Seven different numbers are selected from the integers 1 to : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 21 Feb 2017, 22:51

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Seven different numbers are selected from the integers 1 to

Author Message
TAGS:

### Hide Tags

Director
Affiliations: FRM Charter holder
Joined: 02 Dec 2006
Posts: 734
Schools: Stanford, Chicago Booth, Babson College
Followers: 16

Kudos [?]: 81 [0], given: 4

Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

07 Feb 2007, 05:04
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:59) correct 48% (00:59) wrong based on 132 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Jul 2014, 13:34, edited 1 time in total.
Edited the question and added the OA.
Director
Joined: 05 Feb 2006
Posts: 898
Followers: 3

Kudos [?]: 108 [0], given: 0

Re: Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

07 Feb 2007, 05:29
Not sure how to approach it really...

Thinking to take: average=sum/#of terms
sum=average * # of terms

1) would be insufficient

2) from this we can say that the sum of the intergers is divisable by 7. So what?

I would guess E on the test day....
Intern
Joined: 13 Jun 2005
Posts: 28
Followers: 0

Kudos [?]: 37 [2] , given: 0

Re: Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

07 Feb 2007, 07:15
2
KUDOS
7 different integers between 1 and 100

(1) Range of remainders is 6

1,2,3,4,5,6,7 each div by 7 is 0,1,2,3,4,5,6 -> sum = 21
But 7,14,21,28,35,49,55 --0,0,0,0,0,0,6 -> sum = 6

(insuff)

(2) If they are consecutive.

1,2,3,4,5,6,7. Sum of remainders when each is divided by 7 = 1+2+3+4+5+6+0 =21

or 2,3,4,5,6,7,8 or 49,50,51,52,53,54,55, any consecutive combination of 7 numbers..they all turn upto be 21
Ans (B) , what is the OA
Senior Manager
Joined: 04 Jan 2006
Posts: 279
Followers: 1

Kudos [?]: 38 [0], given: 0

Re: Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

07 Feb 2007, 07:25
aurobindo wrote:
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.

Question: Seven number are selected: n1, ..., n7, Each divided by 7, What is the sum of the remainders?

Info(1): All remainders of number divided by 7 will be less than 7. INSUFF

Info(2): Assuming n, n+1, n+2, ..., n+6

Dividing by 7: = (1/7) x (n, n+1, ..., n+6) = (1/7) x (7n + (1+2+3+4+5+6))
= 7n/7 + (21/7) = n+3
The sum of the remainders = 3

Manager
Joined: 10 Dec 2005
Posts: 112
Followers: 1

Kudos [?]: 4 [0], given: 0

Re: Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

07 Feb 2007, 08:55
aurobindo wrote:
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.

Condition 1:

Let's say we take 1,2,3,4,5,6,7 divide this by 7 then the remainders are
3,6,2,5,1,4,0 = 21... If we pick some different numbers like...

7,14,21,28,35,42,49 the remainders are 0 and hence the sum = 0

So condition 1 is insufficient.

Condition 2:

let say the first number is n
7 consecutive numbers are n, n+1,..,n+6

sum of remainder = (n + n+1 + n+2 + n+3 + n+4 + n+5 + n+6)/7
= (7n + 21)/7 = n+3

Therefore condition 2 is sufficient. Answer B
_________________

"Live as if you were to die tomorrow. Learn as if you were to live forever." - Mahatma Gandhi

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13904
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

22 Jul 2014, 13:05
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37063
Followers: 7241

Kudos [?]: 96266 [1] , given: 10729

Re: Seven different numbers are selected from the integers 1 to [#permalink]

### Show Tags

22 Jul 2014, 13:35
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.

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
_________________
Re: Seven different numbers are selected from the integers 1 to   [#permalink] 22 Jul 2014, 13:35
Similar topics Replies Last post
Similar
Topics:
2 One number, n, is selected at random from a set of 10 intege 3 05 May 2013, 21:20
18 Eight consecutive integers are selected from the integers 1 10 06 Nov 2012, 18:05
10 Seven different numbers are selected from the integers 1 to 6 28 Aug 2010, 01:58
1 Seven different numbers are selected from the integers 1 to 1 01 Aug 2010, 09:39
4 Seven different numbers are selected from the integers 1 to 100, and 7 22 Jun 2010, 18:02
Display posts from previous: Sort by