MathRevolution wrote:
Is x < 1/y?
1) y > 0
2) xy < 1
Target question: Is x < 1/y? Statement 1: y > 0 No information about x, so statement 1 is NOT SUFFICIENT
Statement 2: xy < 1 IMPORTANT: some students will want to divide both sides by y to get x < 1/y, HOWEVER doing so is incorrect, because we don't know whether y is POSITIVE or NEGATIVE.
If y is POSITIVE, then dividing both sides by y gives us
x < 1/yIf y is NEGATIVE, then dividing both sides by y gives us
x > 1/y [when we divide both sides by a negative value, we must REVERSE the direction of the inequality]Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that y is POSITIVE
Statement 2 tells us that xy < 1
Since we know that y is POSITIVE, we can safely divide both sides by y to get the inequality
x < 1/y.
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
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