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OG - 98 Data Sufficiency

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by batbond007 » Wed Dec 23, 2009 9:05 pm
Seven different numbers are selected from the integers 1 to 100, an each number is divided by 7. What is the sum of remainders?

1) The range of the seven remainders is 6.
2) The seven numbers selected are consecutive integers.

OA B

Are ppl really able to solve this q in 2 mins.
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by papgust » Wed Dec 23, 2009 9:45 pm
For any n consecutive integers, if they are divided by n, the remainders will range from 0 to (n-1).

Say, we have 7 numbers 1,2,3,4,5,6,7. When each is divided by 7, then remainders will be 1,2,3,4,5,6,0 respectively. Sum of remainders is 21.

Similarly, if we have numbers 10, 11, 12, 13, 14, 15, 16. When each is divided by 7, then remainders will be 3,4,5,6,0,1,2 respectively. Again, sum of remainders is 21.

Hence B is sufficient.
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by MBAorBust » Sat Dec 26, 2009 11:40 pm
As a general tip, usually when you are doing large calculations or doing something that would take way longer than 2 minutes, it means you are approaching the problem incorrectly. There has to be a simpler way to do it, so if it happens to me, I usually reread the problem and look for clues in the question.
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