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# Seven different numbers are selected from the integers 1 to

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

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17 May 2008, 11:16
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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 eslected are consecutive integers
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17 May 2008, 12:03
puma 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 eslected are consecutive integers

The stem of the question makes no sense: "and each number is divided by 7. What is the sum of the remainders?"

Is it "each number is divisible by 7"? OR "What is the sum of the remainderswhen each number is divided by 7?"

If the latter is correct, B is the answer

statement 2: when each of the 7 consecutive integers is divided by 7, the sum of their remainders is 21
Suff

statement 1: you can have 6, 7, 14, 28, 35, 42, 49 --> sum of the remainders is 6
or 1, 2, 3, 4, 5, 6, 7 ---> sum of the remainders is 21
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17 May 2008, 16:35
I think D.

in 1), range of 6 from 7 different numbers means consecutive numbers. so no matter which 6 consecutive numbers you choose, the sum of remainders will always be 21.
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18 May 2008, 00:08
The question is correct and B is the OA
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08 Jun 2008, 07:44
The range of the seven remainders is 6 does not imply that the numbers are consecutive. It just implies that the difference between maximum value - minimum value is 6.

SO I think the answer should be C but OA isB. Not sure how - consecutive numbers does not mean the sum will always be 21!
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08 Jun 2008, 14:49
THe answer is B and can be explained as follows -

stmt 1 - Range is 6. but this only means the diff between smallest and largest numbers in the range. So I can have 2 ranges like - 9,10,11,12,13,14,15 or 9,9,9,9,9,9,15
so insuff

stmt 2 - All numbers are consecutive - hence the range will always have 7 numbers of which 1 is exactly divisible by 7 and the others will leave a remainder of 1 to 6. so the sum of remainders will always be 21.

so sufficient
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09 Jun 2008, 12:21
Great! Tnx for the explanation
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09 Jun 2008, 12:37
mandy12 wrote:
THe answer is B and can be explained as follows -

stmt 1 - Range is 6. but this only means the diff between smallest and largest numbers in the range. So I can have 2 ranges like - 9,10,11,12,13,14,15 or 9,9,9,9,9,9,15
so insuff

stmt 2 - All numbers are consecutive - hence the range will always have 7 numbers of which 1 is exactly divisible by 7 and the others will leave a remainder of 1 to 6. so the sum of remainders will always be 21.

so sufficient

No i think the OA is wrong, D should be..

The question clearly says 7 DIFFERENT numbers are selected...

we cannot therefore have 9999915 as a possibility..
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09 Jun 2008, 12:56
fresinha12 wrote:
mandy12 wrote:
THe answer is B and can be explained as follows -

stmt 1 - Range is 6. but this only means the diff between smallest and largest numbers in the range. So I can have 2 ranges like - 9,10,11,12,13,14,15 or 9,9,9,9,9,9,15
so insuff

stmt 2 - All numbers are consecutive - hence the range will always have 7 numbers of which 1 is exactly divisible by 7 and the others will leave a remainder of 1 to 6. so the sum of remainders will always be 21.

so sufficient

No i think the OA is wrong, D should be..

The question clearly says 7 DIFFERENT numbers are selected...

we cannot therefore have 9999915 as a possibility..

Even if the numbers are different ..u can still have a series like 7,14,21,28,35,42,49..here the sum of remainders will be 0..hence u can not say anything from stmnt A
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09 Jun 2008, 12:58
mandy12 wrote:
fresinha12 wrote:
mandy12 wrote:
THe answer is B and can be explained as follows -

stmt 1 - Range is 6. but this only means the diff between smallest and largest numbers in the range. So I can have 2 ranges like - 9,10,11,12,13,14,15 or 9,9,9,9,9,9,15
so insuff

stmt 2 - All numbers are consecutive - hence the range will always have 7 numbers of which 1 is exactly divisible by 7 and the others will leave a remainder of 1 to 6. so the sum of remainders will always be 21.

so sufficient

No i think the OA is wrong, D should be..

The question clearly says 7 DIFFERENT numbers are selected...

we cannot therefore have 9999915 as a possibility..

Even if the numbers are different ..u can still have a series like 7,14,21,28,35,42,49..here the sum of remainders will be 0..hence u can not say anything from stmnt A

you are correct but your numbers are wrong..i stand corrected

suppose
numbers are 6,8, 13, 27, 34, 41, 48, then you have the sum of remainders=6(5)+1

supposed numbers are 1,2,3,4,5,6,7 the sum of remainders is =1+2+3+4+5+6=21

B it is.
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09 Jun 2008, 13:16
puma 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 eslected are consecutive integers

Did anyone notice that statement 1 does NOT say "range of the seven numbers" but in fact says "range of the seven remainders"? This has huge significance, and essentially tells us NOTHING!!

If you divide any number by seven and get remainders, the only possibilities for remainders when dividing by 7 is 0 through 6! (exclamation, not factorial) If the range is 6, that's telling us what we already knew, or what we could already figure out. Because it tells us no additional information it's insufficient.

I agree, the stem says "different" so number repeats like 9,9,9 are not allowed.
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Manager Joined: 28 May 2008 Posts: 94 Followers: 2 Kudos [?]: 9 [0], given: 0 Re: DS: remainders [#permalink] ### Show Tags 09 Jun 2008, 22:25 jallenmorris wrote: puma 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 eslected are consecutive integers Did anyone notice that statement 1 does NOT say "range of the seven numbers" but in fact says "range of the seven remainders"? This has huge significance, and essentially tells us NOTHING!! If you divide any number by seven and get remainders, the only possibilities for remainders when dividing by 7 is 0 through 6! (exclamation, not factorial) If the range is 6, that's telling us what we already knew, or what we could already figure out. Because it tells us no additional information it's insufficient. I agree, the stem says "different" so number repeats like 9,9,9 are not allowed. Absolutely ! If the range of the remainders is 6 we could still have different numbers with the same remainder. 6,20,27 are all different but the remainder is 6 for all of them. so we cant determine the sum of Remainders . I will go with B Manager Joined: 11 Apr 2008 Posts: 155 Schools: Kellogg(A), Wharton(W), Columbia(D) Followers: 1 Kudos [?]: 65 [0], given: 0 Re: DS: remainders [#permalink] ### Show Tags 10 Jun 2008, 00:24 zeenie wrote: jallenmorris wrote: puma 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 eslected are consecutive integers Did anyone notice that statement 1 does NOT say "range of the seven numbers" but in fact says "range of the seven remainders"? This has huge significance, and essentially tells us NOTHING!! If you divide any number by seven and get remainders, the only possibilities for remainders when dividing by 7 is 0 through 6! (exclamation, not factorial) If the range is 6, that's telling us what we already knew, or what we could already figure out. Because it tells us no additional information it's insufficient. I agree, the stem says "different" so number repeats like 9,9,9 are not allowed. Absolutely ! If the range of the remainders is 6 we could still have different numbers with the same remainder. 6,20,27 are all different but the remainder is 6 for all of them. so we cant determine the sum of Remainders . I will go with B range of [0-6] ... all possible remainders inclusive of 0 and 6 is 7 isn't it? Neverthless, statement one shouldn't add much. So IMO B. SVP Joined: 30 Apr 2008 Posts: 1874 Location: Oklahoma City Schools: Hard Knocks Followers: 42 Kudos [?]: 590 [0], given: 32 Re: DS: remainders [#permalink] ### Show Tags 10 Jun 2008, 06:30 A remainder of 0 isn't really a remainder. It's like a bucket full of nothing. It's empty! _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Re: DS: remainders   [#permalink] 10 Jun 2008, 06:30
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