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the sum of the remainders?

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the sum of the remainders?

by sanju09 » Mon Mar 12, 2012 2:46 am
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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by Anurag@Gurome » Mon Mar 12, 2012 5:44 am
sanju09 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) Let us assume that the numbers are 1, 2, 3, 4, 5, 6, 7. If we divide these by 7, then the remainders are 3, 6, 5, 2, 1, 4, and 0, whose sum is 21.

In case the numbers are 7, 14, 21, 28, 35, 42, 49, then the remainders are 0, so the sum of remainders is also 0.

We do not get a definite answer; NOT sufficient.

(2) Let us assume that the 1st number is x.
Then the 7 numbers will be x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6
Sum of the remainders = (x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6)/7 = (7x + 21)/7 = x + 3, which is fixed.
So, (2) is SUFFICIENT.

The correct answer is B.
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