# CAT 2023 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 1

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. 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 1 : Let $a, b, m$ and $n$ be natural numbers such that $a>1$ and $b>1$. If $a^m b^n=144^{145}$, then the largest possible value of $n-m$ is

1. 580
2. 290
3. 579
4. 289

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### Explanatory Answer

$a ^ { m } b ^ { n } = 144 ^ { 145 }$
$a ^ { m } b ^ { n } = $left$ 2 ^ { 4 } $times 3 ^ { 2 } $right$ ^ { 145 }$ $a ^ { m } b ^ { n } = 3 ^ { 290 } $times 2 ^ { 580 }$ Since the highest power of a prime in the prime factorization of $144 ^ { 145 }$ is 580, n can never be more than 580. Since m is a natural number the smallest value that m can take is 1. So, the maximum value of$n – m$ is 580 – 1 = 579.
But is that possible??
Yes!
When $a ^ { m } b ^ { n } = $left$ 3 ^ { 290 } $right) ^ { 1 } $times 2 ^ { 580 }$, where $a = 3 ^ { 290 } ; m = 1 ; b = 2 ; n = 580$. The question is " Let $a, b, m$ and $n$ be natural numbers such that $a>1$ and $b>1$. If $a^m b^n=144^{145}$, then the largest possible value of $n-m$ is " ##### Hence, the answer is '579' Choice C 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? ###### 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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