If mn ≠0, is m > n?
(1) 1/m < 1/n
(2) m^2 > n^2
OA E
Source: Manhattan Prep
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If mn ≠0, is m > n?
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BTGmoderatorDC
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$$m,n\,\, \ne 0$$BTGmoderatorDC wrote:If mn ≠0, is m > n?
(1) 1/m < 1/n
(2) m^2 > n^2
Source: Manhattan Prep
$$m\mathop > \limits^? n$$
$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( { - 2,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{E}} \right)$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Target question: Is m > n?BTGmoderatorDC wrote: ↑Sat Dec 22, 2018 5:28 amIf mn ≠0, is m > n?
(1) 1/m < 1/n
(2) m^2 > n^2
OA E
Source: Manhattan Prep
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
Brent Hanneson - Creator of GMATPrepNow.com
