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06 May 2021, 01:19
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B
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Difficulty:
95%
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Question Stats:
42% (01:42) correct
58%
(01:40)
wrong
based on 363
sessions
History
Date
Time
Result
Not Attempted Yet
If m/n = 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
M37-43
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
M37-43
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24 Nov 2021, 07:51
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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
General Discussion
Bunuel
Given: \(\frac{m}{n}\) = \(\frac{3}{8} \)
\(m = \frac{3}{8}n\)
Asked: n - m?
\(n - m = n - \frac{3}{8}n\) = \(\frac{5n}{8}\)
1) Possible. \(\frac{5n}{8} = -25\)
\(n = -40, m = \frac{3}{8} * -40 = -15\), n - m = -25
2) \(\frac{5n}{8} = 0, n = 0, m = 0, but \frac{n}{m} = undefined\).
3) Possible. \(n =\frac{ 96}{5}, m = \frac{36}{5}\) = 12
B. IMO
Updated point 2.
