Data Sufficiency

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.

magical cook 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.

1) We know the range, but we dont know what the individual nos are. So INSUFF.

2) Since the numbers selected are consecutive, the remainders will always be the sum of numbers from 1 to 6. So SUFF.

Answer is B. [/b]

Agree.. B

Sorry, I still think it's D...


for 1), 7 different numbers within 1-100 means the range of the 7 numbers 6? how about like 77, 22, 5, etc...

magical cook wrote:Sorry, I still think it's D...


for 1), 7 different numbers within 1-100 means the range of the 7 numbers 6? how about like 77, 22, 5, etc...

Hi, Can someone explain to me what does RANGE of 6 mean? TIA!

preciousrain7 wrote:

magical cook wrote:Sorry, I still think it's D...


for 1), 7 different numbers within 1-100 means the range of the 7 numbers 6? how about like 77, 22, 5, etc...

Hi, Can someone explain to me what does RANGE of 6 mean? TIA!

It means that the difference between the lowest and highest number is 6. The following sets of numbers all have a range of 6:

2, 3, 4, 5, 6, 7, 8
145, 147, 151
33, 33, 34, 35, 35.6, 37.5, 38, 39

As it applies to this problem, if the range of the remainder is 6 then the remainders have to be between 0 and 6, since you can't have a remainder of 7 or higher when dividing by 7. Knowing this is insufficient to give us the sum of the remainders because they could be 0, 0, 0, 0, 0, 0, 6 or 0, 6, 6, 6, 6, 6, 6, 6, which give us completely different sums.

Thanks - yeah range dose not mean equally aart.... so it must be B.

imo D. any further discussions?

gmatguy16 wrote:imo D. any further discussions?

How can it be D? It must be B.

One question though....what about the numbers from 1-6 (both inclusive)??

I mean: 1/7...what is the remainder?? I belive the remander is the number that is left before starting with the decimals, right?

cris wrote:One question though....what about the numbers from 1-6 (both inclusive)??

I mean: 1/7...what is the remainder?? I belive the remander is the number that is left before starting with the decimals, right?

If you take 1, 2, 3, 4, 5, 6, 7

1/7 > Remainder = 1, (7 x 0 = 0)

2/7 > Remainder = 2 ...and so on till 6

7/7 > Remainder = 0

So, we have Remainers are {1,2,3,4,5,6,0}, which will be the same as the set of remainders for any set of 7 consequtive 7 numbers.

sankruth wrote:

cris wrote:One question though....what about the numbers from 1-6 (both inclusive)??

I mean: 1/7...what is the remainder?? I belive the remander is the number that is left before starting with the decimals, right?

If you take 1, 2, 3, 4, 5, 6, 7

1/7 > Remainder = 1, (7 x 0 = 0)

2/7 > Remainder = 2 ...and so on till 6

7/7 > Remainder = 0

So, we have Remainers are {1,2,3,4,5,6,0}, which will be the same as the set of remainders for any set of 7 consequtive 7 numbers.

I think answer is D not B.

I go with the answer B.

Because the range of the remainders is 6 does not mean that all the remainders are completely different. there may be some remainders whihc are same or all remainders that are 6.

So A---- data insufficent

Hence I go with B.

Please correct me if I am wrong

i am sorry ,i incorrectly read the first statement as range of numbers instead of range of remainders, yes answer in that case should be b.

I think its D bcoz in the question stem it says that each number is divided by 7 (integers 1 - 100) and statment 1 says that remainder range shud b 6 so we can 7 numbers divide by 7 such that range is 6.

Any suggestions???