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Apr 2808:00 AM PDT
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hideyoshi
Joined: 09 Feb 2010
Last visit: 05 Dec 2020
Posts: 72
Given Kudos: 18
Affiliations: Scrum Alliance
Location: United States (MI)
Concentration: Strategy, General Management
Schools: Ross Weekend"19 Booth PT '20 (M)
GMAT 1: 600 Q48 V25
GMAT 2: 710 Q48 V38
WE:Information Technology (Retail: E-commerce)
07 Sep 2015, 17:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
49% (00:54) correct
51%
(00:42)
wrong
based on 169
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(m\) positive?
1). \(m^3 = m\)
2). \(|m| = m\)
Source: Prep4GMAT iOS app
1). \(m^3 = m\)
2). \(|m| = m\)
Source: Prep4GMAT iOS app
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
07 Sep 2015, 17:53
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hideyoshi
Question asks is m >0?
Per statement 1, \(m^3=m\) ---> m is either = 0 or =1 or =-1. Thus not sufficient.
Per statement 2, |m| = m ---> \(m \geq\) 0. Thus not sufficient.
Combining, we still get m = 0 and m=1 satisfying both the statements and hence E is the correct answer.
13 Feb 2017, 17:54
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hideyoshi
Target question: Is m positive?
Statement 1: m³ = m
Subtract m from both sides to get: m³ - m = 0
Factor: m(m² - 1) = 0
Factor more: (m)(m + 1)(m - 1) = 0
This means m = 0, or m + 1 = 0, or m - 1 = 0
So, there are three possible cases:
case a: m = 0, in which case m is NOT positive
case b: m = -1, in which case m is NOT positive
case c: m = 1, in which case m IS positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |m| = m
When solving equations involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
So, applying the above rule, we have two equations to solve: m = m, and m = -m
If m = m, then m can equal ANY number, as long as m is POSITIVE. So, m can be ANY positive number.
If m = -m, then m = 0, which means m is NOT positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that m can equal 0, -1, or 1
Statement 2 tells us that m can equal any positive number, or m can equal 0
When we combine the statements, we can see that m can equal 0 or 1.
If m = 0, then m is NOT positive
If m = 1, then m IS positive
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
