Is kx

Question

Is kx < ky?

(1) 2x < 3y
(2) 2x < y

Archit3110 · Answer

Given
K(x-y)<0
K<0 or x<y or
0<k(x-y)
Value can be + or -ve
#1
2x-3y<0
At x =y=3 we get no
And x =2 ,y=5 we get yes to target 
Insufficient
#2
2x<y
2x-y<0
For this to be sufficient value of y>x always but value of k is not known so insufficient
From 1 &2 value of k is unknown

Option e

Posted from my mobile device

BrentGMATPrepNow · Answer

Target question :    Is kx < ky?

I created this question to highlight a common mistake among test makers. 
Some students will incorrectly rephrase the target question by dividing both sides of the inequality by k to get: " Is x < y? " 
The problem here is that  we don't know whether k is POSITIVE or NEGATIVE . 
If k is NEGATIVE, then we must REVERSE the direction of the inequality symbol when we divide both sides by k, which means the rephrased target question becomes " Is x > y? " 
If k is POSITIVE, then the inequality symbol is UNCHANGED when we divide both sides by k, which means the rephrased target question becomes " Is x < y? "

Since neither statement provides any information about whether k is positive or negative, we can jump straight to . . .

Statements 1 and 2 combined    
Statement 1 tells us that  2x < 3y 
Statement 2 tells us that  2x < y

Since the inequality symbols of the two inequalities are facing the same direction, we can add the inequalities to get:  4x < 4y 
When we divide both sides of the inequality by 4 we get:  x < y 
This, however, is not enough information to answer the  target question  
Consider these two possible cases: 
 Case a : x = 1, y = 2 and k = 1. In this case, kx = (1)(1) = 1 and ky = (1)(2) = 2, which means the answer to the target question is  YES, kx is less than ky 
 Case b : x = 1, y = 3 and k = -1. In this case, kx = (-1)(1) = -1 and ky = (-1)(3) = -3, which means the answer to the target question is  NO, kx is not less than ky 
Since we can’t answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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Is kx < ky? (1) 2x < 3y (2) 2x < y

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