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7 different numbers selected

by money9111 » Tue Feb 09, 2010 1:36 am
Hello... I'm having some difficulty with this question... hope you can help:

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.

Standard Data Sufficiency Answer Choices.

OA B
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by papgust » Tue Feb 09, 2010 1:49 am
You just need to remember that when a number is divided by 'n', the maximum remainder that you could get is (n-1). Basically, remainders range from 0 to (n-1).

Here, the question asks for the sum of remainders. The seven integers could be any integer.

A. Range of seven remainders is 6.

Firstly, we don't know the seven integers. With this info, we could try some numbers.

Let's say the set of remainders are 0, 0, 0, 0, 0, 0, 6. Range is 6. Sum of Remainders is 6
Let's consider this set (0,1,2,3,4,5,6). Range is again 6. Sum of Remainders is 21

Insufficient.

B. Seven numbers are consecutive.

The remainders are going to be the same whatever consecutive numbers you are dividing by n (here 7). Let's try some numbers,

1,2,3,4,5,6,7 - Remainders when divided by 7 gives the same set of remainders (0 to 6). Sum of remainders is 21.
23,24,25,26,27,28,29 - Remainders when divided by 7 gives (2,3,4,5,6,0,1) respectively. Sum of remainders is 21.

Sufficient.
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by thephoenix » Tue Feb 09, 2010 2:09 am
money9111 wrote:Hello... I'm having some difficulty with this question... hope you can help:

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.

Standard Data Sufficiency Answer Choices.

OA B
s1) there can be various seven number for which sum is varying
insuff
s2)
let no be 2,3,4,5,6,7,8 rem are 2,3,4,5,6,0,1
sum=21
let another set of no's=20,21,22,23,24,25,26;rem r 6,0,1,2,3,4,5 sum=21
let another set of no's
43,44,45,46,47,48,49 rem r 1,2,3,4,5,6,0 aum=21
hence we can conclude that sum is 21
hence suff
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by sanju09 » Tue Feb 09, 2010 2:49 am
money9111 wrote:Hello... I'm having some difficulty with this question... hope you can help:

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.

Standard Data Sufficiency Answer Choices.

OA B
(1) There's no marvel if the range of those seven remainders is 6, when 7 is the divisor, 0 through 6 are the seven possible remainders whose range is 6. But one thing can be surely drawn out from it and that's that at least one integer is a multiple of 7 and that at least one integer is 1 less than a multiple of 7, from the seven different numbers that are to be selected from the integers 1 to 100. Other 5 remainders could take any value 0 through 6. Insufficient

(2) It works! When the seven numbers selected are consecutive integers, and then each one is divided by 7, irrespective of the fact that which one is the first, the seven remainders taken in order would include each integer 0 through 6 just once. Sufficient

[spoiler]B[/spoiler]
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by MBA » Sun Jul 03, 2011 4:56 am
Hi,

If we take 4,5,6,7,8,9,10(7 consecutive numbers) and divide each one by 7,we have remainders 3,2,1,0,1,2,3.The sum is not equal to 21 but is 12.Thus we can conclude that B is not sufficient.

can anyone explain,plz.

Thanks
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by sanju09 » Mon Jul 04, 2011 12:56 am
MBA wrote:Hi,

If we take 4,5,6,7,8,9,10(7 consecutive numbers) and divide each one by 7,we have remainders 3,2,1,0,1,2,3.The sum is not equal to 21 but is 12.Thus we can conclude that B is not sufficient.

can anyone explain,plz.

Thanks
But I believe that when 4,5,6,7,8,9,10 are divided by 7, the remainders are 4,5,6,0,1,2,3 respectively NOT 3,2,1,0,1,2,3, so please re-examine your work.
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