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Manager  G
Joined: 08 Sep 2017
Posts: 77
Location: Colombia
GMAT 1: 710 Q49 V39 If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:27) correct 37% (01:23) wrong based on 150 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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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1429
Location: India
Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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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.

Senior Manager  P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 434
Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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

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

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
Director  D
Joined: 24 Oct 2016
Posts: 532
GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?  [#permalink]

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

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

Simplify the Q:
mx + ky > kx + my ?
m (x-y) > K(x-y)
(x-y)(m-k)>0?

1) x - y > 0. Don't know anything about (m - k). Not sufficient
2) m - k > 0. Don't know anything about (x - y). Not sufficient

1+2) Sufficient

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If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything. Re: If m, k, x, and y are positive numbers, is mx + ky > kx + my ?   [#permalink] 10 Oct 2019, 03:47
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