If k is a positive integer, and k divided by divided by 2337 leaves a

Question

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

v12345 · Answer

k divided by 2337 leaves a remainder of 247
2337 is divisible by 123.
k divided by 123 will leave remainder 247/123 = 1 (remainder)

Hence, OA is (A).

Abhishek009 · Answer

Least possible value of k = 247

Now, when k is divided by 123 remainder will be 1 as 123*2 = 246 , Thus Answer must be (A)

BrentGMATPrepNow · Answer

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

BrushMyQuant · Answer

Given that k divided by 2337 leaves a remainder of 247 and we need to find the remainder when k is divided by 123

Theory: Dividend = Divisor*Quotient + Remainder

k divided by 2337 leaves a remainder of 247 
k -> Dividend
2337 -> Divisor
a -> Quotient (Assume)
247 -> Remainders
=> k = 2337*a + 247 ...(1)

Now,  we need to find the remainder when k is divided by 123 
Note that 2337 = 123 * 19

=> k = 123*19*a + 246 + 1 = 123*19*a + 123*2 + 1
=> k = 123(19a + 2) + 1

=> k when divided by 123 gives 19a + 2 as quotient and 1 as remainder.

So,  Answer will be A 
Hope it helps!

Watch the following video to learn the Basics of Remainders

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

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If k is a positive integer, and k divided by divided by 2337 leaves a

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