Oct 22 08:00 AM PDT  09:00 AM PDT Join to learn strategies for tackling the longest, wordiest examples of Counting, Sets, & Series GMAT questions Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58396

What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
30 Jan 2015, 07:24
Question Stats:
63% (01:16) correct 37% (01:14) wrong based on 602 sessions
HideShow timer Statistics
What is the remainder when \(10^{49} + 2\) is divided by 11? A. 1 B. 2 C. 3 D. 5 E. 7
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Intern
Joined: 24 Jan 2014
Posts: 34
Location: France
Concentration: General Management, International Business
GPA: 3
WE: General Management (Advertising and PR)

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
30 Jan 2015, 09:42
Hello Bunuel, I gave it a try: I tried to find a pattern of remainder of (10 at any power) + 2 as following: 10^1 + 2 = 12/11 = 1 x 11 remainder 1 10^2 + 2 = 100 + 2 = 9 x 11 remainder 3 10^3 + 2 = 1000 + 2 = 91 x11 remainder 1 10^4 + 2 = 10000 + 2 = 909 x 11 remainder 3 It seems that any off power of 10, + 2 will results in a reminder = 1 Then CORRECT ANSWER A. 1 Bunuel wrote: What is the remainder when 10^49 + 2 is divided by 11?
A. 1 B. 2 C. 3 D. 5 E. 7
Kudos for a correct solution.
The OA will be revealed on Sunday
_________________
THANKS = KUDOS. Kudos if my post helped you! Napoleon Hill — 'Whatever the mind can conceive and believe, it can achieve.'




Intern
Joined: 15 Jan 2015
Posts: 1

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
30 Jan 2015, 09:10
Going by the logic When 10^2/11 reminder is 1, Similarly 10^3/11 reminder will be 1 and this would just continue regardless of 10 power anything (10^x)/11
just add 2 to this reminder, and hence the answer is 3.



Math Expert
Joined: 02 Aug 2009
Posts: 8004

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
30 Jan 2015, 09:54
Bunuel wrote: What is the remainder when 10^49 + 2 is divided by 11?
A. 1 B. 2 C. 3 D. 5 E. 7
Kudos for a correct solution.
The OA will be revealed on Sunday the property of 11 as divisor is (sum of odd digits sum of even digits)=0 starting from rightmost digit.. this means for 10^even number, (sum of odd digits sum of even digits) =10=1 so 1 is the remainder... and for 10^odd number, (sum of odd digits sum of even digits) =01=1 so 10 is the remainder... therefore 10^49 will have a remainder of 10.. so ans =12/11 ie rem=1 ans A
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15300
Location: United States (CA)

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
30 Jan 2015, 13:12
Hi quitdreaming, You have to be very careful with your generalizations. If you're "off", even a little bit, then you'll likely get whatever question you're working on wrong. With this calculation, you ARE correct: 100/11 = 9r1 But with this one, your generalization is incorrect: 1,000/11 = 90r10 (NOT remainder 1) Knowing this, what would you do differently to solve this problem? GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 18 Aug 2014
Posts: 112
Location: Hong Kong

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
Updated on: 31 Jan 2015, 07:38
10^49 + 2 / 11
> +2 (111)^49 / 11
> +2 1 = 1
Answer A
Originally posted by LaxAvenger on 30 Jan 2015, 15:38.
Last edited by LaxAvenger on 31 Jan 2015, 07:38, edited 1 time in total.



Intern
Joined: 23 Nov 2014
Posts: 21
Location: China
Concentration: Entrepreneurship, General Management
GMAT 1: 550 Q41 V25 GMAT 2: 680 Q47 V35
WE: General Management (Hospitality and Tourism)

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
31 Jan 2015, 01:13
Bunuel wrote: What is the remainder when 10^49 + 2 is divided by 11?
A. 1 B. 2 C. 3 D. 5 E. 7
Kudos for a correct solution.
The OA will be revealed on Sunday Answer is A. \(10^odd\)+2 = Remainder 1 I tested the following cases\(10^2\), \(10^3\) and \(10^5\) + 2



Manager
Joined: 04 Oct 2013
Posts: 160
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30 GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
31 Jan 2015, 02:00
when 10^odd/11 reminder is 10; when 10^even/11 reminder is 1. R10+R2 = R12. Since R 12 is not acceptable because it is greater than the divisor. R=1 Answer A
_________________
learn the rules of the game, then play better than anyone else.



