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# Is 0<m<1?

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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02 Sep 2016, 05:58
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Difficulty:

45% (medium)

Question Stats:

60% (01:08) correct 40% (01:16) wrong based on 103 sessions

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Is 0<m<1?

(1) m^2 is less than 1.

(2) m^2<m

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Joined: 03 Jul 2016
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02 Sep 2016, 06:07
Statement 1 : m^2 < 0, m can be <=0. NOT SUFFICIENT.

Statement 2: m^2 < m , m can only be <1 and >0. SUFFICIENT.

B.
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Re: Is 0 < m < 1?  [#permalink]

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20 Nov 2016, 10:30
1
Bunuel wrote:
Is 0 < m < 1?

(1) m^2 is less than 1.

(2) m^2 < m

1. m^2 < 1.
m can be 0.5
m can be -0.5
one satisfies the condition, other not.
statement 1 alone is not sufficient.

2. m^2 < m -> we know for sure that m^2 is positive. therefore, m must be positive, and m must be between 0 and 1. sufficient.
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Re: Is 0 < m < 1?  [#permalink]

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10 Mar 2017, 04:00
D

Statement 1
Let m =0.2 / 1.2
m^2 = .04 / 1.44
So yes m s between 0 and 1
Sufficient

Statement 2
m = 0.9 / 0.1 / 1.1 / 1.9
m^2 = 0.81 / 0.01 / 1.21 / 3.61
So m^2 < m satisfies only fr
M between 0 and 1
Sufficient

So D

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Re: Is 0 < m < 1?  [#permalink]

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10 Mar 2017, 08:18
1

Stmnt 1:
m^2 < 1
or, |m|<1
or, -1<m<1 __________Not Suff

Stmnt 2:
m^2<m
or, m^2 - m <0
or, m(m-1) < 0
or, o<m<1___________Suff
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Re: Is 0 < m < 1?  [#permalink]

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10 Mar 2017, 08:59
1. m can be -1/2 or 1/2
2. m squared < m --> m < 1
m is -1/2 then 1/4 < -1/2 false.
so m must be > 0

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Re: Is 0 < m < 1?  [#permalink]

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10 Mar 2017, 22:24
I would also go with B.

Statement 1 : Simplifying : 1>m>-1
Statement 2 : m>m^2. Now only positive fractions between 0 and 1 will satisfy this. Hence sufficient
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Re: Is 0 < m < 1?  [#permalink]

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23 May 2017, 16:35
Q: is 0<m<1?

(1) m^2 <1
if m = 1/2, m^2 = 1/4 which is <1..... thus 0<m<1 is true
if m = 0, m^2 = 0 which is <1..... thus 0<m<1 is not true
NSF

(2) m^2 <m
this is only the case when m is 0<m<1, thus this matches prompt.

:. B
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07 Jun 2017, 13:49
How is it B?

If M = -1/2

(-1/2)^2 would be greater than -1/2?
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Re: Is 0 < m < 1?  [#permalink]

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06 Jul 2017, 17:06
Bunuel wrote:
Is 0 < m < 1?

(1) m^2 is less than 1.

(2) m^2 < m

We need to determine whether m is between 0 and 1.

Statement One Alone:

m^2 is less than 1

We can simplify the information in statement one:

m^2 < 1

√m^2 < √1

Thus:

m < 1

or

-m < 1

m > -1

That is, -1 < m < 1. Thus, m is not necessarily between 0 and 1, since m could be between 0 and -1.
Statement one is not sufficient to answer the question.

Statement Two Alone:

m^2 < m

Since m^2 is less than m, the only values that satisfy such an inequality are when m is between 0 and 1. Thus, statement two is sufficient to answer the question.

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Re: Is 0 < m < 1?   [#permalink] 06 Jul 2017, 17:06
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