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# Seven different numbers are selected from the integers 1

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Seven different numbers are selected from the integers 1 [#permalink]  22 Jun 2010, 18:02
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100% (01:37) correct 0% (00:00) wrong based on 1 sessions
Question 98 Data Sufficiency Official Guide

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.

But I think its E, let me tell you why.

(1) Range is 6, I believe when the range is 6, it means the numbers are consecutive. Can range be 6 if not consecutive, I do not think so.

Any set with a range of 6 starting with 3 would be have same sum of remainder but different sum of reminder if starting from 2 i.e for set 2 to 8 is different from set 3 to 9.

So -- Not sufficient.

(2) It says the set is consecutive numbers... Now we do not know the range.. but we know that any set of 7 consecutive numbers > 2 has to have a range of 6. So for the same reasons explained in (1) This is also not sufficient.

1 + 2 ) Together we still have the same info. What if the set starts with 2??? Remainders will be R5, R4, R3, R2, R1, R0, R1... right????

If it starts from 3 to 9... It would be R4, R3, R2, R1, R0, R1, R2

Sum of these remainders are different ... So I think E is the answer....but MGMAT says its B.

MGMT says, (1) is insufficient... but (2) is sufficient because any 7 consecutive nos will have sum of remainders = 21

Can someone explain?
[Reveal] Spoiler: OA
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Re: OG - DS - Q98 - I think OG & MGMAT are Wrong. [#permalink]  22 Jun 2010, 20:37
What is the sum of the remainders?

1. The range is 6. This actually only means that the highest remainder - lowest remainder is 6
Thus the set could consist of numbers that yield the remainders {0,0,6,6,6,6,6} OR {0,3,4,5,6,6,6} etc. The sum will be different depending on the actual contents of the set. INSUFFICIENT

2. They are consecutive integers. Your example has a few flaws in it:
For 3 to 9 : 3 has a quotient of zero and a remainder of 3
4 has a quotient of zero and a remainder of 4

And so on, yielding remainders {3,4,5,6,0,1,2} TOTAL = 21

For 2 to 8 : The remainders are {2,3,4,5,6,0,1} TOTAL = 21

SUFFICIENT

Pick B.
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Re: OG - DS - Q98 - I think OG & MGMAT are Wrong. [#permalink]  22 Jun 2010, 22:17
AbhayPrasanna, thanks a lot.

yes you are right. (1) says the range of remainders = 6... I was reading as the range of the set = 6...

(2) yes you are right.. I made some mistake on calculating the remainders... you are right.

Thanks a lot. I am getting a bit nervous, today I have been quite a lot of mistakes, because am not reading the question right. !!! what's happening to me !!!
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Re: OG - DS - Q98 - I think OG & MGMAT are Wrong. [#permalink]  24 Jun 2010, 01:42
Ya..its B..
@ cebenez: You dont need to panic..Sometimes it happens that the logic goes haywire....
Just ensure...its not happening on regular basis...
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Re: OG - DS - Q98 - I think OG & MGMAT are Wrong. [#permalink]  24 Jun 2010, 12:27
Expert's post
Answer is B. Here's my explanation.

1. Range is 6.

This statement is insufficient as you can have a range of numbers with six as follows;

{0,0,0,0,0,1,6} or {0,3,4,4,5,5,6}

Range is the difference between the largest and smallest number but that doesn't say anything.

So now we're down to options B,C or E

2. Consecutive numbers.

Since we are choosing 7 consecutive numbers, one of it must be a multiple of 7. So, let's assume its the first number for convenience sake. You can draw a table as follows:

Number Reminder
x - 0
x+1 - 1
x+2 - 2
x+3 - 3
x+4 - 4
x+5 - 5
x+6 - 6

So now you can find out what's asked for.

cebenez wrote:
Question 98 Data Sufficiency Official Guide

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.

But I think its E, let me tell you why.

(1) Range is 6, I believe when the range is 6, it means the numbers are consecutive. Can range be 6 if not consecutive, I do not think so.

Any set with a range of 6 starting with 3 would be have same sum of remainder but different sum of reminder if starting from 2 i.e for set 2 to 8 is different from set 3 to 9.

So -- Not sufficient.

(2) It says the set is consecutive numbers... Now we do not know the range.. but we know that any set of 7 consecutive numbers > 2 has to have a range of 6. So for the same reasons explained in (1) This is also not sufficient.

1 + 2 ) Together we still have the same info. What if the set starts with 2??? Remainders will be R5, R4, R3, R2, R1, R0, R1... right????

If it starts from 3 to 9... It would be R4, R3, R2, R1, R0, R1, R2

Sum of these remainders are different ... So I think E is the answer....but MGMAT says its B.

MGMT says, (1) is insufficient... but (2) is sufficient because any 7 consecutive nos will have sum of remainders = 21

Can someone explain?
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Re: OG - DS - Q98 - I think OG & MGMAT are Wrong. [#permalink]  24 Jun 2010, 17:11
Just a quick note that I thought of when looking at the problem.

(1) is actually something we already know given the question. The range of the remainder of any number divided by 7 is going to be 6. The remainder of any number divided by seven will be between 0-6. A remainder of 7 or more would need to be adjusted so that the appropriate number is added to the quotient leaving only a remainder that within the range of 0-6.

If you caught this you can quickly dismiss (1) as redundant information and move on to (2). This can save time for those of you who tried to go about (1) by testing numbers or doing other mathematical exercises.

Hope this helps.

Thanks,

Jared
Re: OG - DS - Q98 - I think OG & MGMAT are Wrong.   [#permalink] 24 Jun 2010, 17:11
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