t2 * r5 = 1000r5 1000r4 > 1 and 1000r5 < 1 $\frac{1}{r^{4}}\\$ < 1000 and $\frac{1}{r^{5}}\\$ > 1000. $\frac{1}{r}\\$ = n. n4 < 1000 and n5 > 1000, where n is a natural number n4 < 1000 => n < 6 n5 > 1000 => n ≥ 4 n could be 4 or 5. Sum of possible values = 9 The question is "what is the sum of all possible values of n?" ##### Hence the answer is "9" Choice B is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Preparation | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Arithmetic Progressions Geometric Progressions Sample Questions ##### 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
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