Always the sum of n proper fractions is lesser than it's sum reciprocal.

Be careful, that concept will get you in trouble. Consider this example:

Quantity A	Quantity B
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\)	\( \frac{1}{ \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}}\)

Here, the correct answer is A.
So we actually need to find the value of Quantity A first (or we can find the approximate value as you'll see in my solution below).
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Key property: If \(0 < k < 1\), then \(k < \frac{1}{k}\)
Example: \(0.4 < \frac{1}{0.4}\)

Important: To apply the above property, we need not actually calculate the sum of the fractions in Quantity A. Instead, we can use some number sense to approximate the value.

We know that \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4} = 1\)

Since \(\frac{1}{5}\), \(\frac{1}{6}\) and \(\frac{1}{7}\) are each LESS THAN \(\frac{1}{4}\), we can be certain that \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\) equals some number less than 1.

So we have:
QUANTITY A: some number that's between 0 and 1
QUANTITY B: 1/(some number that's between 0 and 1)

When we apply the above property, we see that Quantity A < Quantity B

Answer: B
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