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Which of the following is the greatest? (A) 1/√2+1/√4+1/

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by hazelnut01 » Sun May 07, 2017 5:36 am
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
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by [email protected] » Sun May 07, 2017 9:23 am
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?

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by Jay@ManhattanReview » Sun May 07, 2017 8:48 pm
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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by GMATGuruNY » Mon May 08, 2017 3:18 am
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
To make it easier to compare the fractions, replace the denominators (2, 4, 6, 8) with PERFECT SQUARES 4, 9, 16, 25.

A --> (1/√4)+(1/√9)+(1/√16)+(1/√25) = 1/2 + 1/3 + 1/4 + 1/5 = 3/4 + 1/3 + 1/5.

B --> (1/4²)+(1/9²)+(1/16²)+(1/25²) = 1/2� + 1/3� + 1/4� + 1/5� = less than A.

C --> 1/2� + 1/2� + 1/2¹� + 1/2²� = less than A.

D --> 1 - 1/4 + 1/9 - 1/16 = 3/4 + 1/9 - 1/16 = 1ess than A.

E --> 1/4 + 1/9 + 1/16 + 1/25 = less than A.

The correct answer is A.
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by Matt@VeritasPrep » Thu May 11, 2017 8:55 pm
We could also just rough it out conceptually:

(A) is the sum of four fractions between 1/1 and 1/3.

(B) is the sum of four fractions from 1/4 to 1/64. Smaller than A.

(C) is the sum of four fractions from 1/4 to 1/256. Smaller than A.

(D) is 1/2 + 1/12. 1/√2 is bigger than 1/2 and 1/√4 is bigger than 1/12. Smaller than A.

(E) is all the terms from (A), but with their denominators squared, making each fraction smaller than its counterpart in A. Smaller than A.
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