Math Expert
Joined: 02 Sep 2009
Posts: 58396

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
02 Feb 2015, 04:26
Bunuel wrote: What is the remainder when 10^49 + 2 is divided by 11?
A. 1 B. 2 C. 3 D. 5 E. 7
Kudos for a correct solution.
The OA will be revealed on Sunday VERITAS PREP OFFICIAL SOLUTION:With exponentbased problems and huge numbers, it's often helpful to try to establish a pattern using small numbers. On this problem, while 1049+2 is a massive number that you'd never want to try to perform calculations with, you can start by using smaller numbers to get a feel for what it would look like: 10^2+2=102, which when divided by 11 produces a remainder of 3 (as 9 * 11 = 99, leaving 3 left over) 10^3+2=1002, which when divided by 11 produces a remainder of 1 (as 9 * 110 = 990, and when you add one more 11 to that you get to 1001, leaving one left) 10^4+2=10002, which when divided by 11 produces a remainder of 3 (as you can get to 9999 as a multiple of 11, which would leave 3 left over) 10^5+2=100002, which when divided by 11 produces a remainder of 1 (as you can get to 99990 and then add 11 more, bringing you to 100001 leaving one left over). By this point, you should see that the pattern will repeat, meaning that when 10 has an even exponent the remainder is 3 and when it has an odd exponent the remainder is 1. Therefore, since 10 has an odd exponent in the problem, the remainder will be 1.
_________________



Intern
Joined: 04 Feb 2015
Posts: 1

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
04 Feb 2015, 03:29
I solved it the following way: 1.10^49+2/11=10^51/11 2. Now i test cases 100/9 ==> Gives remainder of 1 3. If you know realize that the nominator has 3 letters you can deduct that 10^51/11 will also have a remainder of 1. 4. Counterproof 1000/11 ==> Remainder of 9 Bunuel wrote: What is the remainder when 10^49 + 2 is divided by 11?
A. 1 B. 2 C. 3 D. 5 E. 7
Kudos for a correct solution.
The OA will be revealed on Sunday



Intern
Joined: 08 Dec 2013
Posts: 30

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
15 Mar 2015, 19:39
what is the problem in solving indivitually like this..
10^49/11 + 2/11 from first part..we get 1 (odd places are 0 and even places are 9, as per cyclicity) from second part, we get 2
1+2=3 =rem.. kindly correct me (we have used this line of method in example 1 also in math remainders theory..so wats the difference)
Thanku in advance



Math Expert
Joined: 02 Aug 2009
Posts: 8004

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
15 Mar 2015, 19:54
shreygupta3192 wrote: what is the problem in solving indivitually like this..
10^49/11 + 2/11 from first part..we get 1 (odd places are 0 and even places are 9, as per cyclicity) from second part, we get 2
1+2=3 =rem.. kindly correct me (we have used this line of method in example 1 also in math remainders theory..so wats the difference)
Thanku in advance hi shreygupta3192, your approach is correct and can be done the way you have solved... however you have to be careful while finding remainder.. when you divide 10^n by 11, the remainder will be 1 or 1, that is 10..... it will depend on n.. when you divide 10 by 11.. remainder is 10 and not 1... you add odd and even from right most digit and then subtract even from odd.. in case of 10... 01=1or 10.... similarily 10^49 will give a remainder of 10.. overall remainder=10+2=12, which will give remainder as 1 when divided by 11.. hope it is clear.. chetan
_________________



Intern
Joined: 13 Dec 2016
Posts: 41

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
20 Jan 2017, 09:57
Bunuel, Can we solve this question using the below approach ? 10^49+2 =(111)^49+2 =11^49  1^49+2 =11^49 1+2 =11^49 +1 Hence, when 10^49+2 is divided by 11 , implies when 11^49 +1 is divided 11, 11^49 is divisible by 11 leaving remainder 1 (due to +1 component).



