dimmak wrote:

If m, k, x, and y are positive numbers, is \(mx + ky > kx + my\) ?

(1) \(m > k\)

(2) \(x > y\)

First thing I see is that the difference between the sides of the inequality is the position of m,k

This makes me think about MIN-MAX. Also, we don't know the signs of the variables and inequalities are often about what is + or -

1) m > k

This means that: BIG*x + small*y > small*x + BIG*y

We don't have any info about k,m so insufficient

2) x > y

This means that m*BIG + k*small > k*BIG + m*small

Again, no info about the values of x,y so insufficient

3) If we combine:

BIG*BIG + small*small > small*BIG + BIG*small

We can see that the right hand side is bigger, so both together are sufficient, C

Testing values:

x>y

3>2

m>k

3>2

3*3+2*2 > 2*3+2*3

13>12

x>y

-1>-2

m>k

3>2

-1*3 + -2*2 > -2*3 + -1*2

-7>-8

x>y

-1>-2

m>k

-2>-3

-1*-2 + -2*-3 > -2*-2 + -1*-3

8>7