Last visit was: 20 Nov 2025, 04:53 It is currently 20 Nov 2025, 04:53
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
605-655 Level|   Remainders|      
User avatar
cebenez
User avatar
Joined: 10 Jun 2010
Last visit: 10 Mar 2012
Posts: 29
Own Kudos:
20
 [19]
Posts: 29
Kudos: 20
 [19]
Seven different numbers are selected from the integers 1 to 100, and Updated on: 19 Jun 2015, 00:31
Originally posted by cebenez on 22 Jun 2010, 19:02.
Last edited by Bunuel on 19 Jun 2015, 00:31, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

60% (01:15) correct 40% (01:38) wrong based on 550 sessions

History

Date
Time
Result
Not Attempted Yet
Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.

OPEN DISCUSSION OF THIS QUESTION IS HERE: seven-different-numbers-are-selected-from-the-integers-1-to-99943.html

Show Spoiler
Official Answer: B

But I think its E, let me tell you why.

(1) Range is 6, I believe when the range is 6, it means the numbers are consecutive. Can range be 6 if not consecutive, I do not think so.

Any set with a range of 6 starting with 3 would be have same sum of remainder but different sum of reminder if starting from 2 i.e for set 2 to 8 is different from set 3 to 9.

So -- Not sufficient.

(2) It says the set is consecutive numbers... Now we do not know the range.. but we know that any set of 7 consecutive numbers > 2 has to have a range of 6. So for the same reasons explained in (1) This is also not sufficient.

1 + 2 ) Together we still have the same info. What if the set starts with 2??? Remainders will be R5, R4, R3, R2, R1, R0, R1... right????

If it starts from 3 to 9... It would be R4, R3, R2, R1, R0, R1, R2

Sum of these remainders are different ... So I think E is the answer....but MGMAT says its B.

MGMT says, (1) is insufficient... but (2) is sufficient because any 7 consecutive nos will have sum of remainders = 21


Can someone explain?
ShowHide Answer
Official Answer
B
User avatar
AbhayPrasanna
User avatar
Joined: 04 May 2010
Last visit: 05 Jan 2025
Posts: 61
Own Kudos:
354
 [3]
Given Kudos: 7
GPA: 3.8
WE 1: 2 yrs - Oilfield Service
Products:
My Reviews
Posts: 61
Kudos: 354
 [3]
Seven different numbers are selected from the integers 1 to 100, and 22 Jun 2010, 21:37
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the sum of the remainders?

1. The range is 6. This actually only means that the highest remainder - lowest remainder is 6
Thus the set could consist of numbers that yield the remainders {0,0,6,6,6,6,6} OR {0,3,4,5,6,6,6} etc. The sum will be different depending on the actual contents of the set. INSUFFICIENT

2. They are consecutive integers. Your example has a few flaws in it:
For 3 to 9 : 3 has a quotient of zero and a remainder of 3
4 has a quotient of zero and a remainder of 4
And so on, yielding remainders {3,4,5,6,0,1,2} TOTAL = 21

For 2 to 8 : The remainders are {2,3,4,5,6,0,1} TOTAL = 21

SUFFICIENT

Pick B.
User avatar
cebenez
User avatar
Joined: 10 Jun 2010
Last visit: 10 Mar 2012
Posts: 29
Own Kudos:
20
Posts: 29
Kudos: 20
Seven different numbers are selected from the integers 1 to 100, and 22 Jun 2010, 23:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AbhayPrasanna, thanks a lot.

yes you are right. (1) says the range of remainders = 6... I was reading as the range of the set = 6...

(2) yes you are right.. I made some mistake on calculating the remainders... you are right.

Thanks a lot. I am getting a bit nervous, today I have been quite a lot of mistakes, because am not reading the question right. !!! what's happening to me !!!
User avatar
praveenism
User avatar
Joined: 28 Feb 2010
Last visit: 12 Dec 2016
Posts: 82
Own Kudos:
134
Given Kudos: 33
GPA: 8.13
WE 1: 3 (Mining Operations)
Posts: 82
Kudos: 134
Seven different numbers are selected from the integers 1 to 100, and 24 Jun 2010, 02:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ya..its B..
@ cebenez: You dont need to panic..Sometimes it happens that the logic goes haywire....
Just ensure...its not happening on regular basis...:)
User avatar
whiplash2411
User avatar
Joined: 09 Jun 2010
Last visit: 02 Mar 2015
Posts: 1,761
Own Kudos:
3,578
Given Kudos: 210
Status:Three Down.
Concentration: General Management, Nonprofit
Schools: HBS '17 (M) Stanford '17 (A)
Schools: HBS '17 (M) Stanford '17 (A)
Posts: 1,761
Kudos: 3,578
Seven different numbers are selected from the integers 1 to 100, and 24 Jun 2010, 13:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer is B. Here's my explanation.

