If 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 Case 1: m=1, p=2, s=1 and v=1 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.

Dear mitch , I have a question . you have written - Case 1: m=1, p=2, s=1 and v=1 ... if the question has given different variables - namely s and V then is it prudent to substitute same value for s and v which is equal to 1 . if varaibales are different should we not take different values for the variable ?

abhasjha wrote:Dear mitch , I have a question . you have written - Case 1: m=1, p=2, s=1 and v=1 ... if the question has given different variables - namely s and V then is it prudent to substitute same value for s and v which is equal to 1 . if varaibales are different should we not take different values for the variable ? Just the opposite. Since we are not told that the values must be distinct, we should consider the consequences of making them equal to one another.