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Number theory problem 2:

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by vipulgoyal » Wed Sep 04, 2013 11:03 pm
Ok lets put it in this way

m = 10,000(a) + 57
now
m/100 = 1000(10a) + 57

reminder will be same and quotient will be 10 times

Alt

Since the remainder is 57 when the number is divided by 10,000, the number can be expressed as 10,000n +57. Dividing this number by 1,000 yields
10,000n+57/1000
=10,000n/1000 +57/1000
=10n+57/1000
Hence, the remainder is 57 (by the alternative form p /k = q + r/k
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by [email protected] » Wed Sep 04, 2013 11:43 pm
Hi manpreet singh,

What is the source of this question? I only ask because it does NOT follow typical GMAT "style".

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by ganeshrkamath » Thu Sep 05, 2013 12:13 am
'manpreet singh wrote:The remainder is 57 when a number is divided by 10,000. What is the remainder when the
same number is divided by 1,000?
(A) 5
(B) 7
(C) 43
(D) 57
(E) 570

OA= D
For the remainder to be 57, the number should be of the form pqr...0057
Example, 10057
When this number is divided by 1000, the remainder is still 57.

Choose D

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by Brent@GMATPrepNow » Thu Sep 05, 2013 6:25 am
'manpreet singh wrote:The remainder is 57 when a number is divided by 10,000. What is the remainder when the
same number is divided by 1,000?
(A) 5
(B) 7
(C) 43
(D) 57
(E) 570
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

A quick solution is to find a number that satisfies the first condition, and then use it to answer the question. More importantly, we want to find a nice SMALL number.

When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

IMPORTANT: A lot of students miss out on the fact that 1 is a possible value of N here.

Likewise, if the remainder is 57 when a number is divided by 10,000, then the number in question could be 57.
So, if we divide 57 by 1000, the remainder will certainly be [spoiler]57 = D[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by \'manpreet singh » Thu Sep 05, 2013 9:37 pm
[email protected] wrote:Hi manpreet singh,

What is the source of this question? I only ask because it does NOT follow typical GMAT "style".

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Rich

This question is from Nova's GMAT bible.
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Re: Number theory problem 2:

by Scott@TargetTestPrep » Sun Mar 15, 2020 7:27 am
\'manpreet singh wrote: ↑
Wed Sep 04, 2013 10:25 pm
 The remainder is 57 when a number is divided by 10,000. What is the remainder when the
same number is divided by 1,000?
(A) 5
(B) 7
(C) 43
(D) 57
(E) 570

OA= D
The number could be 57, and when 57 is divided by 1,000, the remainder is 57.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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