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Remainders -GMAT PREP

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by Stockmoose16 » Wed Nov 12, 2008 7:46 pm
This GMAT prep question has been dealt with a couple times on this board, but I haven't seen anyone post a definitive OA.

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 the answer is D, but many seem to think it's B

For (1)
1,2,3,4,5,6,7

have remainders of:

1,2,3,4,5,6,0

That's a range of 6 and the sum of the remainders equals 21

just to double check:

12,13,14,15,16,17,18

have remainders of:

5, 6, 0, 1, 2, 3, 4 = 21

STMNT #1 is sufficient

Stmnt #2

2,3,4,5,6,7,8

have remainders of:

2+3+4+5+6+0+1 = 21 (same as consecutive set tested for stmt #1.

So I get D. Why are people getting B?
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Source: — Data Sufficiency |
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by cramya » Wed Nov 12, 2008 7:50 pm
Hi StockMoose,
Refer to https://www.beatthegmat.com/logitech-ds4-t22370.html

Let me know if u still have questions.

Regards,
Cramya
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by Stockmoose16 » Wed Nov 12, 2008 8:00 pm
Cramya,

I believe both of your responses in that thread are incorrect. Your last post says:


I picked the wrong example. Your are right about 7 different numbers but still its B) and not D)

Lets say the numbers are

1 2 3 4 7 6 11

1 2 3 4 7 6 13

Range of the reminders is 6 in both sets but the sum different

The range of the remainders of the first set of numbers above is not 6, it's only 5. Here's why:

The remainder of 1 is 1. The remainder of 2 is 2. The remainder of 3 is 3. The remainder of 4 is 4. The remainder of 5 is 5. The remainder of 6 is 6. The remainder of 7 is 0. The remainder of 11 is 4.

So, the range in that set is from 1-6 ... which is only 5. So your explanation is incorrect.

EDITED: Nevermind, you are correct, the range is 6. Thanks.
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by cramya » Wed Nov 12, 2008 8:05 pm
StockMoose,
Are we cool now? :-)

Good luck for your exam thats coming up!

Regards,
Cramya
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by stop@800 » Thu Nov 13, 2008 10:02 am
A
range of remainder is 6

remainders can be
0 1 2 3 4 5 6
or
0 6 6 6 6 6 6

so insuff


B
7 consecutive intergers
remainder will always
0 1 2 3 4 5 6
so sum can easily be found

hence answer is B

Let me know if you still have any doubt....
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by 4meonly » Mon Nov 17, 2008 10:04 am
summ of 7 conseq integers will be
7x+21
this will be divisible by 7 with R=0 cause 7x and 21 are divisible by 7
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