Is kx < ky?

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Is kx < ky?

by Brent@GMATPrepNow » Sun Oct 24, 2021 7:35 am

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Is kx < ky?

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

Answer: E
Source: www.gmatprepnow.com
Brent Hanneson - Creator of GMATPrepNow.com
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GMAT/MBA Expert

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Re: Is kx < ky?

by Brent@GMATPrepNow » Mon Oct 25, 2021 6:17 am

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Brent@GMATPrepNow wrote:
Sun Oct 24, 2021 7:35 am
Is kx < ky?

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

Answer: E
Source: www.gmatprepnow.com
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
Brent Hanneson - Creator of GMATPrepNow.com
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