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The positive integers k, m, and n have the property that k i
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02 Dec 2020, 09:28
02 Dec 2020, 09:28
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The positive integers \(k, m,\) and \(n\) have the property that \(k\) is a factor of \(m\), and \(m\) is a factor of \(n\). Which of the following must be true?
Indicate all that apply.
A. \(k\) is a factor of \(n\).
B. \(m\) is a factor of \(kn\).
C. \(n\) is a factor of \(km\).
D. \(\frac{n}{k}\) and \(\frac{n}{m}\) are both integers
Kudos for the right answer and explanation
Indicate all that apply.
A. \(k\) is a factor of \(n\).
B. \(m\) is a factor of \(kn\).
C. \(n\) is a factor of \(km\).
D. \(\frac{n}{k}\) and \(\frac{n}{m}\) are both integers
Kudos for the right answer and explanation
Re: The positive integers k, m, and n have the property that k i
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01 Jan 2021, 06:45
01 Jan 2021, 06:45
2
Carcass wrote:
The positive integers \(k, m,\) and \(n\) have the property that \(k\) is a factor of \(m\), and \(m\) is a factor of \(n\). Which of the following must be true?
Indicate all that apply.
A. \(k\) is a factor of \(n\).
B. \(m\) is a factor of \(kn\).
C. \(n\) is a factor of \(km\).
D. \(\frac{n}{k}\) and \(\frac{n}{m}\) are both integers
Kudos for the right answer and explanation
Indicate all that apply.
A. \(k\) is a factor of \(n\).
B. \(m\) is a factor of \(kn\).
C. \(n\) is a factor of \(km\).
D. \(\frac{n}{k}\) and \(\frac{n}{m}\) are both integers
Kudos for the right answer and explanation
If we take k as 1, m as 2 and n as 4 and check:
A. k is a factor of n --> 1 is a factor of 4. This option is satisfied.
B. m is a factor of kn --> 2 is a factor of 4 x 1. This option is satisfied.
C. n is a factor of km --> 4 is not a factor of 2. This option is not getting satisfied.
D. n/k and n/m are both integers --> 4/1 = 4 and 4/2 = 2. This option is also getting satisfied.
Hence the correct answer choices are A, B and D.
The positive integers k, m, and n have the property that k i
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17 Jan 2021, 20:29
17 Jan 2021, 20:29
1
Try to intrinsically visualize the problem to eliminate options.
since k is a factor of m and m is a factor of n
It is obvious that K is also a factor of n since M is a multiple of K and N is a multiple of M so it is only the question that N is what multiple of K. This will eliminate option A
Option B is really a question designed to drain your time. Since it is already mentioned that M is a factor of N; It follows that M is also factor of KN or \(K *\) anything.
Here If N acquires the same value as M then N can be a factor of KM however if N is much larger then KM then N is not perfectly divisible by KM. Let us take the two case of \(M=4\), \(N=4\) ,\(K =2\) and \(M=4\), \(N=12\), \(K=2\)
K is a factor of M so K is automatically a factor of N since M is a factor of N hence \(\frac{n}{k}\) is an integer. Since the question clearly mentions M to be a factor of N; \(\frac{M}{N}\) is also an integer.
since k is a factor of m and m is a factor of n
It is obvious that K is also a factor of n since M is a multiple of K and N is a multiple of M so it is only the question that N is what multiple of K. This will eliminate option A
Option B is really a question designed to drain your time. Since it is already mentioned that M is a factor of N; It follows that M is also factor of KN or \(K *\) anything.
Here If N acquires the same value as M then N can be a factor of KM however if N is much larger then KM then N is not perfectly divisible by KM. Let us take the two case of \(M=4\), \(N=4\) ,\(K =2\) and \(M=4\), \(N=12\), \(K=2\)
K is a factor of M so K is automatically a factor of N since M is a factor of N hence \(\frac{n}{k}\) is an integer. Since the question clearly mentions M to be a factor of N; \(\frac{M}{N}\) is also an integer.
