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If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1
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07 Apr 2019, 06:49
07 Apr 2019, 06:49
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If \(mn = 3\) and \(\frac{1}{m} + \frac{1}{n} = \frac{4}{3}\), then what is the value of \((0.1) + (0.1)^\frac{1}{m} + (0.1)^\frac{1}{n}\) ?
(A) \(0.2 + 0.1^\frac{1}{3}\)
(B) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{1}{2}\)
(C) \(0.1 + 0.1^\frac{4}{3} + 0.1^\frac{1}{2}\)
(D) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{3}{2}\)
(E) \(0.1 + 0.1^\frac{1}{4} + 0.1^\frac{1}{2}\)
(A) \(0.2 + 0.1^\frac{1}{3}\)
(B) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{1}{2}\)
(C) \(0.1 + 0.1^\frac{4}{3} + 0.1^\frac{1}{2}\)
(D) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{3}{2}\)
(E) \(0.1 + 0.1^\frac{1}{4} + 0.1^\frac{1}{2}\)
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Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1
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07 Apr 2019, 07:14
07 Apr 2019, 07:14
1
Carcass wrote:
If \(mn = 3\) and \(\frac{1}{m} + \frac{1}{n} = \frac{4}{3}\), then what is the value of \((0.1) + (0.1)^\frac{1}{m} + (0.1)^\frac{1}{n}\) ?
(A) \(0.2 + 0.1^\frac{1}{3}\)
(B) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{1}{2}\)
(C) \(0.1 + 0.1^\frac{4}{3} + 0.1^\frac{1}{2}\)
(D) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{3}{2}\)
(E) \(0.1 + 0.1^\frac{1}{4} + 0.1^\frac{1}{2}\)
(A) \(0.2 + 0.1^\frac{1}{3}\)
(B) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{1}{2}\)
(C) \(0.1 + 0.1^\frac{4}{3} + 0.1^\frac{1}{2}\)
(D) \(0.1 + 0.1^\frac{1}{3} + 0.1^\frac{3}{2}\)
(E) \(0.1 + 0.1^\frac{1}{4} + 0.1^\frac{1}{2}\)
GIVEN:
mn = 3
1/m + 1/n = 4/3
Upon inspection, we might recognize that one possible solution to the above system is m = 1 and n = 3
So, 0.1 + 0.1^(1/m) + 0.1^(1/n) = 0.1 + 0.1^(1/1) + 0.1^(1/3)
= 0.1 + 0.1^(1) + 0.1^(1/3)
= 0.1 + 0.1 + 0.1^(1/3)
= 0.2 + 0.1^(1/3)
Answer: A
Cheers,
Brent
gmatclubot
Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 [#permalink]
07 Apr 2019, 07:14
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