If a positive integer N leaves a remainder 3 when divided by 204, what

Question

If a positive integer N leaves a remainder 3 when divided by 204, what is the remainder when N is divided by 4?

A. 0
B. 1
C. 2
D. 3
E. Cannot be determined

abelka · Answer

We can write N=k*204 + (remainder 3)
A number is divisible by 4 if its last two digits are divisible by 4. So 204 is divisible by 4.
So k*204 is divisible by 4 without any remainder. So the remainder will be the same = 3.
Answer D

dcn1102 · Answer

IMO D 4

Since 204 is divisible by 4 i.e. 51 x 4 and since 3 is less than 4 the remainder is 3.

VAditi · Answer

Can someone please explain this in a bit more detail? Since 204 is divisible by 4, shouldn't the remainder be 0?

Raghav9906 · Answer

The question asks that what will be the remainder when N is divided by 4 (not when 204 is divided by 4).

Now,

Since 4 if a factor of 204, the remainder when N is divided by 4 will be same as that when N is divided by 204. Hence, 3 is the answer.

Also, note that remainder must always be less than the divisor, which in this case is true (3<4).

Hope this helps!

BrushMyQuant · Answer

If a positive integer N leaves a remainder 3 when divided by 204

Dividend = Divisor * Quotient + Remainder

=> N = 204*k + 3 (where k is the quotient)
=> N = 204k + 3

What is the remainder when N is divided by 4?

=> Remainder of N by 4 = Remainder of 204k + 3 by 4
= Remainder of 204k by 4 + Remainder of 3 by 4
= 0 + 3 = 3

So,  Answer will be D 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

unraveled · Answer

If a positive integer N leaves a remainder 3 when divided by 204, what is the remainder when N is divided by 4?

A. 0
B. 1
C. 2
D. 3
E. Cannot be determined

Since 204 is divisible by 4, any remainder that is left by dividing N by 204 would also be left in the case of 4. 
Hence it should 3 in this case. Eg. R  = R  = 3

Answer D.

If a positive integer N leaves a remainder 3 when divided by 204, what

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GMAT Problem Solving (PS) Questions

If a positive integer N leaves a remainder 3 when divided by 204, what

Prep Toolkit

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