# CAT 2021 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 20

CAT 2021 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 20 : If $n$ is a positive integer such that $($sqrt[7]{10})$$sqrt[7]{10})^{2} $ldots$$sqrt[7]{10}$^{n}>999$, then the smallest value of $n$ is ## 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 $$ $sqrt [ 7 ] { 10 } )$ $sqrt [ 7 ] { 10 } ) ^ { 2 }$ $sqrt [ 7 ] { 10 } ) ^ { 3 }$ $sqrt [ 7 ] { 10 } ) ^ { 4 }$ $sqrt [ 7 ] { 10 } ) ^ { 5 } $ldots \ldots$ $sqrt [ 7 ] { 10 }$ ^ { n } > 999$ 999 can be approximated as 1000 as we are dealing with powers of 10, 1000 can be written as 103. $$ $sqrt [ 7 ] { 10 } )$ $sqrt [ 7 ] { 10 } ) ^ { 2 }$ $sqrt [ 7 ] { 10 } ) ^ { 3 }$ $sqrt [ 7 ] { 10 } ) ^ { 4 }$ $sqrt [ 7 ] { 10 } ) ^ { 5 } $ldots \ldots$ $sqrt [ 7 ] { 10 }$ ^ { n } > 10 ^ { 3 }$ The bases are the same in the product so the powers will get added up till n. So, $$ 10 ) ^ { $frac { 1 } { 7 } } $cdot \frac { n$ n + 1$ } { 2 } > 10 ^ { 3 }$
Comparing the bases on both the sides of the inequality,
$$frac { n$ n + 1 ) } { 14 } > 3$
n(n+1) > 42
Can n be 6?
If n was 6, then 6×7 = 42
Which just works, because we approximated 999 as 1000 and so without the approximation the right hand side would be smaller than 42.
Hence 6 satisfies the condition.

The question is " If $n$ is a positive integer such that $($sqrt[7]{10})$$sqrt[7]{10})^{2} $ldots$$sqrt[7]{10}$^{n}>999$, then the smallest value of $n$ is " ##### Hence, the answer is '6' ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- 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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