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Sub 505 Level|   Remainders|      
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BrentGMATPrepNow
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If k is a positive integer, and k divided by divided by 2337 leaves a 12 Oct 2021, 08:29
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

94% (01:26) correct 6% (02:09) wrong based on 99 sessions

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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
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A
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If k is a positive integer, and k divided by divided by 2337 leaves a 12 Oct 2021, 11:01
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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).
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If k is a positive integer, and k divided by divided by 2337 leaves a 12 Oct 2021, 11:03
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BrentGMATPrepNow
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
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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)
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If k is a positive integer, and k divided by divided by 2337 leaves a 12 Oct 2021, 11:09
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BrentGMATPrepNow
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
Show more

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
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If k is a positive integer, and k divided by divided by 2337 leaves a 10 Jan 2022, 10:07
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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

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