Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 2110:00 AM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.
May 2208:30 AM PDT
-09:30 AM PDT
For many Indian MBA applicants, the default dream has long been a top US MBA. But as career goals, visa considerations, timelines, and global mobility priorities evolve, more candidates are seriously considering MBA programs in Europe.
May 2211:00 AM EDT
-11:59 PM EDT
Take 30% off all study plans with code PICNIC - Expires on Monday, May 25th- Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
Updated on: 29 Mar 2023, 12:44
Originally posted by CrackverbalGMAT on 26 May 2021, 04:34.
Last edited by CrackverbalGMAT on 29 Mar 2023, 12:44, edited 2 times in total.
Last edited by CrackverbalGMAT on 29 Mar 2023, 12:44, edited 2 times in total.
Kudos
Bookmarks
Solution:
Every 3*3 = 9 on dividing with 5 gives -1 as remainder
We have 243 3s =>121 3s paired and one additional unpaired 3
=> 3^243 / 5 ----> 9^121 * 3 /5 ----->(-1)^121 * 3/5-----> -1*3/5 -------> -3/5
= -3 as negative remainder
= +2 as a positive remainder
(option c)
Devmitra
Every 3*3 = 9 on dividing with 5 gives -1 as remainder
We have 243 3s =>121 3s paired and one additional unpaired 3
=> 3^243 / 5 ----> 9^121 * 3 /5 ----->(-1)^121 * 3/5-----> -1*3/5 -------> -3/5
= -3 as negative remainder
= +2 as a positive remainder
(option c)
Devmitra
13 Aug 2021, 05:58
Kudos
Bookmarks
If 3^243 + 2^243 is divided by 5, then the remainder is (I WANT SOLUTION TO THIS)
Updated on: 16 Sep 2024, 06:16
Originally posted by BrushMyQuant on 15 Sep 2022, 09:51.
Last edited by BrushMyQuant on 16 Sep 2024, 06:16, edited 2 times in total.
Last edited by BrushMyQuant on 16 Sep 2024, 06:16, edited 2 times in total.
Kudos
Bookmarks
We know to find what is the remainder when \(3^{243}\) is divided by 5
Theory: Remainder of a number by 5 is same as the Remainder of the unit's digit of the number by 5
(Watch this Video to Learn How to find Remainders of Numbers by 5)
Using Above theory , Let's find the unit's digit of \(3^{243}\) first.
We can do this by finding the pattern / cycle of unit's digit of power of 3 and then generalizing it.
Unit's digit of \(3^1\) = 3
Unit's digit of \(3^2\) = 9
Unit's digit of \(3^3\) = 7
Unit's digit of \(3^4\) = 1
Unit's digit of \(3^5\) = 3
So, unit's digit of power of 3 repeats after every \(4^{th}\) number.
=> We need to divided 243 by 4 and check what is the remainder
=> 243 divided by 4 gives 3 remainder
=> \(3^{243}\) will have the same unit's digit as \(3^3\) = 7
=> Unit's digits of \(3^{243}\) = 7
But remainder of \(3^{243}\) by 5 cannot be more than 5
=> Remainder = Remainder of 7 by 5 = 2
So, Answer will be C
Hope it helps!
MASTER How to Find Remainders with 2, 3, 5, 9, 10 and Binomial Theorem
Theory: Remainder of a number by 5 is same as the Remainder of the unit's digit of the number by 5
(Watch this Video to Learn How to find Remainders of Numbers by 5)
Using Above theory , Let's find the unit's digit of \(3^{243}\) first.
We can do this by finding the pattern / cycle of unit's digit of power of 3 and then generalizing it.
Unit's digit of \(3^1\) = 3
Unit's digit of \(3^2\) = 9
Unit's digit of \(3^3\) = 7
Unit's digit of \(3^4\) = 1
Unit's digit of \(3^5\) = 3
So, unit's digit of power of 3 repeats after every \(4^{th}\) number.
=> We need to divided 243 by 4 and check what is the remainder
=> 243 divided by 4 gives 3 remainder
=> \(3^{243}\) will have the same unit's digit as \(3^3\) = 7
=> Unit's digits of \(3^{243}\) = 7
But remainder of \(3^{243}\) by 5 cannot be more than 5
=> Remainder = Remainder of 7 by 5 = 2
So, Answer will be C
Hope it helps!
MASTER How to Find Remainders with 2, 3, 5, 9, 10 and Binomial Theorem
