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16 Nov 2021, 02:11
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If \(x^2y^3 = 200\), what is the value of \(xy\) ?
(1) \(y\) is an integer
(2) \(x\) is an integer
(1) \(y\) is an integer
(2) \(x\) is an integer
16 Nov 2021, 02:11
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Official Solution:
If \(x^2y^3 = 200\), what is the value of \(xy\) ?
Factorize: \(200=5^2*2^3=x^2*y^3\).
(1) \(y\) is an integer
If \(y=1\), then \(x=\sqrt{200}\) or \(x=-\sqrt{200}\) and in this case \(xy=\sqrt{200}\) or \(-\sqrt{200}\)
Of course there are infinitely many other solutions possible.
Not sufficient.
(2) \(x\) is an integer
If \(x=1\), then \(y=\sqrt[3]{200}\) and in this case \(xy=\sqrt[3]{200}\)
If \(x=2\), then \(y=\sqrt[3]{50}\) and in this case \(xy=2\sqrt[3]{50}\)
Of course there are infinitely many other solutions possible.
Not sufficient.
(1)+(2) Since both \(x\) and \(y\) are integers, then \(y\) must be 2 but because of even power, \(x\) could be 5 or -5. So, \(xy\) could be 10 or -10. Not sufficient.
Answer: E
If \(x^2y^3 = 200\), what is the value of \(xy\) ?
Factorize: \(200=5^2*2^3=x^2*y^3\).
(1) \(y\) is an integer
If \(y=1\), then \(x=\sqrt{200}\) or \(x=-\sqrt{200}\) and in this case \(xy=\sqrt{200}\) or \(-\sqrt{200}\)
Of course there are infinitely many other solutions possible.
Not sufficient.
(2) \(x\) is an integer
If \(x=1\), then \(y=\sqrt[3]{200}\) and in this case \(xy=\sqrt[3]{200}\)
If \(x=2\), then \(y=\sqrt[3]{50}\) and in this case \(xy=2\sqrt[3]{50}\)
Of course there are infinitely many other solutions possible.
Not sufficient.
(1)+(2) Since both \(x\) and \(y\) are integers, then \(y\) must be 2 but because of even power, \(x\) could be 5 or -5. So, \(xy\) could be 10 or -10. Not sufficient.
Answer: E
26 Sep 2024, 10:05
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