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# Is 4m - 5n > m^2 ?

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Math Expert
Joined: 02 Sep 2009
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Is 4m - 5n > m^2 ?  [#permalink]

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24 Dec 2017, 01:46
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Difficulty:

25% (medium)

Question Stats:

85% (01:52) correct 15% (02:43) wrong based on 41 sessions

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Is 4m - 5n > m^2 ?

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

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Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
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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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24 Dec 2017, 14:26
Bunuel wrote:
Is 4m - 5n > m^2 ?

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

(1) n is negative. If m = 4, n = -1, then 4(4)-5(-1)=16+5>16, true; If m = -1, n = -1, then 4(-1)-5(-1)=1=1, false; insufficient.

(2) m is an integer between 0 and 4, inclusive. If m = 4, n = -1, then 4(4)-5(-1)=16+5>16, true; If m = 1, n = 5, then 4(1)-5(5)=-21<1, false; insufficient.

(1) & (2). If m = 4, n = -1, then 4(4)-5(-1)=16+5>16, true; If m = 0, n = -1, then 4(0)-5(-1)=5>0, true; sufficient.

Re: Is 4m - 5n > m^2 ?   [#permalink] 24 Dec 2017, 14:26
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