jamifahad wrote:

Solve this under 2 mins.

Which of the following represents the greatest value?

A) \(\sqrt{2} / \sqrt{3} + \sqrt{3}/\sqrt{4}+\sqrt{4}/\sqrt{5}+\sqrt{5}/\sqrt{6}\)

B) \(2/3 + 3/4 + 4/5 + 5/6\)

C) \(2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2\)

D) \(1-1/3 + 4/5 - 3/4\)

E) \(1-3/4 + 4/5 + 1/3\)

I think for most people the only confusing options will be A and B.

You can compare fractions very easily by making either their denominator or numerator same.

Say I want to compare \(\sqrt{2} / \sqrt{3}\) with 2/3.

I just multiply and divide \(\sqrt{2} / \sqrt{3}\) by \(\sqrt{2}\) to get 2/\(\sqrt{6}\).

Since \(\sqrt{6}\) is less than 3, 2/\(\sqrt{6}\) (i.e. \(\sqrt{2} / \sqrt{3}\)) is greater than 2/3.

Similarly, all terms of option A will be greater than all corresponding terms of option B.

Perfect example of how complicated looking questions are also based on very fundamental concepts.

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Karishma

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