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