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01 Aug 2010, 10:39
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B
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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.
OPEN DISCUSSION OF THIS QUESTION IS HERE: seven-different-numbers-are-selected-from-the-integers-1-to-99943.html
(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.
OPEN DISCUSSION OF THIS QUESTION IS HERE: seven-different-numbers-are-selected-from-the-integers-1-to-99943.html
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01 Aug 2010, 16:43
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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.
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.
14 Aug 2017, 02:07
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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?
The trick here is to know that remainder is always non-negative integer less than divisor [m]0\leq{r} if we pick 6 different multiples of 7 (all remainders 0) and the 7th number 6 (remainder 6) then the range would be 6 and the sum also 6. But if we pick 7 consecutive integers then we'll have all possible remainders: 0, 1, 2, 3, 4, 5, and 6 and their sum will be 21. Not sufficient.
(2) The seven numbers selected are consecutive integers --> ANY 7 consecutive integers will give us all remainders possible: 0, 1, 2, 3, 4, 5, and 6. It does not matter what the starting integer will be: if it's say 11 then the remainder of 7 consecutive integers from 11 divided by 7 will be: 4, 5, 6, 0, 1, 2, and 3 and if starting number is say 14 then the remainder of 7 consecutive integers from 14 divided by 7 will be: 0, 1, 2, 3, 4, 5 and 6. So in any case sum=0+1+2+3+4+5+6=21. Sufficient.
Answer: B.
Similar questions to practice:
n-consecutive-integers-are-selected-from-the-integers-131349.html
seven-integers-x1-x2-x3-x4-x5-x6-and-x7-are-picked-73611.html
OPEN DISCUSSION OF THIS QUESTION IS HERE: seven-different-numbers-are-selected-from-the-integers-1-to-99943.html
The trick here is to know that remainder is always non-negative integer less than divisor [m]0\leq{r} if we pick 6 different multiples of 7 (all remainders 0) and the 7th number 6 (remainder 6) then the range would be 6 and the sum also 6. But if we pick 7 consecutive integers then we'll have all possible remainders: 0, 1, 2, 3, 4, 5, and 6 and their sum will be 21. Not sufficient.
(2) The seven numbers selected are consecutive integers --> ANY 7 consecutive integers will give us all remainders possible: 0, 1, 2, 3, 4, 5, and 6. It does not matter what the starting integer will be: if it's say 11 then the remainder of 7 consecutive integers from 11 divided by 7 will be: 4, 5, 6, 0, 1, 2, and 3 and if starting number is say 14 then the remainder of 7 consecutive integers from 14 divided by 7 will be: 0, 1, 2, 3, 4, 5 and 6. So in any case sum=0+1+2+3+4+5+6=21. Sufficient.
Answer: B.
Similar questions to practice:
n-consecutive-integers-are-selected-from-the-integers-131349.html
seven-integers-x1-x2-x3-x4-x5-x6-and-x7-are-picked-73611.html
OPEN DISCUSSION OF THIS QUESTION IS HERE: seven-different-numbers-are-selected-from-the-integers-1-to-99943.html
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
