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03 Sep 2022, 04:33
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (00:57) correct
25%
(00:37)
wrong
based on 32
sessions
History
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Time
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Not Attempted Yet
If x and y are none zero, is \(\frac{x^3y^5}{x^2y^3} > 0\)?
(1) x > 0
(2) y > 0
(1) x > 0
(2) y > 0
06 Sep 2022, 00:32
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Bunuel
Solution:
We are given that x and y are non zero
Disclaimer: assuming imaginary numbers are not part of it
We are asked if \(\frac{x^3y^5}{x^2y^3}\) is positive or not
A fraction can be positive only if both numerator and denominator are either negative or positive
An interesting thing to notice here is we have \(y^5\) and \(y^3\) in the numerator and the denominator has odd powers which mean their positive-negative nature will be the same i.e., either both negative or both positive
So, the whole \(\frac{x^3y^5}{x^2y^3}\) being positive or not depends on the nature of \(x\) alone
Statement 1: \(x>0\)
If x is positive, we can be sure that \(\frac{x^3y^5}{x^2y^3}\) will be positive
Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: \(y>0\)
It doesn't matter what the nature of y is
Thus, statement 2 alone is not sufficient
Hence the right answer is Option A
06 Sep 2022, 01:16
Kudos
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\(\frac{x^3 y^5 }{ x^2 y^3} > 0\)
\(x y^2 > 0\)
The value of \(y^2\) will be positive no matter the value of \(y\). Therefore, in order for the the inequality to hold \(x\) must be positive \((x>0)\).
(1) x > 0
As \(x\) is positive, the inequality holds and therefore we can answer the question with a definite "yes".
Sufficient
(2) y > 0
Irrelevant to the inequality as we know that no matter the value of \(y\), \(y^2\) will be positive. We need to know whether or not \(x\) is positive
Insufficient
Answer A
\(x y^2 > 0\)
The value of \(y^2\) will be positive no matter the value of \(y\). Therefore, in order for the the inequality to hold \(x\) must be positive \((x>0)\).
(1) x > 0
As \(x\) is positive, the inequality holds and therefore we can answer the question with a definite "yes".
Sufficient
(2) y > 0
Irrelevant to the inequality as we know that no matter the value of \(y\), \(y^2\) will be positive. We need to know whether or not \(x\) is positive
Insufficient
Answer A
