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Remainder when divisor > dividend

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by tnkippen » Wed Oct 31, 2012 6:53 pm
If 30 is divided by 100 (or divided by any number over 30, for that matter), does the remainder = 30?

The following Problem Solving question in TOG 13th Edition seems to say no (and that the only 130, 230, 330 divided by 100 would have a remainder of 30). Just wondering how you would calculate the official remainder when the divisor is larger than the dividend.

58. What is the tens digit of positive integer x ? (1) x divided by 100 has a remainder of 30. (2) x divided by 110 has a remainder of 30.

(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.

OA: A

Thanks!
Thomas
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by tnkippen » Fri Nov 02, 2012 7:47 pm
Anything?
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by Brent@GMATPrepNow » Sat Nov 03, 2012 8:09 am
tnkippen wrote:If 30 is divided by 100 (or divided by any number over 30, for that matter), does the remainder = 30?
Hey Thomas,

The answer to your question is yes. The remainder will be 30.

To answer questions involving remainders, it's useful to be able to list possible values. So, here's the rule for this:

If N divided by D has remainder R, then the possible values of N = R, R+D, R+2D, R+3D, . . .

Example: If N divided by 7 has remainder 3, then the possible values of N are as follows: 3, 10, 17, 24, 31, 38, etc

Cheers,
Brent
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by Brent@GMATPrepNow » Sat Nov 03, 2012 8:40 am
tnkippen wrote: What is the tens digit of positive integer x ?

(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.
Target question: What is the tens digit of positive integer x ?

Statement 1: x divided by 100 has a remainder of 30.
So, x could equal 30, 130, 230, 330, 430, . . .
As you can see the tens digit will always be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x divided by 110 has a remainder of 30.
So, x could equal 30, 140, 250, 360, 470, . . .
As you can see the tens digit could be 3 or 4 or 5 or 6 or . . .
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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