[Math Revolution GMAT math practice question]
Is xy>0?
1) x^3y>0
2) x^2y>0
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Is xy>0?
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Max@Math Revolution
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Target question: Is xy > 0?Max@Math Revolution wrote: Is xy > 0?
1) x³y > 0
2) x²y > 0
Statement 1: x³y > 0
Since x² is POSITIVE, we can safely divide both sides of the inequality by x²
When we do this, we get xy > 0
So, the answer to the target question is YES, xy IS greater than 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x²y > 0
Once again, we can safely divide both sides of the inequality by x²
However, this time we get y > 0
So, we now know that y is POSITIVE, but we don't know whether x is positive or negative.
As such statement 2 is NOT SUFFICIENT
If you're not convinced, we can always test some values
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 1. In this case, xy = (1)(1) = 1. So, the answer to the target question is YES, xy IS greater than 0
Case b: x = -1 and y = 1. In this case, xy = (-1)(1) = -1. So, the answer to the target question is NO, xy is NOT greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Max@Math Revolution
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Since even powers are always non-negative, we can ignore the even exponents.
Condition 1)
x^3y > 0 is equivalent to xy > 0, which is the question itself. Therefore, condition 1) is sufficient.
Condition 2)
x^2y>0 is equivalent to y > 0.
It is not sufficient
Therefore, A is the answer.
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Since even powers are always non-negative, we can ignore the even exponents.
Condition 1)
x^3y > 0 is equivalent to xy > 0, which is the question itself. Therefore, condition 1) is sufficient.
Condition 2)
x^2y>0 is equivalent to y > 0.
It is not sufficient
Therefore, A is the answer.
Answer: A
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