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1/[(1/0.03) + (1/0.37)] =

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1/[(1/0.03) + (1/0.37)] = [#permalink] New post   22 Sep 2016, 22:50
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\(\frac{1}{\frac{1}{0.03} + \frac{1}{0.37}} = \)


(A) 0.004
(B) 0.02775
(C) 2.775
(D) 3.6036
(E) 36.036
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Re: 1/[(1/0.03) + (1/0.37)] = [#permalink] New post   12 Mar 2022, 07:14
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sidoknowia wrote:
1/[(1/0.03) + (1/0.37)] = ?


(A) 0.004
(B) 0.02775
(C) 2.775
(D) 3.6036
(E) 36.036


STRATEGY: When I scan the answer choices, I see that they're very spread apart. For example, answer choice B is 6 times answer choice A; answer choice C is 100 times answer choice B, and so on.
This means we can be very aggressive with our estimation and still identify the correct answer.

PRO TIP #1: If you're having difficulty estimating the value of \(\frac{1}{0.03}\), recognize that we can create an equivalent fraction by multiplying numerator and denominator by 100 to get \(\frac{100}{3}\), which is approximately \(33\)

Applying the same strategy to the other fraction in the denominator we get \(\frac{1}{0.37}=\frac{100}{37} ≈ 3\)


Now substitute these values into the given expression to get: \(\frac{1}{\frac{1}{0.03} + \frac{1}{0.37}} ≈ \frac{1}{33 + 3} ≈ \frac{1}{36} \)

PRO TIP #2: Taking a fraction that has a denominator that's a power of \(10\) is easy to convert to a decimal. For example \(\frac{8}{100} = 0.08\) and \(\frac{123}{100,000} = 0.00123\)

So, let's write \(\frac{1}{36}\) with a denominator of \(100\).

Since \(3 \times 36\) is pretty close to \(100\), so let's take \(\frac{1}{36}\) and multiply numerator and denominator by \(3\) to get approximately \(\frac{3}{100}\), which equals \(0.03\)

Check the answer choices . . . B is the only option that's close to \(0.03\)

Answer: B
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Re: 1/[(1/0.03) + (1/0.37)] = [#permalink] New post   22 Sep 2016, 22:55
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sidoknowia wrote:
1 / [ (1 / 0.03) + ( 1 / 0.37) ] = ?


(A) 0.004
(B) 0.02775
(C) 2.775
(D) 3.6036
(E) 36.036


Source 1000 Series

Is there any other way apart from doing tedious-math? :?


Approximate.

1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36

1/36 = .02something

Answer (B)
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Re: 1/[(1/0.03) + (1/0.37)] = [#permalink] New post   04 Jan 2019, 01:01
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sidoknowia wrote:
1/[(1/0.03) + (1/0.37)] = ?


(A) 0.004
(B) 0.02775
(C) 2.775
(D) 3.6036
(E) 36.036


Project PS Butler : Question #107


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By inspection Denominator > 1 , So Choices C, D, and E are ruled out

Also, if Choice A were the answer, denominator would be (1/0.004) = 250, Which is not the case ( By Inspection)

So, Choice B remains
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Re: 1/[(1/0.03) + (1/0.37)] = [#permalink] New post   29 Dec 2018, 12:02
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\(\frac{1}{(1/0.03+1/0.37)}\)

\(\frac{1}{((0.37+0.03)/(0.03 * 0.37))}\)

\(\frac{(0.03 * 0.37)}{0.40}\)

Here we see that 0.37 ≈ 0.40
Just consider 0.37/0.40 Denominator is slightly greater than Numerator so the answer is close to 0.03 is less than 0.03.
From the answer choices we see that 0.02775 matches our required value.

Answer Option B is Correct
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Re: 1/[(1/0.03) + (1/0.37)] = [#permalink] New post   11 Aug 2023, 22:27
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Re: 1/[(1/0.03) + (1/0.37)] = [#permalink]
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