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16 Sep 2014, 00:28
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What is the value of \(6x^2 + 9y^2\)?
(1) \(x = 2\)
(2) \(6y^2 + 4x^2 = 22\)
(1) \(x = 2\)
(2) \(6y^2 + 4x^2 = 22\)
16 Sep 2014, 00:28
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Official Solution:
What is the value of \(6x^2 + 9y^2\)?
By factoring out 3 from the given expression, we can reframe the question to: what is the value of \(3(2x^2 + 3y^2)\)?
(1) \(x = 2\)
This statement is insufficient as it provides no information about \(y\).
(2) \(6y^2 + 4x^2 = 22\)
Factoring out 2 from the above equation, we get: \(2(3y^2 + 2x^2) = 22\). This simplifies to \(3y^2 + 2x^2 = 11\). Therefore, \(3(2x^2 + 3y^2) = 3*11 = 33\). Sufficient.
Answer: B
What is the value of \(6x^2 + 9y^2\)?
By factoring out 3 from the given expression, we can reframe the question to: what is the value of \(3(2x^2 + 3y^2)\)?
(1) \(x = 2\)
This statement is insufficient as it provides no information about \(y\).
(2) \(6y^2 + 4x^2 = 22\)
Factoring out 2 from the above equation, we get: \(2(3y^2 + 2x^2) = 22\). This simplifies to \(3y^2 + 2x^2 = 11\). Therefore, \(3(2x^2 + 3y^2) = 3*11 = 33\). Sufficient.
Answer: B
19 Oct 2023, 00:34
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
