Last visit was: 19 Jul 2025, 17:29 It is currently 19 Jul 2025, 17:29
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
555-605 Level|   Remainders|      
User avatar
LM
User avatar
Joined: 03 Sep 2006
Last visit: 04 Apr 2015
Posts: 445
Own Kudos:
7,481
 [22]
Given Kudos: 33
Posts: 445
Kudos: 7,481
 [22]
What is the value of length n<100 meter of wire? 24 Jan 2012, 10:01
3
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

69% (01:57) correct 31% (01:49) wrong based on 596 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of length n<100 meter of wire?

(1) When divided equal part of 10 meter each, a piece of 5 meter is left.

(2) When divided equal of 6 meter each, a piece of 1 meter is left.
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
742,792
 [14]
Given Kudos: 98,235
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
 [14]
What is the value of length n<100 meter of wire? 24 Jan 2012, 10:12
3
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
LM
What is the value of length n<100 meter of wire?

1) When divided equal part of 10 meter each, a piece of 5 meter is left.

2) When divided equal of 6 meter each, a piece of 1 meter is left.

What is the value of length n<100 meter of wire?

(1) When divided equal part of 10 meter each, a piece of 5 meter is left --> \(n=10q+5\): 5, 15, 25, ..., 95. Not sufficient.

(2) When divided equal of 6 meter each, a piece of 1 meter is left --> \(n=6p+1\): 1, 7, 13, 19, 25, ..., 97. Not sufficient.

(1)+(2) General formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\) would be \(n=30m+25\) --> \(n\) can be: 25, 55 or 85. Not sufficient.

Answer: E.

To elaborate more. How to derive general formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\): divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, \(n\) must be of a type \(n=30m+25\): 25, 55 or 85.

For more about this concept see:
manhattan-remainder-problem-93752.html#p721341
when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552
when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654

Hope it helps.
General Discussion
User avatar
Runner2
User avatar
Joined: 12 Nov 2011
Last visit: 26 Jul 2013
Posts: 43
Own Kudos:
109
Given Kudos: 24
Posts: 43
Kudos: 109
What is the value of length n<100 meter of wire? 25 Jan 2012, 10:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
clear explanation
User avatar
LM
User avatar
Joined: 03 Sep 2006
Last visit: 04 Apr 2015
Posts: 445
Own Kudos:
7,481
Given Kudos: 33
Posts: 445
Kudos: 7,481
What is the value of length n<100 meter of wire? 25 Jan 2012, 20:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
LM
What is the value of length n<100 meter of wire?

1) When divided equal part of 10 meter each, a piece of 5 meter is left.

2) When divided equal of 6 meter each, a piece of 1 meter is left.

What is the value of length n<100 meter of wire?

(1) When divided equal part of 10 meter each, a piece of 5 meter is left --> \(n=10q+5\): 5, 15, 25, ..., 95. Not sufficient.

(2) When divided equal of 6 meter each, a piece of 1 meter is left --> \(n=6p+1\): 1, 7, 13, 19, 25, ..., 97. Not sufficient.

(1)+(2) General formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\) would be \(n=30m+25\) --> \(n\) can be: 25, 55 or 85. Not sufficient.

Answer: E.

To elaborate more. How to derive general formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\): divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, \(n\) must be of a type \(n=30m+25\): 25, 55 or 85.

For more about this concept see:
manhattan-remainder-problem-93752.html#p721341
when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552
when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654

Hope it helps.

To elaborate more. How to derive general formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\): divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, \(n\) must be of a type \(n=30m+25\): 25, 55 or 85.

Thanks very much. Above would have been very difficult to figure out in the real exam.
User avatar
TGC
User avatar
Joined: 03 Aug 2012
Last visit: 19 Jul 2017
Posts: 581
Own Kudos:
3,492
Given Kudos: 322
Concentration: General Management, General Management
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE:Information Technology (Finance: Investment Banking)
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 2: 680 Q50 V32
Posts: 581
Kudos: 3,492
What is the value of length n<100 meter of wire? 11 Aug 2013, 09:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
N<100

What is N?

(1).

N =10A +5 ..... N can be 5,15,25,35 and so on

INSUFFICIENT

(2).

N= 6B + 1 .... N can be 1,7,13,19,25 and so on

INSUFFICIENT

Combining (1).& (2).

