# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 3

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 3 : For some real numbers $a$ and $b$, the system of equations $x+y=4$ and $(a+5) x+$left$b^2-15$right) y=8 b$ has infinitely many solutions for $x$ and $y$. Then, the maximum possible value of $a b$ is 1. 15 2. 33 3. 55 4. 25 ## 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 $x + y = 4$ $$ a + 5 ) x + $left$ b ^ { 2 } - 15 $right) y = 8 b$ if $a _ { 1 } x + b _ { 1 } y + c _ { 1 } = 0 , a _ { 2 } x + b _ { 2 } y + c _ { 2 } = 0$have ∞ solutions, then the equations are multiples of one another. That is, $$frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } = \frac { c _ { 1 } } { c _ { 2 } } = k$ So, we have, $\frac { a + 5 } { 1 } = \frac { b ^ { 2 } - 15 } { 1 } = \frac { 8 b } { 4 } = k$ $a + 5 = b ^ { 2 } - 15 = 2 b$ $b ^ { 2 } - 15 = 2 b$ $b ^ { 2 } - 2 b - 15 = 0$ $b ^ { 2 } - 5 b + 3 b - 15 = 0$ $b$ b - 5$ + 3 ( b - 5 ) = 0$
$b = 5$ or $b = - 3$
$a + 5 = 2 b$
if $b = 5$;
$a + 5 = 10$
$a = 5$
$a b = 25$
if $b = - 3$
$a + 5 = - 6$
$a = - 11$
$a b = 33$
So, the maximum possible value of $a b = 33$

The question is " or some real numbers $a$ and $b$, the system of equations $x+y=4$ and $(a+5) x+$left$b^2-15$right) y=8 b$ has infinitely many solutions for $x$ and $y$. Then, the maximum possible value of $a b$ is " ##### The answer is '33' Choice B is the correct answer. ###### 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! ## CAT Questions | CAT Quantitative Aptitude ## 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? Mobile:$91) 99626 48484 / 94459 38484
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