# CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

###### CAT Questions | Algebra | Progressions - AP GP HP

The question is about type of a progression. Roots of two quadratic progression is in a progression, what type it is? 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 19: If the equation px2 + 2qx + r = 0 and dx2 + 2ex + f = 0 have a common root, and p,q,r are in G.P., then in which type of progression is $$frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$ 1. $\frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$ are in G.P 2. $\frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$ are in A.P 3. $\frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$ are in H.P 4. Insufficient Data ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Progressions: How you would find out the type of a progression? Since p,q,r are in G.P. we have q2 = pr. On solving px2 +2qx +r = 0 we get x = $\frac{-2q ± √$4q^2 - 4pr$}{2p}$ => x = $\frac{-2q}{2p}\\$$q2 = pr)
=> x = $$frac{-q}{p}\\$ Thus x = $\frac{-q}{p}\\$ is the repeated root of px2+2qx+r = 0 ∴ x = $\frac{-q}{p}\\$ is also a root of dx2+2ex+f = 0 => d$$$frac{-q}{p}\\$)2 + 2e$$$frac{-q}{p}\\$) + f = 0 => $\frac{dq^2 - 2eqp + fp^2}{p^2}\\$ = 0 => dq2 - 2eqp + fp2 = 0 => $\frac{d}{p}\\$ - 2 * $\frac{e}{q}\\$ + $\frac{fp}{q^2}\\$ = 0 [On dividing by pq2] => $\frac{d}{p}\\$ - 2 * $\frac{e}{q}\\$ + $\frac{f}{r}\\$ = 0 => $\frac{d}{p}\\$ + $\frac{f}{r}\\$ = 2 * $\frac{e}{q}\\$ Hence it can be clearly seen that $\frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$ are in A.P The question is "If the equation px2 + 2qx + r = 0 and dx2 + 2ex + f = 0 have a common root, and p,q,r are in G.P., then in which type of progression is $\frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$" ##### Hence the answer is "$\frac{d}{p}\\$ , $\frac{e}{q}\\$ , $\frac{f}{r}\\$ are in A.P." 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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