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B
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Difficulty:
45%
(medium)
Question Stats:
63% (01:21) correct
37%
(01:34)
wrong
based on 272
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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
22 Jul 2014, 14:35
Kudos
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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 \(0\leq{r}<d\), so in our case \(0\leq{r}<7\).
So the remainder upon division of any integer by 7 can be: 0, 1, 2, 3, 4, 5, or 6 (7 values).
(1) The range of the seven remainders is 6 --> 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 \(0\leq{r}<d\), so in our case \(0\leq{r}<7\).
So the remainder upon division of any integer by 7 can be: 0, 1, 2, 3, 4, 5, or 6 (7 values).
(1) The range of the seven remainders is 6 --> 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
General Discussion
07 Feb 2007, 06:29
Kudos
Bookmarks
Not sure how to approach it really...
Thinking to take: average=sum/#of terms
sum=average * # of terms
1) would be insufficient
2) from this we can say that the sum of the intergers is divisable by 7. So what?
I would guess E on the test day....
Thinking to take: average=sum/#of terms
sum=average * # of terms
1) would be insufficient
2) from this we can say that the sum of the intergers is divisable by 7. So what?
I would guess E on the test day....
