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Properties of numbers

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Properties of numbers

by EdWood » Fri Jun 18, 2010 10:51 pm
Q) from OG 12th edition , DS Q# 98.
Seven different numbers are selected from the integers 1 to 100, and each is number is divided by 7. What is the sum of the remainders.
1) The range of the seven numbers is 6.
2) The seven numbers selected are consecutive integers.

I am not able to understand the explanation given in OG. Plz help.
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by amising6 » Fri Jun 18, 2010 11:04 pm
EdWood wrote:Q) from OG 12th edition , DS Q# 98.
Seven different numbers are selected from the integers 1 to 100, and each is number is divided by 7. What is the sum of the remainders.
1) The range of the seven numbers is 6.
2) The seven numbers selected are consecutive integers.

I am not able to understand the explanation given in OG. Plz help.
statement 1)
that means difference between maximum and minimum is 6 and they re seven different numbers so it will have to be 7 consective numbers
for eg 1,2,3,4,5,6,7 os the range is is 6

now in number system propertie sum of continious 7 number is divisible by 7(property every n th number is divisible by n)

so remainder will be zero

statement 2)
The seven numbers selected are consecutive integers
we have just seen now in number system propertie sum of continious 7 number is divisible by 7
so statement 2 is also sufficien

so either statement or statement 1 is sufficient to answer

D
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by Patrick_GMATFix » Sat Jun 19, 2010 5:01 am
amising6, there is an error in your logic because the OA is B. As EdWood pointed out, this is from the OG12, #98.

Edwood, perhaps the attached detailed explanation will help you. If you cannot see the solution, read it here
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by Stuart@KaplanGMAT » Sat Jun 19, 2010 6:20 am
Patrick_GMATFix wrote:amising6, there is an error in your logic because the OA is B. As EdWood pointed out, this is from the OG12, #98.

Edwood, perhaps the attached detailed explanation will help you. If you cannot see the solution, read it here
Hi,

amising6's solution is 100% correct (good job!); however, the question has been misposted.

According to the post, statement (1) gives us 7 consecutive integers (we have to choose 7 different integers with a range of 6, so the only possible set is 7 consecutive ones).

However, OG #98 reads:

(1) The range of the seven remainders is 6.

Since the range of the remainders allows us to pick either consecutive or non-consecutive integers (for example, the set {7, 14, 21, 28, 35, 42, 48} satisfies the statement), (1) is insufficient.
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by Patrick_GMATFix » Sat Jun 19, 2010 6:32 am
Good catch. Thanks Stuart
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by EdWood » Sat Jun 19, 2010 9:45 pm
Thanks to all, Patrick your solution and detail explanation really helped o understand the problem.
Somehow I misunderstood the problem and posted the same, sorry for that.
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by Patrick_GMATFix » Sun Jun 20, 2010 3:48 am
You're welcome EdWood. Glad to hear it!
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