# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Number Theory Questions | Question 28

Looking out to strengthen your hold on the Number Theory part of the Quantitative Aptitude section in the CAT Exam? You've come to the right place! CAT previous year paper are the best way to go about achieving expertise in any topic and here we have a beautiful question from Number Theory taken from CAT Question paper 2017 Slot 2. Try out this question and see if you can solve it without looking at the solutions provided!
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Question 28 : How many different pairs (a, b) of positive integers are there such that a ≤ b and $$frac{1}{a}$ + $\frac{1}{b}$ = $\frac{1}{9}$ ? [TITA] ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Number Theory Given that $\frac{1}{a}$ + $\frac{1}{b}$ = $\frac{1}{9}$ Let us assume that a ≤ b. For first case, let a = b, then $\frac{1}{18}$ + $\frac{1}{18}$ = $\frac{1}{9}$ Hence$18 , 18) is one pair of possibility.
In all the cases, both a and b should be greater than 9 to satisfy the equation.
So, we can take a = 10 , 11 , 12 , ..... , 18 and check for the different possibilities.
For example, let us take a = 15
⟹ $$frac{1}{b}$ = $\frac{1}{9}$ - $\frac{1}{15}$ ⟹ $\frac{5 - 3}{45}$ = $\frac{2}{45}$ Hence a = 15 is not possible. Similarly when a = 17, 16, 14, 13, and 11 does not work either. Now let us take a = 12, ⟹ $\frac{1}{b}$ = $\frac{1}{9}$ - $\frac{1}{12}$ ⟹ $\frac{4 - 3}{36}$ = $\frac{1}{36}$ Hence, a = 12 and b = 36 is the other pair of possibility. When a = 10, ⟹ $\frac{1}{b}$ = $\frac{1}{9}$ - $\frac{1}{10}$ ⟹ $\frac{10 - 9}{90}$ = $\frac{1}{90}$ Hence, a = 10 and b = 90 is the other pair of possibility. Therefore$18,18) , (12,36) and (9,90) are the three different pairs of positive integers which satisfy the condition

The question is "How many different pairs (a, b) of positive integers are there such that a ≤ b and $$frac{1}{a}$ + $\frac{1}{b}$ = $\frac{1}{9}$ ? [TITA]" ##### Hence, the answer is 3 ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### 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! ##### 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? Mobile:$91) 99626 48484 / 94459 38484
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