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Joined: 10 Apr 2015
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If k is a positive integer, such that k divided by 2337 leaves a remai
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24 Oct 2021, 07:39
24 Oct 2021, 07:39
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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
A) 1
B) 3
C) 5
D) 7
E) 9
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If k is a positive integer, such that k divided by 2337 leaves a remai
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25 Oct 2021, 06:14
25 Oct 2021, 06:14
1
GreenlightTestPrep wrote:
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
A) 1
B) 3
C) 5
D) 7
E) 9
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
General Discussion
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If k is a positive integer, such that k divided by 2337 leaves a remai
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10 Jan 2022, 09:06
10 Jan 2022, 09:06
1
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
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
