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If a, b, c are three consecutive positive even integers
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27 Sep 2020, 17:57
27 Sep 2020, 17:57
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Question Stats:
54% (01:28) correct
45% (00:45) wrong based on 22 sessions
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If a, b, c are three consecutive positive even integers, which of the following must be an integer?
Indicate all that's possible.
A. \(\frac{(a+b+c)}{2}\)
B. \(\frac{(a+b+c)}{4}\)
C. \(\frac{(a+b+c)}{6}\)
D. \(\frac{(a+b+c)}{12}\)
E. \(\frac{(a+b+c)}{15}\)
Indicate all that's possible.
A. \(\frac{(a+b+c)}{2}\)
B. \(\frac{(a+b+c)}{4}\)
C. \(\frac{(a+b+c)}{6}\)
D. \(\frac{(a+b+c)}{12}\)
E. \(\frac{(a+b+c)}{15}\)
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Re: If a, b, c are three consecutive positive even integers
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28 Sep 2020, 05:30
28 Sep 2020, 05:30
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lazyashell wrote:
If a, b, c are three consecutive positive even integers, which of the following must be an integer?
Indicate all that's possible.
A. \(\frac{(a+b+c)}{2}\)
B. \(\frac{(a+b+c)}{4}\)
C. \(\frac{(a+b+c)}{6}\)
D. \(\frac{(a+b+c)}{12}\)
E. \(\frac{(a+b+c)}{15}\)
Indicate all that's possible.
A. \(\frac{(a+b+c)}{2}\)
B. \(\frac{(a+b+c)}{4}\)
C. \(\frac{(a+b+c)}{6}\)
D. \(\frac{(a+b+c)}{12}\)
E. \(\frac{(a+b+c)}{15}\)
All even integers can be written as \(2k\), where \(k\) is an integer.
So, let \(2k\) = the smallest integer (\(a\))
So, \(2k + 2\) = the next consecutive even integer (\(b\))
And \(2k + 4\) = the last consecutive even integer (\(c\))
So, \(a + b + c = 2k + (2k+2)+ (2k+4) = 6k + 6\)
We get:
A. \(\frac{(a+b+c)}{2}=\frac{6k+6}{2}=3k+3\). Definitely an integer.
B. \(\frac{(a+b+c)}{4}=\frac{6k+6}{4}=1.5k+1.5\). This need not be an integer.
C. \(\frac{(a+b+c)}{6}=\frac{6k+6}{6}=k+1\). Definitely an integer.
D. \(\frac{(a+b+c)}{12}=\frac{6k+6}{12}=0.5k+0.5\). This need not be an integer.
E. \(\frac{(a+b+c)}{15}=\frac{6k+6}{15}=0.4k+0.4\). This need not be an integer.
Answer: A, C
Re: If a, b, c are three consecutive positive even integers
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06 Oct 2020, 07:26
06 Oct 2020, 07:26
1
I first plug 2,4,6
And I fell into ETS trap
Then I plug 100,102,104
I got A and C
Posted from my mobile device
And I fell into ETS trap
Then I plug 100,102,104
I got A and C
Posted from my mobile device
