Is x<1/y?
1) y>0
2) xy<1
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Is x<1/y?
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- Max@Math Revolution
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Target question: Is x < 1/y?Max@Math Revolution wrote:Is x < 1/y?
1) y > 0
2) xy < 1
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/y
If 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 = C
RELATED VIDEO
Inequalities - Part I: https://www.gmatprepnow.com/module/gmat ... /video/979
- Max@Math Revolution
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If we modify the original condition and the question, in case of inequality, square is very important. If we multiply y^2 to both sides, we get xy^2<y?, xy^2-y<0?, y(xy-1)<0?. There are 2 variables (x and y) and there is a high chance that C is the correct answer. Using 1) & 2), the answer is always yes and the condition is sufficient. Thus, the correct answer is C.
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