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Is 4m - 5n > m^2

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Director
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Is 4m - 5n > m^2  [#permalink]

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New post 25 Jan 2011, 05:51
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:59) correct 25% (01:55) wrong based on 128 sessions

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Is 4m - 5n > m^2

(1) n < 0

(2) m is an integer between 0 and 4 inclusive
Math Expert
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V
Joined: 02 Sep 2009
Posts: 52938
Re: inequality ds  [#permalink]

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New post 25 Jan 2011, 06:01
1
rxs0005 wrote:
is 4m - 5n > m^2


1. n < 0

2. m is an integer between 0 and 4 inclusive


Is \(4m-5n>m^2\)? --> is \(m(4-m)>5n\)?

(1) n<0. Well this statement is clearly insufficient as we know nothing about \(m\), though from it we know that \(RHS=5n<0\) (RHS is negative).

(2) m is an integer between 0 and 4 inclusive. Insufficient because of the same reason: no info about \(n\), but again from this statement we know that the least value of \(LHS=m(4-m)\) is zero (when \(m=4\) or \(m=0\)) in all other cases \(LHS=m(4-m)>0\).

(1)+(2) \(LHS=m(4-m)\geq{0}\) and \(RHS<0\): \(m(4-m)>5n\). Sufficient.

Answer: C.
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Re: Is 4m - 5n > m^2  [#permalink]

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New post 23 Feb 2014, 03:32
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Re: Is 4m - 5n > m^2  [#permalink]

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New post 22 Apr 2014, 06:24
My way

Is 4m-5n>m^2?

5n<4m-m^2
5n<n(4-m)?

Statement 1

n<0

Therefore, n(4-m)>0 given that n<0 thus is m>4?

Can't know this so insufficient

Statement 2

We are told that 0<m<4 but nothing else.

Insufficient

Statements 1 and 2 together

We have that m>4 is not possible since 0<m<4 therefore sufficient

C

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Re: Is 4m - 5n > m^2  [#permalink]

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New post 13 Mar 2016, 06:34
Director
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Re: Is 4m - 5n > m^2  [#permalink]

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New post 26 Jan 2019, 07:13
rxs0005 wrote:
Is 4m - 5n > m^2

(1) n < 0

(2) m is an integer between 0 and 4 inclusive


Never take assumptions

(1) n < 0
Insufficient, cant say anything about m

(2) m is an integer between 0 and 4 inclusive
Insufficient, cant say anything about n

Combine

Is 4m - 5n > m^2

This will always be true.
4m +5n > m^2, will become +ive and for the given values it will always be true.

C
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Re: Is 4m - 5n > m^2   [#permalink] 26 Jan 2019, 07:13
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