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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

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

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

Re: Seven different numbers are selected from the integers 1 to [#permalink]
22 Jul 2014, 13:35

Expert's 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.