Math Expert
Joined: 02 Sep 2009
Posts: 58396

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
21 Jan 2017, 04:20
grichagupta wrote: Bunuel, Can we solve this question using the below approach ? 10^49+2 =(111)^49+2 =11^49  1^49+2
=11^49 1+2 =11^49 +1 Hence, when 10^49+2 is divided by 11 , implies when 11^49 +1 is divided 11, 11^49 is divisible by 11 leaving remainder 1 (due to +1 component). No, that's wrong. (111)^49 does not equal to 11^49 1^49. Does (ab)^2 equals to a^2  b^2?
_________________



Intern
Joined: 13 Dec 2016
Posts: 41

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
21 Jan 2017, 04:38
Bunuel wrote: grichagupta wrote: Bunuel, Can we solve this question using the below approach ? 10^49+2 =(111)^49+2 =11^49  1^49+2
=11^49 1+2 =11^49 +1 Hence, when 10^49+2 is divided by 11 , implies when 11^49 +1 is divided 11, 11^49 is divisible by 11 leaving remainder 1 (due to +1 component). No, that's wrong. (111)^49 does not equal to 11^49 1^49. Does (ab)^2 equals to a^2  b^2? Bunuel : Thank You. How silly of me ! I did some reading on this concept and now understand it. Thank you once again.



Math Expert
Joined: 02 Sep 2009
Posts: 58396

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
21 Jan 2017, 04:44
grichagupta wrote: Bunuel wrote: grichagupta wrote: Bunuel, Can we solve this question using the below approach ? 10^49+2 =(111)^49+2 =11^49  1^49+2
=11^49 1+2 =11^49 +1 Hence, when 10^49+2 is divided by 11 , implies when 11^49 +1 is divided 11, 11^49 is divisible by 11 leaving remainder 1 (due to +1 component). No, that's wrong. (111)^49 does not equal to 11^49 1^49. Does (ab)^2 equals to a^2  b^2? Bunuel : Thank You. How silly of me ! I did some reading on this concept and now understand it. Thank you once again. Glad I could help. Check the following post. It should help you in preparation: ALL YOU NEED FOR QUANT ! ! !.
_________________



Intern
Joined: 17 May 2016
Posts: 7
WE: Information Technology (Computer Software)

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
21 Jan 2017, 12:49
10^2+2=102 and 102/11 Reminder is 3 10^3+2=1002 and now Reminder is 1 10^4+2=10002 Reminder is 3
So for 10^odd Reminder is 1 and for 10^even reminder is 3
As per the question we need reminder for 10^49 I.e. 10^odd
Hence and is A.(1)
Posted from my mobile device



Intern
Joined: 17 May 2016
Posts: 7
WE: Information Technology (Computer Software)

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
21 Jan 2017, 12:52
[quote="Vianand4"]10^2+2=102 and 102/11 Reminder is 3 10^3+2=1002 and now Reminder is 1 10^4+2=10002 Reminder is 3
So for 10^odd Reminder is 1 and for 10^even reminder is 3
As per the question we need reminder for 10^49 I.e. 10^odd
Hence and is A.(1)
Please correct me if I am wrong.
Posted from my mobile device



Intern
Joined: 19 Aug 2017
Posts: 3

What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
19 Sep 2017, 04:24
Rem10/11 = 1
Rem10^49/11 = (1)^49 = 1
The FINAL remainder is :
Rem(10^49 + 2)/11 = 1 + 2 = 1



Intern
Joined: 03 Nov 2016
Posts: 4

Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
Show Tags
19 Sep 2017, 05:05
Remainder of (10^49+2) when divided by 11 would be
=Remainder of 10^49 when divided by 11 + Remainder of 2 when divided by 11 =R (1)^49/11 + 2/11 = 1+2 =1




Re: What is the remainder when 10^49 + 2 is divided by 11?
[#permalink]
19 Sep 2017, 05:05



Go to page
1 2
Next
[ 21 posts ]



