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24 Nov 2021, 07:50
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If \(\frac{m}{n} = \frac{3}{8}\) then which of the following cannot be the value of \(n - m\) ?
I. \(-25\)
II. \(0\)
III. \(12\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
I. \(-25\)
II. \(0\)
III. \(12\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
24 Nov 2021, 07:50
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Official Solution:
If \(\frac{m}{n} = \frac{3}{8}\) then which of the following cannot be the value of \(n - m\) ?
I. \(-25\)
II. \(0\)
III. \(12\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
First of all, notice that we are NOT told that \(m\) and \(n\) are integers.
\(\frac{m}{n} = \frac{3}{8}\), and \(n - m=-25\) has a solution: \(m = -15\), and \(n = -40\).
\(\frac{m}{n} = \frac{3}{8}\), and \(n - m=12\) has a solution: \(m =\frac{36}{5}\), and \(n =\frac{96}{5}\)
\(\frac{m}{n} = \frac{3}{8}\), and \(n - m=0\) does NOT have a solution because \(n - m=0\) means that \(n = m\) but \(\frac{m}{n} = \frac{3}{8}\) means that \(n \neq m\) .
Answer: B
If \(\frac{m}{n} = \frac{3}{8}\) then which of the following cannot be the value of \(n - m\) ?
I. \(-25\)
II. \(0\)
III. \(12\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
First of all, notice that we are NOT told that \(m\) and \(n\) are integers.
\(\frac{m}{n} = \frac{3}{8}\), and \(n - m=-25\) has a solution: \(m = -15\), and \(n = -40\).
\(\frac{m}{n} = \frac{3}{8}\), and \(n - m=12\) has a solution: \(m =\frac{36}{5}\), and \(n =\frac{96}{5}\)
\(\frac{m}{n} = \frac{3}{8}\), and \(n - m=0\) does NOT have a solution because \(n - m=0\) means that \(n = m\) but \(\frac{m}{n} = \frac{3}{8}\) means that \(n \neq m\) .
Answer: B
