If xy<0, is (x^2)y<0?
1) x>0
2) (x^3)y<0
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If xy<0, is (x^2)y<0?
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- Max@Math Revolution
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Target question: Is x²y < 0 ?Max@Math Revolution wrote:If xy < 0, is x²y < 0?
1) x > 0
2) x³y < 0
Given: xy < 0
If the product xy is NEGATIVE, then there are only 2 possibilities
Possibility #1: x is positive and y is negative
Possibility #2: x is negative and y is positive
Statement 1: x > 0
If x is positive, then we can eliminate Possibility #2, leaving only Possibility #1
This means that x is POSITIVE and y is NEGATIVE
So, x²y = (POSITIVE²)(NEGATIVE) = NEGATIVE
In other words, we can conclude that x²y < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x³y < 0
What can we conclude from this?
Well, we can conclude that EITHER possibility #1 is true, OR EITHER possibility #2 is true
If possibility #1 is true, then x is POSITIVE and y is NEGATIVE, which means x²y = (POSITIVE²)(NEGATIVE) = NEGATIVE. So, x²y < 0
If possibility #2 is true, then x is NEGATIVE and y is POSITIVE, which means x²y = (NEGATIVE²)(POSITIVE) = POSITIVE. So, x²y > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
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Since xy < 0, x is NONZERO.If xy<0, is x²y<0?
1) x>0
2) x³y < 0
Since the square of a nonzero value is POSITIVE, x² > 0.
Implication:
We can safely divide both sides of the question stem by x²:
x²y < 0 ?
x²y/x² < 0/x² ?
y < 0?
Question stem, rephrased:
Is y < 0?
Statement 1:
Since x>0 and xy<0, y<0.
SUFFICIENT.
Statement 2:
Dividing both sides by x², we get:
x³y/x² < 0/x²
xy < 0.
Since the resulting inequality is given in the prompt, Statement 2 offers no new information about x or y.
INSUFFICIENT.
The correct answer is A.
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- Max@Math Revolution
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Answer is A
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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