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Thelegend2631
Posts: 371
Updated on: 31 Aug 2021, 00:31
Originally posted by Thelegend2631 on 30 Aug 2021, 22:11.
Last edited by Bunuel on 31 Aug 2021, 00:31, edited 5 times in total.
Last edited by Bunuel on 31 Aug 2021, 00:31, edited 5 times in total.
Renamed the topic and edited the question.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
48% (00:57) correct
52%
(00:53)
wrong
based on 112
sessions
History
Date
Time
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Not Attempted Yet
30 Aug 2021, 22:33
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hD13
\(\sqrt{X^6} \)= \( x^{\frac{6}{2}}\) = \(x^3\)
so \(x^3 = y^3\) which implies x = y
Can x be negative ?
Even roots of negative number are not real, so expression inside the square root has to be positive and in the case in hand no matter x is negative or positive \(x^6\) will be positive. so the condition is always met for for negative or positive values of x.
Statement 1 is sufficient IMO, as statement 2 is not a necessary condition.
what is OA?
31 Aug 2021, 00:39
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Is \(x = y\) ?
(1) \(\sqrt{x^6} = y^3\);
Take the square root from x^6: \(|x^3| = y^3\) (recall that \(\sqrt{a^2}=|a|\), so \(\sqrt{x^6} = \sqrt{(x^3)^2}=|x^3|\)).
So, we have \(|x^3| = y^3\);
If \(x < 0\), then we'd get \(-x^3 = y^3\), which in turn means that \(-x = y\). So, in this case \(x \neq y\). For example, \(-x = y = -1\);
If \(x \geq 0\), then we'd get \(x^3 = y^3\), which in turn means that \(x = y\). So, in this case \(x = y\). For example, \(x = y = 1\).
Not sufficient.
(2) \(x > 0\). Not sufficient.
(1)+(2) Since from (2) we are given that x > 0, then we have the second case from (1), so x = y. Sufficient.
Answer: C.
(1) \(\sqrt{x^6} = y^3\);
Take the square root from x^6: \(|x^3| = y^3\) (recall that \(\sqrt{a^2}=|a|\), so \(\sqrt{x^6} = \sqrt{(x^3)^2}=|x^3|\)).
So, we have \(|x^3| = y^3\);
If \(x < 0\), then we'd get \(-x^3 = y^3\), which in turn means that \(-x = y\). So, in this case \(x \neq y\). For example, \(-x = y = -1\);
If \(x \geq 0\), then we'd get \(x^3 = y^3\), which in turn means that \(x = y\). So, in this case \(x = y\). For example, \(x = y = 1\).
Not sufficient.
(2) \(x > 0\). Not sufficient.
(1)+(2) Since from (2) we are given that x > 0, then we have the second case from (1), so x = y. Sufficient.
Answer: C.
