Is 4m - 5n > m^2

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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Is 4m - 5n > m^2 ?

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

The answer is C
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

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

(1) n < 0

No information on m. However, we can conclude 5n is negative. Insufficient.

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

No information on n. Insufficient.

(1&2) Is 4m - m^2 > 5n?
Is 4m - m^2 > negative number?
Any value of m (between 0 and 4 inclusive) > negative number.

Sufficient.

Answer is C.
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