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# Is 4m - 5n > m^2

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Is 4m - 5n > m^2  [#permalink]

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25 Jan 2011, 06:51
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25% (medium)

Question Stats:

77% (01:56) correct 23% (01:53) wrong based on 117 sessions

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Is 4m - 5n > m^2

(1) n < 0

(2) m is an integer between 0 and 4 inclusive
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Joined: 02 Sep 2009
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25 Jan 2011, 07:01
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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.

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Is 4m - 5n > m^2 ?  [#permalink]

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24 Dec 2017, 09:02
Is 4m - 5n > m^2 ?

(1) n is negative.
(2) m is an integer between 0 and 4, inclusive.

Statement 1 is insufficient as we do not know antthing about m it can be negative and positive
Suppose n=-1
and m=0
then 5>0 true but when m = -2 we have for the same value of n
-8+5> -2^2
-3>4 false
So statement 1 is insufficient
Statement 2 is also insufficient as we do know anything about n
suppose m=1 and n=0
4>1 true
now let us say m=4 then
16>16 no true hence insufficient .
Taken together they they are sufficient as
4m-5n>m^2
Let n=-1
4m+5>m^2
m=0 true when m=1 it is true
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Re: Is 4m - 5n > m^2 ?  [#permalink]

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24 Dec 2017, 10:52
Bunuel wrote:
Is 4m - 5n > m^2 ?

(1) n is negative.
(2) m is an integer between 0 and 4, inclusive.

We'll solve this with a Logical approach using equation properties.
This often works for Data Sufficiency question involving simple inequalities.

(1) We have no information on m so cannot solve.
Insufficient.

(2) Now we have no information about n so cannot solve.
Insufficient.

We know through (1) that -5n is positive so we need to find out the relation between 4m and m^2.
There are 5 possible values of m, giving
m = 0: 4m = m^2
m = 1: 4m > m^2
m = 2: 4m > m^2
m = 3: 4m > m^2
m = 4: 4m = m^2
In all cases we're adding a positive number (-5n) to the left hand side so we're making it larger than it was before.
Therefore 4m - 5n > m^2 and (C) is our answer.
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Re: Is 4m - 5n > m^2  [#permalink]

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06 Sep 2019, 11:04
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Re: Is 4m - 5n > m^2   [#permalink] 06 Sep 2019, 11:04
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