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Seven different numbers are selected from the integers 1 to [#permalink]
20 Oct 2004, 07:55

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

100% (01:29) correct
0% (00:00) wrong based on 7 sessions

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

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.

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. _________________

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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