rahulms wrote:

which of the following has the greatest value?

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

B) \(\frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6}\)

C) \(\frac{2^2}{3^2} + \frac{3^2}{4^2} + \frac{4^2}{5^2} + \frac{5^2}{6^2}\)

D) \(1 - \frac{1}{3} + \frac{4}{5} - \frac{3}{4}\)

E) \(1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}\)

One of this type question is also in the

GMATclub tests as well i didn't remember which one it was. However in order to solve the greatest value for the options available we have to find out the lowest denominator of the options available and use POE method.

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

B) \(\frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6}\)

C) \(\frac{2^2}{3^2} + \frac{3^2}{4^2} + \frac{4^2}{5^2} + \frac{5^2}{6^2}\)

For all these options it is quite evident that option A has the lowest denominator so it will result in greater value because of the root.

D) \(1 - \frac{1}{3} + \frac{4}{5} - \frac{3}{4}\)

E) \(1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}\)

if you quickly solve D and E will reveal that denominator is greater than the option A

So it must be A

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