1. Range is 6.

This statement is insufficient as you can have a range of numbers with six as follows;

{0,0,0,0,0,1,6} or {0,3,4,4,5,5,6}

Range is the difference between the largest and smallest number but that doesn't say anything.

So now we're down to options B,C or E

2. Consecutive numbers.

Since we are choosing 7 consecutive numbers, one of it must be a multiple of 7. So, let's assume its the first number for convenience sake. You can draw a table as follows:

Number Reminder
x - 0
x+1 - 1
x+2 - 2
x+3 - 3
x+4 - 4
x+5 - 5
x+6 - 6

So now you can find out what's asked for.

Hence answer is B.



cebenez
Question 98 Data Sufficiency Official Guide

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7.
What is the sum of the remainders?

(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.


Official Answer: B

But I think its E, let me tell you why.

(1) Range is 6, I believe when the range is 6, it means the numbers are consecutive. Can range be 6 if not consecutive, I do not think so.

Any set with a range of 6 starting with 3 would be have same sum of remainder but different sum of reminder if starting from 2 i.e for set 2 to 8 is different from set 3 to 9.

So -- Not sufficient.

(2) It says the set is consecutive numbers... Now we do not know the range.. but we know that any set of 7 consecutive numbers > 2 has to have a range of 6. So for the same reasons explained in (1) This is also not sufficient.

1 + 2 ) Together we still have the same info. What if the set starts with 2??? Remainders will be R5, R4, R3, R2, R1, R0, R1... right????

If it starts from 3 to 9... It would be R4, R3, R2, R1, R0, R1, R2

Sum of these remainders are different ... So I think E is the answer....but MGMAT says its B.

MGMT says, (1) is insufficient... but (2) is sufficient because any 7 consecutive nos will have sum of remainders = 21


Can someone explain?
Show more
User avatar
sk818020
User avatar
Joined: 24 Mar 2010
Last visit: 15 Sep 2011
Posts: 38
Own Kudos:
77
Given Kudos: 3
Posts: 38
Kudos: 77
Seven different numbers are selected from the integers 1 to 100, and 24 Jun 2010, 18:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Just a quick note that I thought of when looking at the problem.

(1) is actually something we already know given the question. The range of the remainder of any number divided by 7 is going to be 6. The remainder of any number divided by seven will be between 0-6. A remainder of 7 or more would need to be adjusted so that the appropriate number is added to the quotient leaving only a remainder that within the range of 0-6.

If you caught this you can quickly dismiss (1) as redundant information and move on to (2). This can save time for those of you who tried to go about (1) by testing numbers or doing other mathematical exercises.

Hope this helps.

Thanks,

Jared
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,414
Own Kudos:
778,486
 [1]
Given Kudos: 99,987
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: 105,414
Kudos: 778,486
 [1]
Seven different numbers are selected from the integers 1 to 100, and 19 Jun 2015, 00:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

The trick here is to know that remainder is always non-negative integer less than divisor \(0\leq{r}<d\), so in our case \(0\leq{r}<7\).

So the remainder upon division of any integer by 7 can be: 0, 1, 2, 3, 4, 5, or 6 (7 values).

(1) The range of the seven remainders is 6 --> if we pick 6 different multiples of 7 (all remainders 0) and the 7th number 6 (remainder 6) then the range would be 6 and the sum also 6. But if we pick 7 consecutive integers then we'll have all possible remainders: 0, 1, 2, 3, 4, 5, and 6 and their sum will be 21. Not sufficient.

(2) The seven numbers selected are consecutive integers --> ANY 7 consecutive integers will give us all remainders possible: 0, 1, 2, 3, 4, 5, and 6. It does not matter what the starting integer will be: if it's say 11 then the remainder of 7 consecutive integers from 11 divided by 7 will be: 4, 5, 6, 0, 1, 2, and 3 and if starting number is say 14 then the remainder of 7 consecutive integers from 14 divided by 7 will be: 0, 1, 2, 3, 4, 5 and 6. So in any case sum=0+1+2+3+4+5+6=21. Sufficient.

Answer: B.

Similar questions to practice:
n-consecutive-integers-are-selected-from-the-integers-131349.html
seven-integers-x1-x2-x3-x4-x5-x6-and-x7-are-picked-73611.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: seven-different-numbers-are-selected-from-the-integers-1-to-99943.html
Moderators:
Bunuel
Math Expert
105414 posts
kingbucky
496 posts