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16 Jan 2020, 04:37
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (02:24) correct
39%
(01:57)
wrong
based on 287
sessions
History
Date
Time
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Not Attempted Yet
If \(\frac{a}{b} = \frac{c}{d} = \frac{4}{5}\), what is the value of \(\frac{4a - 3c}{5b + 4d}\) ?
A. -8/65
B. 4/45
C. 8/45
D. 12/45
E. Cannot be determined.
A. -8/65
B. 4/45
C. 8/45
D. 12/45
E. Cannot be determined.
16 Jan 2020, 07:14
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Bunuel
If \(\frac{a}{b} = \frac{c}{d} = \frac{4}{5}\), what is the value of \(\frac{4a - 3c}{5b + 4d}\) ?
A. -8/65
B. 4/45
C. 8/45
D. 12/45
E. Cannot be determined.
A. -8/65
B. 4/45
C. 8/45
D. 12/45
E. Cannot be determined.
Typically, when we add or subtract parts of a ratio, the resulting ratio does not remain constant.
Given this, let's test some possible values
If \(\frac{a}{b} = \frac{c}{d} = \frac{4}{5}\), then it COULD be the case that a = 4, b = 5, c = 4 and d = 5
In this case, \(\frac{4a - 3c}{5b + 4d}=\frac{4(4) - 3(4)}{5(5) + 4(5)}=\frac{16 - 12}{25 + 20}=\frac{4}{45}\)
If \(\frac{a}{b} = \frac{c}{d} = \frac{4}{5}\), then it could ALSO be the case that a = 4, b = 5, c = 8 and d = 10
In this case, \(\frac{4a - 3c}{5b + 4d}=\frac{4(4) - 3(8)}{5(5) + 4(10)}=\frac{16 - 24}{25 + 40}=\frac{-8}{65}\)
Answer: E
Cheers,
Brent
General Discussion
21 Aug 2020, 21:32
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Given that \(\frac{a}{b} = \frac{4}{5}\) or a = 0.8b
Also \(\frac{c}{d} = \frac{4}{5}\) or c = 0.8d
\(\frac{4a - 3c}{5b + 4d} = \frac{4*(0.8b) - 3(0.8d)}{5b + 4d}= \frac{3.2b - 2.4b }{ 5b + 4d}\)
Since b and d cannot be cancelled,
Option E
Arun Kumar
Also \(\frac{c}{d} = \frac{4}{5}\) or c = 0.8d
\(\frac{4a - 3c}{5b + 4d} = \frac{4*(0.8b) - 3(0.8d)}{5b + 4d}= \frac{3.2b - 2.4b }{ 5b + 4d}\)
Since b and d cannot be cancelled,
Option E
Arun Kumar
