Case 1: m=1, p=2, s=1 and v=1If m, p, s and v are positive, and m/p < s/v, which of the following must be between m/p and s/v?
I. (m+s)/(p+v)
II. ms/pv
III. s/v - m/p
A. None
B. I only
C. II only
D. III only
E. I and II both
In this case, m/p = 1/2 and s/v = 1/1 = 1.
Eliminate any statement that does not yield a value between 1/2 and 1.
I: (m+s)/(p+v) = (1+1)/(2+1) = 2/3.
Since 2/3 is between 1/2 and 1, hold onto I.
II: ms/pv = (1*1)/(2*1) = 1/2.
Since 1/2 is NOT between 1/2 and 1, eliminate any answer choice that includes II.
Eliminate C and E.
III: s/v - m/p = 1/1 - 1/2 = 1/2.
Since 1/2 is NOT between 1/2 and 1, eliminate any remaining answer choice that includes III.
Eliminate D.
Test whether Statement I holds true when m/p and s/v are VERY CLOSE.
Case 2: m=9, p=10, s=1, and v=1
In this case, m/p = 9/10 = 9/10 and s/v = 1/1 = 1.
I: (m+s)/(p+v) = (9+1)/(10+11) = 10/11.
Since 10/11 is between 9/10 and 1, statement I holds true.
Since statement 1 holds true even when the distance between m/p and s/v is extremely small, we should be satisfied:
Statement I must yield a value between m/p and s/v.
The correct answer is B.
