Last visit was: 17 Jul 2025, 10:53 It is currently 17 Jul 2025, 10:53
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,603
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,603
Kudos: 742,233
 [11]
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,116
 [4]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,116
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 2,052
Own Kudos:
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
Posts: 2,052
Kudos: 9,701
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 17 Jul 2025
Posts: 21,133
Own Kudos:
26,186
 [1]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,133
Kudos: 26,186
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5?

A. 3
B. 4
C. 5
D. 6
E. 7


Of all the 2-digit numbers that have a remainder of 1 when divided by 10, only 11, 11 + LCM(6, 10) = 11 + 30 = 41, and 41 + 30 = 71, when divided by 6, yield a remainder of 5.

Answer: A
User avatar
David nguyen
Joined: 15 May 2017
Last visit: 18 Aug 2020
Posts: 139
Own Kudos:
Given Kudos: 132
Status:Discipline & Consistency always beats talent
Location: United States (CA)
GPA: 3.59
WE:Sales (Retail: E-commerce)
Posts: 139
Kudos: 135
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ScottTargetTestPrep
Bunuel
How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5?

A. 3
B. 4
C. 5
D. 6
E. 7


Of all the 2-digit numbers that have a remainder of 1 when divided by 10, only 11, 11 + GCF(6, 10) = 11 + 30 = 41, and 41 + 30 = 71, when divided by 6, yield a remainder of 5.

Answer: A

Isn’t GCF(6,10) 2 how did you get to 30?

I tried the n=24x + …. But I can’t find the value of …
Could someone please advise? Thanks
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 17 Jul 2025
Posts: 21,133
Own Kudos:
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,133
Kudos: 26,186
Kudos
Add Kudos
Bookmarks
Bookmark this Post
David nguyen
ScottTargetTestPrep
Bunuel
How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5?

A. 3
B. 4
C. 5
D. 6
E. 7


Of all the 2-digit numbers that have a remainder of 1 when divided by 10, only 11, 11 + GCF(6, 10) = 11 + 30 = 41, and 41 + 30 = 71, when divided by 6, yield a remainder of 5.

Answer: A

Isn’t GCF(6,10) 2 how did you get to 30?

I tried the n=24x + …. But I can’t find the value of …
Could someone please advise? Thanks

We actually meant LCM(6, 10) instead of GCD(6, 10); you're absolutely right that GCD(6, 10) is 2. Thanks for pointing it out.

If the "n" in your equation represents a two digit number that produces a remainder of 1 when divided by 10 and a remainder of 5 when divided by 6; I don't think you'll be able to find the numbers using any equation of the sort n = 24x + ... You can proceed as follows in order to find the numbers that way:

Since n produces a remainder of 1 when divided by 10, n = 10k + 1 for some k.

Since n produces a remainder of 5 when divided by 6, n = 6s + 5 for some s.

Let's add 19 to each equation:

n + 19 = 10k + 20

n + 19 = 6s + 24

Notice that 10k + 20 is divisible by 10 and 6s + 24 is divisible by 6. Since n + 19 is both divisible by 10 and by 6, n + 19 must be divisible by the LCM of 10 and 6, which is 30. Thus, the smallest possible value of n + 19 is 30; which yields the smallest possible value of n is 30 - 19 = 11.

Once we find the smallest possible value of n, we can just add LCM of 6 and 10 to find other two digit numbers which satisfy the requirements of the question; the numbers are 11, 11 + 30 = 41 and 41 + 30 = 71.
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 17 July 2025
Posts: 2,247
Own Kudos:
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,247
Kudos: 2,465
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We need to find the total number of two-digit numbers whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5

Let's solve the problem using two methods

Let n be the two digit number which gives 1 remainder when divided by 10 and 5 remainder when divided by 6

Dividend = Divisor * Quotient + Remainder
n when divided by 10 gives 1 remainder
Dividend = n
Divisor = 10
Quotient = a (Assume)
Remainder = 1
=> n = 10a + 1 ...(1)

n when divided by 6 gives 5 remainder
Dividend = n
Divisor = 6
Quotient = b (Assume)
Remainder = 5
=> n = 6b + 5 ...(2)

Method 1: Writing Values

n = 10a + 1 [ From (1) ]
Putting a = 1, 2,... we get values of n as
n = 11, 21, 31, 41, ...., 91 (we need to consider only two digit values)

n = 6b + 5 [ From (2) ]
Putting b = 1, 2,... we get values of n as
n = 11, 17, 23, 29, ...., 95 (we need to consider only two digit values)
For common values we need unit's digit to be 1
=> units' digit of 6b + 5 = 1
=> units' digit of 6b = 11-5 = 6
This will happen when b = 1, 6, 11, 16,
=> n = 6b + 5 = 11 (for b=1)
n = 41 (for b=6)
n = 71 (for b=11)
n = 101 (for b= 16.. but we need only two digit values of n)

=> Common values of n in both the cases is 11, 41 and 71
=> 3 values

Method 2: Algebra

n = 10a + 1 [ From (1) ] and n = 6b + 5 [ From (2) ]
=> 10a + 1 = 6b + 5
=> 10a = 6b + 4
=> a = \(\frac{6b+4}{10}\)
Now, only those values of "b" which also make "a" an integer will give us common values of n in both the cases

=> 6b + 4 has to be a multiple of 10
=> unit's digit of 6b = 10-4 = 6
=> b = 1, 6, 11 (As shown above)

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Remainders

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,437
Own Kudos:
Posts: 37,437
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102603 posts
PS Forum Moderator
697 posts