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# Seven different numbers are selected from the integers 1 to

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Seven different numbers are selected from the integers 1 to [#permalink]  12 Jan 2008, 04:37
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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Re: consecutive integers - remainders [#permalink]  12 Jan 2008, 04:54
marcodonzelli 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.

I think it is C
if we know that integers are consecutive (II), so remainders should be consecutive too(I am sure about that) so 6+5+4+3+2+1+0=21

Last edited by kbulse on 12 Jan 2008, 05:04, edited 1 time in total.
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Re: consecutive integers - remainders [#permalink]  12 Jan 2008, 04:59
I think it is B.

st 2. 7 consequitive integers means one of them will definetly divide by 7 evenly. so 0+1+2+3+4+5+6 will be a solution. suff
st 1. does not imply integers are consequitive. insuff
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Re: consecutive integers - remainders [#permalink]  12 Jan 2008, 06:53
CaspAreaGuy wrote:
I think it is B.

st 2. 7 consequitive integers means one of them will definetly divide by 7 evenly. so 0+1+2+3+4+5+6 will be a solution. suff
st 1. does not imply integers are consequitive. insuff

B states that integers are consecutive...remainders are 1,2,3,4,5,6. we can sum them...OA is B
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Re: consecutive integers - remainders [#permalink]  13 Jan 2008, 18:20
i think its E.

why cant the remainders also be 6+7+8+9+10+11+12
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Re: consecutive integers - remainders [#permalink]  13 Jan 2008, 19:24
The answer is E Statement 1: Range is 6. That means if nos are X1 to X7, then X7-X1=6
Not sufficient
Statement 2: Nos. are consecutive integers. Insufficient to give sum of reminders.
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Re: consecutive integers - remainders [#permalink]  13 Jan 2008, 23:40
akhi wrote:
The answer is E Statement 1: Range is 6. That means if nos are X1 to X7, then X7-X1=6
Not sufficient
Statement 2: Nos. are consecutive integers. Insufficient to give sum of reminders.

OA is B guys...source GMAT Prep
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Re: consecutive integers - remainders [#permalink]  14 Jan 2008, 02:10
marcodonzelli 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.

B.

Stat 1: Doesn't tell us anything. Remainders could be 0,0,0,0,0,0,6 or 0,0,2,3,4,5,6; Insuff.
Stat 2: If the numbers are consecutive then the remainders have to be 1,2,3,4,5,6,0 in this order or some other. Regardless, sum will always be the same. Suff.
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Re: consecutive integers - remainders [#permalink]  14 Jan 2008, 07:38
B
remainders of n consecutive nos divided by n will be 0,1,2,....n-1,n-1.
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Re: consecutive integers - remainders [#permalink]  15 Jan 2008, 23:55
marcodonzelli 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.

B.

S1: no help here.

S2: try any set of consecutive integers. 1,2,3,4,5,6,7 remainders are 1,2,3,4,5,6,0

Try another set 19,20,21,22,23,24,25 --> R: 5,6,0,1,2,3,4 remainders will always be these.

Suff.
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Re: consecutive integers - remainders [#permalink]  16 Jan 2008, 20:08
singaks wrote:
i think its E.

why cant the remainders also be 6+7+8+9+10+11+12

singaks,
Remainder cannot be greater than the denominator.
For example 45/7 . Reminder is 3.
45=7*6+3.
You can also put 45 as 7*5 +10 . But notice 10 can still be expressed as 7*1+3.

Remainder by definition is difference between numerator and product of divisor and largest possible multiple.

Hope this helps.
Re: consecutive integers - remainders   [#permalink] 16 Jan 2008, 20:08
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# Seven different numbers are selected from the integers 1 to

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