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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] New post 01 Aug 2010, 09:39
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A
B
C
D
E

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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 remainders?
A) The range of the seven remainders is 6
B) The seven numbers selected are consecutive integers
[Reveal] Spoiler: OA
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Re: Number Properties [#permalink] New post 01 Aug 2010, 15:43
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Here is my attempt.


Statement A: The range only tells us the spread between the highest and the lowest. It is possible to have different values for remainders and still have the same range.

i.e., remainders could be 0,6,6,6,6,6 or 0,6, a, b, c, d, e with a, b, c, d and e being any integer between 0 and 6.

Hence statement A is insufficient

Statement B: Seven consecutive numbers would definitely have one number that is a multiple of 7 and other numbers would contribute a remainder that is less than 7.

Numbers could be 7x, 7x+1, 7x+2, ...... 7x+6

Hence statement B is sufficient.
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Re: Number Properties   [#permalink] 01 Aug 2010, 15:43
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Seven different numbers are selected from the integers 1 to

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