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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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20 Oct 2004, 07:55
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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 selected are consecutive integers
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20 Oct 2004, 10:25
I pick B.

1) Insufficient, since we don't know the numbers, some of the may have the same remainder.

2) Sufficient. Sum of remainders is always 21.
Examples:
1,2,3,4,5,6,7 => Sum of remainders=21.
6,7,8,9,10,11,12 => Sum of remainders=21.
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22 Oct 2004, 14:53
Hey guys, I think the answer is C

The questions states that each number is divided by 7.

So 1,2,3,4,5,6 divided by 7 does not give us remainders. Thats why I think B isnt sufficient.

With C, knowing from statement 1 that the remainders range from 0-6, the smallest number divisible by 7 is 7. So, 7,8,9,10,11,12,13 divided by 7 will all have remainders adding up to 21.

or 21,22,23,24,25,26,27 all will have remainders adding up to 21 when divided by 7.
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22 Oct 2004, 15:23
kingpin333 wrote:
Hey guys, I think the answer is C

The questions states that each number is divided by 7.

So 1,2,3,4,5,6 divided by 7 does not give us remainders. Thats why I think B isnt sufficient.

With C, knowing from statement 1 that the remainders range from 0-6, the smallest number divisible by 7 is 7. So, 7,8,9,10,11,12,13 divided by 7 will all have remainders adding up to 21.

or 21,22,23,24,25,26,27 all will have remainders adding up to 21 when divided by 7.

1,2,3,4,5,6 when divided by 7 does give reminders and they are 1,2,3,4,5,6.
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23 Oct 2004, 13:56
Agree with B.

Please note that it is OK since there are 7 consecutive integers which is the same as the divisor... with 7 consecutive and a divisor = 13 answer would have been C...
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24 Oct 2004, 01:09
"B" it is.

In any case, we will end up adding 1 to 6

cheers,
Dharmin
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24 Oct 2004, 02:33
add on to my previous post : I was thinking E in place of C...
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