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If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m

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Bunuel
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If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink] New post   07 Apr 2019, 21:26
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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) \(0.1 + 0.1^\frac{1}{4} + 0.1^\frac{1}{2}\)
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lynnglenda
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If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink] New post   07 Apr 2019, 21:47
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mn = 3 => m = n/3 1/m + 1/n = 4/3 =>m+n/mn = 4/3 (we know that mn = 3) => m+n = 4
Substituting for m below:
m+n=4 => n/3 + n = 4 => we get the equation to solve for n(n2-4n+3=0) and we get n=1 or n=3.
Using these values, we know that m will also be either 1 or 3.
Hence Answer is A.

Answer : A
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Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink] New post   08 Apr 2019, 11:50
An easy way to solve the question is by options:

We know 1/m + 1/n = 4/3

In all the options from B thru E, there is an initial (.1) with unity power and two .1s with a fractional power

Since question statement asks us to evaluate .1 + .1^(1/m) + .1^(1/n), we can see that the fractional powers in the options(from B to E) must be equal to 1/m + 1/n (which we know to be 4/3)

Considering each option from B to E, adding the fractional powers we see no fractions getting added to 4/3

Hence we can eliminate B to E and select A as the answer
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Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink] New post   23 Apr 2019, 05:46
lynnglenda wrote:
mn = 3 => m = n/3 1/m + 1/n = 4/3 =>m+n/mn = 4/3 (we know that mn = 3) => m+n = 4
Substituting for m below:
m+n=4 => n/3 + n = 4 => we get the equation to solve for n(n2-4n+3=0) and we get n=1 or n=3.
Using these values, we know that m will also be either 1 or 3.
Hence Answer is A.

Answer : A


how did you get to the step in bold above?
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Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink] New post   07 Sep 2020, 08:41
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Getting a common denominator, 1/m + 1/n = (m + n)/mn. But we know this is equal to 4/3 from the information in the question, so (m+n)/mn = 4/3. Since mn = 3, by substituting we find (m+n)/3 = 4/3, and m+n = 4. Now we know mn = 3 and m+n = 4, so we're looking for two numbers with a product of 3 and a sum of 4 (notice algebraically that this is exactly the situation you're in every time you factor a simple quadratic -- you know the sum and product of two numbers, and to factor, you find those two numbers). Those numbers are 3 and 1.

So 0.1 + 0.1^(1/m) + 0.1^(1/n) = 0.1 + 0.1^(1/1) + 0.1^(1/3) = 0.2 + 0.1^(1/3), which is answer A.
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Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink] New post   11 Jan 2023, 01:08
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Re: If mn = 3 and 1/m + 1/n = 4/3, then what is the value of 0.1 + 0.1^1/m [#permalink]
11 Jan 2023, 01:08
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