We get N = 30X + 25

N can be 25,55,85

Hence INSUFFICIENT

(E) it is !!
User avatar
smyarga
User avatar
Tutor
Joined: 20 Apr 2012
Last visit: 06 Aug 2020
Posts: 82
Own Kudos:
799
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Expert
Expert reply
GMAT 2: 730 Q51 V38
Posts: 82
Kudos: 799
What is the value of length n<100 meter of wire? 30 Jul 2014, 03:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Actually, this problem you can solve at most in 10 seconds:)

The main point here is that all numbers with exact remainder form arithmetic progression with difference=divisor.

For example, all x such that "when x is divided by 5 the remainder is 1" form arithmetic progression with first element 1 and difference 5:
1, 6, 11, 16, 21.....

If 50<x<100 for example, I can definitely say that there are several such x, because the distance between all such numbers is 5.

To solve this problem you need just to check if the divisor=(distance between numbers) large enough to have only 1 number inside interval.


So, I need to find exact number less than 100.
(1) The difference=divisor=10 is quite small for 100. Insufficient.
(2) The difference=divisor=6 is quite small for 100. Insufficient.

(1)+(2) The new difference=least common multiple of 10 and 6=30 is small for 100. Insufficient.

The correct answer is E


You don't really need here to write formula for x and first several values for each statement.
avatar
shreyast
avatar
Joined: 17 Feb 2015
Last visit: 03 Nov 2015
Posts: 23
Own Kudos:
107
Given Kudos: 13
GPA: 3
Products:
My Reviews
Posts: 23
Kudos: 107
What is the value of length n<100 meter of wire? 10 Mar 2015, 11:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
smyarga
Actually, this problem you can solve at most in 10 seconds:)

The main point here is that all numbers with exact remainder form arithmetic progression with difference=divisor.

For example, all x such that "when x is divided by 5 the remainder is 1" form arithmetic progression with first element 1 and difference 5:
1, 6, 11, 16, 21.....

If 50<x<100 for example, I can definitely say that there are several such x, because the distance between all such numbers is 5.

To solve this problem you need just to check if the divisor=(distance between numbers) large enough to have only 1 number inside interval.


So, I need to find exact number less than 100.
(1) The difference=divisor=10 is quite small for 100. Insufficient.
(2) The difference=divisor=6 is quite small for 100. Insufficient.

(1)+(2) The new difference=least common multiple of 10 and 6=30 is small for 100. Insufficient.

The correct answer is E


You don't really need here to write formula for x and first several values for each statement.

For (1)+(2), we need to know that the first number is 25. Only then we could say that this is insufficient. If the first number was >70, (1)+(2), could've been sufficient.
avatar
sudhirgupta93
avatar
Joined: 16 Mar 2016
Last visit: 29 Jan 2018
Posts: 60
Own Kudos:
16
Given Kudos: 112
Schools: Tuck '19
GMAT 1: 660 Q48 V33
GMAT 2: 710 Q50 V35
Schools: Tuck '19
GMAT 2: 710 Q50 V35
Posts: 60
Kudos: 16
What is the value of length n<100 meter of wire? 21 Jul 2016, 03:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LM
What is the value of length n<100 meter of wire?

(1) When divided equal part of 10 meter each, a piece of 5 meter is left.

(2) When divided equal of 6 meter each, a piece of 1 meter is left.

How about this?

n < 100 ----- (1)

S1- When divided equal part of 10 meter each, a piece of 5 meter is left.

implies n = 10k + 5, where k is some integer

10k + 5 < 100 (from 1)

solving k < 9.5 implies no unique solution for n as it can have multiple values. Therefore insufficient.

S2- When divided equal part of 6 meter each, a piece of 1 meter is left.

solving as above we get k < 16.5 which again means it is insufficient.

Even combining S1 and S2 we don't reach a definite solution. Hence answer is E.
User avatar
gracie
User avatar
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,035
Own Kudos:
1,862
Given Kudos: 27
Posts: 1,035
Kudos: 1,862
What is the value of length n<100 meter of wire? 24 Jan 2020, 11:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LM
What is the value of length n<100 meter of wire?

(1) When divided equal part of 10 meter each, a piece of 5 meter is left.

(2) When divided equal of 6 meter each, a piece of 1 meter is left.

n=10q+5
n=6p+1
→10q-6p=-4
least values of q and p are 2 and 4 respectively
substituting, least value of n=25
lcm of divisors 10 and 6=30
so 3 possible <100 meter values of n: 25, 55, 85
neither 1 nor 2 sufficient
E
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,451
Own Kudos:
1,013
Posts: 37,451
Kudos: 1,013
What is the value of length n<100 meter of wire? 15 Jan 2023, 07:17
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:
Bunuel
Math Expert
102627 posts
kingbucky
455 posts