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

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If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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New post 05 Nov 2018, 18:53
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Question Stats:

61% (01:37) correct 39% (01:31) wrong based on 101 sessions

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

(1) \(m > k\)
(2) \(x > y\)

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Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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New post 05 Nov 2018, 20:21
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dimmak wrote:
If m, k, x, and y are positive numbers, is \(mx + ky > kx + my\) ?

(1) \(m > k\)
(2) \(x > y\)


Question asks: Is mx + ky > kx + my
or Is mx - kx > my - ky
or Is (m-k)x > (m-k)y

(1) If m > k, then m-k is positive, but we dont know that which is greater out of x and y. So we cant say whether the product of (m-k)x is greater or the product of (m-k)y is greater. So this statement is not sufficient.

(2) x > y. Now if m > k, then m-k is positive and the product of same positive number with x will yield a higher number than the product of same positive number with y: and in this case the answer to the question would be YES. But if m < k, then m-k is negative and the answer to the question would be NO. So this statement is not sufficient.

Combining the two statements, m > k so m-k is positive and x > y so the product of (m-k)x is greater than the product of (m-k)y. Answer to the question is YES. sufficient.

Hence C answer
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Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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New post 19 Jan 2019, 07:02
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
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Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?   [#permalink] 19 Jan 2019, 07:02
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If m, k, x, and y are positive numbers, is mx + ky > kx + my ?

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