Number theory problem 2:

[\'manpreet singh]

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

[vipulgoyal]

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

[[email protected]]

Hi manpreet singh,

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

GMAT assassins aren't born, they're made,
Rich

[ganeshrkamath]

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

Cheers

[Brent@GMATPrepNow]

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

[\'manpreet singh]

Hi manpreet singh,

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

GMAT assassins aren't born, they're made,
Rich

This question is from Nova's GMAT bible.

[Scott@TargetTestPrep]

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