If mn ≠0, is m > n?

[BTGmoderatorDC]

If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2

OA E

Source: Manhattan Prep

[fskilnik@GMATH]

If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2
Source: Manhattan Prep

$$m,n\,\, \ne 0$$
$$m\mathop > \limits^? n$$
$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( { - 2,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{E}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Brent@GMATPrepNow]

If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2

OA E

Source: Manhattan Prep

Target question: Is m > n?

Given: mn ≠ 0

Statement 1: 1/m < 1/n
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of m and n that satisfy statement 1. Here are two:
Case a: m = 2 and n = 1. In this case m > n
Case b: m = -3 and n = 1. In this case m < n
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: m² > n²
Before I start choosing numbers to test, I'll see if I can REUSE my numbers from statement 1.
Yes I can! Those same values satisfy the conditions in statement 2.
Case a: m = 2 and n = 1. In this case m > n
Case b: m = -3 and n = 1. In this case m < n
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: m = 2 and n = 1. In this case m > n
Case b: m = -3 and n = 1. In this case m < n
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent