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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