If k is a positive integer, such that k divided by 2337 leaves a remainder of 247, what is the remainder

Brent@GMATPrepNow wrote: ↑

Tue Oct 26, 2021 2:27 pm

If k is a positive integer, such that k divided by 2337 leaves a remainder of 247, what is the remainder when k is divided by 123?

A) 1
B) 3
C) 5
D) 7
E) 9

Answer: A
Source: www.gmatprepnow.com

I created this question to expose a common time-draining habit some students have when it comes to identifying values that satisfy the given information in a remainder question.
For example, if w divided by 10 leaves a remainder of 5, what is a possible value of w?
The most common response I get from students is w = 15, which is true (but it's not the smallest possible value of w).
In fact, many students will find a possible w-value by adding the divisor (10) and the remainder (5) to get 15.
However, if you follow the same strategy for this question, you get 2337 + 247 which equals 2584, which means you must now determine the remainder when 2584 is divided by 123, which is no fun!

Instead, we should apply a nice remainder property 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 y divided by 5 leaves a remainder of 1, then the possible values of y are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for this question, the possible values of k are: 247, 247+2337, 247+(2)2337, 247+(3)2337, etc

Since 247 is the easiest possible value to work with, we'll use that to answer the question.

What is the remainder when k is divided by 123
247 divided by 123 = 2 with remainder 1

Answer: A