Hi ziyuenlau,

To solve this question quickly, you should focus on COMPARING answers and NOT on calculating them. I'm going to give you some hints so that you can retry this question on your own:

1) 'Squaring' and 'square-rooting' are "opposite" functions. Consider the fractions in Answer A and Answer B. Would you end up with a greater result by squaring the denominator or square-rooting it?
2) Answers B and C are NOT the same. Figure out why.
3) What do answers D and E have in common? How are they different?

GMAT assassins aren't born, they're made,
Rich

ziyuenlau wrote:Which of the following is the greatest?

(A) (1/√2)+(1/√4)+(1/√6)+(1/√8)

(B) [1/(2^2)]+[1/(4^2)]+[1/(6^2)]+[1/(8^2)]

(C) [1/(2^2)]+[1/(2^4)]+[1/(2^6)]+[1/(2^8)]

(D) 1-(1/2)+(1/4)-(1/6)

(E) (1/2)+(1/4)+(1/6)+(1/8)

Source : GMATNinja
OA=A

For a number greater than 1, say 'a,'

1/√a > 1/a > 1/a^2;

For example, say a = 2, then 1/2 = 0.5; 1/√2 = 1/1.414 = 0.707; 1/2^2 = 1/4 = 0.25

With these results in mind, let's analyze the values of the options.

(A) (1/√2)+(1/√4)+(1/√6)+(1/√8): It can be greatest as the four terms are of form 1/√a.

(B) [1/(2^2)]+[1/(4^2)]+[1/(6^2)]+[1/(8^2)]: Compared with Option A, it cannot be the greatest as the four terms are of form 1/a^2.

(C) [1/(2^2)]+[1/(2^4)]+[1/(2^6)]+[1/(2^8)]: Compared with Option B, it cannot be the greatest as its last two terms are less than the respective last two terms of Option B.

(D) 1-(1/2)+(1/4)-(1/6) = 1/2 + 1/12: Compared with Option A, it cannot be the greatest as its last term (1/12) is less than each of the last three terms of Option A.

(E) (1/2)+(1/4)+(1/6)+(1/8): compared with Option A, it cannot be the greatest as the four terms are of form 1/a.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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