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

Question

\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

BrentGMATPrepNow · Accepted Answer

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 \(\frac{1}{0.37}=\frac{100}{37} ≈ 3\)

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 	imes 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

KarishmaB · Answer

Approximate.

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

1/36 = .02something

Answer (B)

UB001 · Answer

\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

ksrutisagar · Answer

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

bishal128 · Answer

1/(1/n+1/m)=n*m/(n+m)=(0.03*0.37)/0.40=0.0111/0.40=111/4000=100/4000+10/4000+1/4000, since 1/4=0.25, 1/40=0.025 and with each numerator with one less zero the decimal will increase with consecutive result being 0.025+0.0025+0.00025 when adding up gives0.02775

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

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

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