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06 Oct 2016, 05:01
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If x > 0, what is the value of x^5?
(1) \(\sqrt{x} =32\)
(2) \(x^2 = 2^{20}\)
(DS05172)
(1) \(\sqrt{x} =32\)
(2) \(x^2 = 2^{20}\)
(DS05172)
02 Aug 2018, 05:27
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If x > 0, what is the value of x^5?
(1) \(\sqrt{x} =32\). Square: \(x = 32^2\). So, \(x^5 = (32^2)^5=32^{10}\). Sufficient.
(2) \(x^2 = 2^{20}\). Take the square root: \(|x| = \sqrt{2^{20}}\). Since given that x > 0, then |x| = x and thus we get: \(x = \sqrt{2^{20}}=2^{10}\). So, \(x^5 = (2^{10})^5=2^{50}\). Sufficient.
Answer: D.
Hope it helps.
(1) \(\sqrt{x} =32\). Square: \(x = 32^2\). So, \(x^5 = (32^2)^5=32^{10}\). Sufficient.
(2) \(x^2 = 2^{20}\). Take the square root: \(|x| = \sqrt{2^{20}}\). Since given that x > 0, then |x| = x and thus we get: \(x = \sqrt{2^{20}}=2^{10}\). So, \(x^5 = (2^{10})^5=2^{50}\). Sufficient.
Answer: D.
Hope it helps.
08 Oct 2016, 13:10
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Bunuel
If x > 0, what is the value of x^5 ?
(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20
(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20
We are given that x is greater than zero and need to determine the value of x^5.
Statement One Alone:
√x = 32
Using the equation in statement one, we can determine a value of x.
√x = 32
(√x)^2 = 32^2
x = 32^2 = (2^5)^2 = 2^10
Since x = 2^10, x^5 = (2^10)^5 = 2^50
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
x^2 = 2^20
Using the equation in statement two, we can determine a value of x.
√(x^2) = +/-√(2^20)
x = +/-2^10
Since x is positive, x = 2^10.
Since x = 2^10, x^5 = (2^10)^5 = 2^50.
Answer: D
