BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Reminder addition and subtraction........Expert needed

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members
Thanked: 14 times
by Mo2men » Sun Jan 22, 2017 3:09 am
What is the remainder when 10^49 + 2 is divided by 11?

A. 1
B. 2
C. 3
D. 5
E. 7

OA:A

Source: Veritas

I solved the problem by this way but the answer is not presented here

(10^49 + 2)/11= 10^49/11 +2/11

Studying each term:
10/11 = reminder is 10
10^2/11= reminder is 1
10^3/11= reminder is 10

so 10^49/11 == reminder is 10
and 2/11 =reminder is 2

so total reminder is 10+2= 12 but the reminder can not be greater than the divisor.

Is adding reminders incorrect?


Any comment please??
Last edited by Mo2men on Sun Jan 22, 2017 3:47 am, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sun Jan 22, 2017 3:44 am
Mo2men wrote:What is the remainder when 10^49 + 2 is divided by 11?

A. 1
B. 2
C. 3
D. 5
E. 7
Generally, remainders repeat in a CYCLE.
(10¹ + 2)/11 = 12/11 = 1 R1.
(10² + 2)/11 = 102/11 = 9 R3.
(10³ + 2)/11 = 1002/11 = 91 R1.
(10� + 2)/11 = 10002/11 = 909 R3.
Here, the remainders ALTERNATE between 1 and 3.
More specifically:
Every ODD exponent yields a remainder of 1.
Every EVEN exponent yields a remainder of 3.
Since 10�� + 2 includes an odd exponent, it will yield a remainder of 1.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members
Thanked: 14 times

by Mo2men » Sun Jan 22, 2017 3:51 am
GMATGuruNY wrote: Generally, remainders repeat in a CYCLE.
(10¹ + 2)/11 = 12/11 = 1 R1.
(10² + 2)/11 = 102/11 = 9 R3.
(10³ + 2)/11 = 1002/11 = 91 R1.
(10� + 2)/11 = 10002/11 = 909 R3.
Here, the remainders ALTERNATE between 1 and 3.
More specifically:
Every ODD exponent yields a remainder of 1.
Every EVEN exponent yields a remainder of 3.
Since 10�� + 2 includes an odd exponent, it will yield a remainder of 1.

The correct answer is A.
Can I subtract or add reminders? what is wrong with my answer above?

Thanks in advance for your help
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sun Jan 22, 2017 3:53 am
Mo2men wrote:I solved the problem by this way but the answer is not presented here

(10^49 + 2)/11= 10^49/11 +2/11

Studying each term:
10/11 = reminder is 10
10^2/11= reminder is 1
10^3/11= reminder is 10

so 10^49/11 == reminder is 10
and 2/11 =reminder is 2

so total reminder is 10+2= 12 but the reminder can not be greater than the divisor.
10��/11 + 2/11 --> R10 + R2 = R12.
Since the resulting remainder (12) cannot be greater than the divisor (11), we divide once more by 11:
12/11 = 1 R1.
Thus, dividing 10�� + 2 by 11 will yield a remainder of 1.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members
Thanked: 14 times

by Mo2men » Sun Jan 22, 2017 3:55 am
Thanks a lot for your help and prompt response :) :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Wed Feb 01, 2017 5:35 pm
Here's a way that generalizes to more of these types of problems:

When 10*10 is divided by 11, the remainder is 1. So if we think of everything in terms of 10², we've got:

10�� =
(10²)²� * 10 =
1²� * 10

Now we'll add the 2, giving us

1 * 10 + 2

or 12. 12 divided by 11 has remainder 1, so we're done.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Wed Feb 01, 2017 5:35 pm
The trick to the approach above is finding a friendly remainder that allows you to greatly reduce the exponent that you're working with. As soon as we find a power of 10 that leaves remainder 1 or -1 when divided by 11, we're in business, and the remainder is a lot easier to tease out.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1