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16 Sep 2014, 00:27
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If \(y(u - c) = 0\) and \(j(u - k) = 0\), which of the following must be true, given \(c < k\)?
A. \(yj \lt 0\)
B. \(yj \gt 0\)
C. \(yj = 0\)
D. \(j = 0\)
E. \(y = 0\)
A. \(yj \lt 0\)
B. \(yj \gt 0\)
C. \(yj = 0\)
D. \(j = 0\)
E. \(y = 0\)
16 Sep 2014, 00:27
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Official Solution:
If \(y(u - c) = 0\) and \(j(u - k) = 0\), which of the following must be true, given \(c < k\)?
A. \(yj \lt 0\)
B. \(yj \gt 0\)
C. \(yj = 0\)
D. \(j = 0\)
E. \(y = 0\)
From \(y(u - c) = 0\), it follows that \(u=c\) or \(y=0\) (or both).
From \(j(u - k) = 0\), it follows that \(u=k\) or \(j=0\) (or both).
Note that \(u=c\) and \(u=k\) cannot simultaneously be correct because if they were, it would imply that \(u=c=k\), but we have been given that \(c < k\). Thus, only one can be correct, which further implies that either \(y=0\) or \(j=0\), making \(yj = 0\) always true.
Answer: C
If \(y(u - c) = 0\) and \(j(u - k) = 0\), which of the following must be true, given \(c < k\)?
A. \(yj \lt 0\)
B. \(yj \gt 0\)
C. \(yj = 0\)
D. \(j = 0\)
E. \(y = 0\)
From \(y(u - c) = 0\), it follows that \(u=c\) or \(y=0\) (or both).
From \(j(u - k) = 0\), it follows that \(u=k\) or \(j=0\) (or both).
Note that \(u=c\) and \(u=k\) cannot simultaneously be correct because if they were, it would imply that \(u=c=k\), but we have been given that \(c < k\). Thus, only one can be correct, which further implies that either \(y=0\) or \(j=0\), making \(yj = 0\) always true.
Answer: C
General Discussion
21 Jun 2020, 07:59
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[y(u-c)]*j = 0*j
[j (u-k)]*y = 0*y
jy (u-c) = 0
jy (u-k) = 0
ADD THEM
jy(u-c) + jy(u-k) = 0
jy (u-c-[u-k]) = 0
jy (u-c-u+k) = 0
jy (k-c) = 0
--> k > c
jy (+ve number) = 0
jy = 0
QED
[j (u-k)]*y = 0*y
jy (u-c) = 0
jy (u-k) = 0
ADD THEM
jy(u-c) + jy(u-k) = 0
jy (u-c-[u-k]) = 0
jy (u-c-u+k) = 0
jy (k-c) = 0
--> k > c
jy (+ve number) = 0
jy = 0
QED
