Last visit was: 29 Apr 2026, 02:33 It is currently 29 Apr 2026, 02:33
Home
Messages
Tests
Schools
Events
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Russ19
User avatar
Joined: 29 Oct 2019
Last visit: 18 Mar 2026
Posts: 1,339
Own Kudos:
1,987
 [4]
Given Kudos: 582
Posts: 1,339
Kudos: 1,987
 [4]
When 10^{60} – m, where m is a two-digit positive integer, written in 21 Oct 2021, 06:16
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

15% (02:37) correct 85% (02:43) wrong based on 67 sessions

History

Date
Time
Result
Not Attempted Yet
When \(10^{60} – m\), where \(m\) is a two-digit positive integer, written in the decimal notation, the sum of the digits of the resulting number is 533. How many distinct values of \(m\) exist?

(A)5

(B) 6

(C) 7

(D) 8

(E) 9
ShowHide Answer
Official Answer
C
User avatar
Gaurav2896
User avatar
Joined: 27 Sep 2020
Last visit: 04 May 2024
Posts: 56
Own Kudos:
27
 [1]
Given Kudos: 52
GMAT 1: 730 Q50 V39
Products:
My Reviews
GMAT 1: 730 Q50 V39
Posts: 56
Kudos: 27
 [1]
When 10^{60} – m, where m is a two-digit positive integer, written in 21 Oct 2021, 06:59
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi sjuniv32 is the answer C? Can you confirm once , i got D ->
sum in 10^60-m = 9*58 + (a+b)
=>522 + a+b
so a+b = 11.
So a and b can be (2,9), (3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2). For all these 8 terms m will be distinct .So answer should be 8.
IMO D. Help if i have done some mistake.
avatar
Krutak
avatar
Current Student
Joined: 14 Jun 2020
Last visit: 25 Nov 2022
Posts: 5
Own Kudos:
2
Given Kudos: 6
Location: India
Schools: DeGroote (A)
GMAT 1: 650 Q47 V32
Schools: DeGroote (A)
GMAT 1: 650 Q47 V32
Posts: 5
Kudos: 2
When 10^{60} – m, where m is a two-digit positive integer, written in 21 Oct 2021, 08:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(9,2) will not be possible as 2 digit number is being subtracted.
m = two digit number

Posted from my mobile device
avatar
Bogei
avatar
Joined: 26 Jan 2020
Last visit: 23 Dec 2025
Posts: 4
Own Kudos:
4
 [2]
Given Kudos: 1
GMAT 1: 650 Q48 V31
GMAT 2: 730 Q50 V39
WE:Human Resources (Human Resources)
GMAT 2: 730 Q50 V39
Posts: 4
Kudos: 4
 [2]
When 10^{60} – m, where m is a two-digit positive integer, written in 21 Oct 2021, 08:44
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi there, still fairly new posting reply so please excuse the format:

Our goal is to find all m's such that sum of the digits of \(10^{60} - m = 533\)

For a simpler case: Let's assume \(m = 99 \) and \(10^4\) instead of \(10^{60}\); \(10^4- m\) we would have \(10000-99 = 9901\),

From that we can see for every n in \(10^n\), we will have at least \(n-2\) 9's (in our case \(n = 4 \) and number of 9's is \(n-2\))

so for \(10^{60} \) we would have 58 9's and the sum of digits so far would be \( (58 * 9) = 522,\) we are still missing \(533-522 = 11.\)

Keep in mind we are not looking for all m's such that the digits of m add up to 11, we are looking for all m's such that the digits of \(100-m\) is 11. (Observe that I'm using 100 here since we are only concerned with the last 2 digits of the sum that add up to 11, the rest are all 9's as stated above)

so we need the sum of digits of \(100-m\) equal to 11, m could be

\(m = 17 -> 100 - 17 = 83, 8+3=11\)
\(m = 26 -> 100 - 26 = 74, 7+4 =11\), and so on. Also observe the reverse of the digits also works (e,g 71, 62)

in the end we have 7 cases (17, 26, 35, 44, 53, 62, 71). Answer is C
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,982
Own Kudos:
1,119
Posts: 38,982
Kudos: 1,119
When 10^{60} – m, where m is a two-digit positive integer, written in 25 Aug 2024, 13:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109963 posts
Krunaal
Tuck School Moderator
852 posts