[Official] Quant Thread for 2016

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Let's see if we can make this bigger and better than the previous year threads. For those who are starting their CAT 2016 prep, this will be a good starting point. Do post your Quant queries over here - I and other Puys will try and answer the same.

Brief intro: I am Ravi Handa and I run an online course for CAT over here:

http://handakafunda.com/online-cat-coaching/

 

Hi all CAT aspirants, you are invited to join this group for queries related to admissions at MBA, IIT Kanpur.

We hope to see you guys in the next stage of selection procedure!

Facebook:

https://www.facebook.com/groups/iitkanpurmba2017admissions/

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https://www.pagalguy.com/discussions/official-iit-kanpur-mba-2017-2019-admissions-5914449359667200

PR Coordinator, AdCom, #mbaiitk
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What is the remainder when 3^21 + 9^21 + 27^21 + 81^21 is divided by (3^20+1)?

Online CAT Coaching Course for CAT 2019 - https://handakafunda.com/online
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Focusonthepain
@Focusonthepain  ·  17 karma

1

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Let me start by asking a question on Remainders.

What is the remainder when the infinite sum (1!)² + (2!)² + (3!)² + ··· is divided by 1152?

Online CAT Coaching Course for CAT 2019 - https://handakafunda.com/online
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ravihanda
@ravihanda  ·  8,557 karma

@ranishroy8 That is correct.

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ravihanda
@ravihanda  ·  8,557 karma

Here is the solution for the same:


We have to find out the remainder when (1!)² + (2!)² + (3!)² + ··· is divided by 1152

1152 = 2^7 * 3^2

= (6!)^2 is divisible by 1152

= All (n!)^2 are divisible by 1152 as long as n > 5

So, our problem is now reduced to

Rem [((1!)² + (2!)² + (3!)² + (4!)² + (5!)²)/1152]

= Rem[(1 + 4 + 36 +576 + 14400) / 1152]

= Rem [15017/1152]

= 41

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