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
