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# Is m positive?

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07 Sep 2015, 17:45
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Difficulty:

45% (medium)

Question Stats:

53% (00:53) correct 47% (00:41) wrong based on 103 sessions

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Is $$m$$ positive?

1). $$m^3 = m$$
2). $$|m| = m$$

Source: Prep4GMAT iOS app

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07 Sep 2015, 17:53
hideyoshi wrote:
Is $$m$$ positive?

1). $$m^3 = m$$
2). $$|m| = m$$

Source: Prep4GMAT iOS app

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.
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13 Feb 2017, 17:54
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Top Contributor
hideyoshi wrote:
Is $$m$$ positive?

1) $$m^3 = m$$
2) $$|m| = m$$

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

Cheers,
Brent
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13 Feb 2017, 18:07
Question : Is m >0

F1 ) m^3=m
So if m^3 =-1 then m= -1 OR m^3 = 0 m = 0 OR m^3 = 1 m =1 => Insufficient

F2) |m| = m
If m = -1 Then -(-1) = -1 1= -1 incorrect hence m is not < 0
m = 0 then 0 =0 correct => m =0
m = 1 then |1| = 1 1 =1 => M >0
Hence we get from F2 M >= 0 => Insufficient

Combining both we get M >= 0 . But still insufficient. Hence E.
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07 May 2019, 22:12
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is m positive?   [#permalink] 07 May 2019, 22:12
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