stonecold wrote:

If \(a*b=\frac{a}{b}-\frac{b}{a}\) and \(m>n>0\), then which of following must be true?

(I) \(\frac{1}{m}*\frac{1}{n} > \frac{1}{n} *\frac{1}{m}\)

(II) \(\frac{1}{m} *\frac{1}{n} < \frac{1}{n} *\frac{1}{m}\)

(III) \(m*n<0\)

(IV) \(m*n>0\)

A) I and III

B) I and IV

C) II and III

D) II and IV

E) only IV

The format of the question is incorrect. It is not given as a function or user defined operator. You cannot use a standard operator as a user defined operator that too without explaining explicitly. We can guess that the relation given for a and b is supposed to hold for m and n too to solve it but an actual GMAT question would need to be formatted differently.

Given the question as is, I would just say that m > n > 0 so m and n are positive and hence m*n > 0. This is the ONLY statement that will be true.

If you define a new operator such as

a#b = a/b - b/a

now, you can worry about (1/m) # (1/n) and (1/n)#(1/m)

(1/m) # (1/n) = n/m - m/n = (n - m)/mn (since n < m, this is negative)

(1/n)#(1/m) = m/n - n/m = (m - n)/mn (since m > n, this is positive)

So II is correct.

m#n = m/n - n/m = (m - n)/mn (since m > n, this is positive)

So IV is correct.

Answer (D)

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Karishma

Veritas Prep GMAT Instructor

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