Which of the following is the greatest? (A) 1/âˆš2+1/âˆš4+1/

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hazelnut01: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Nov 19, 2016 5:34 amFollowed by: 4 members; Thanked: 2 times

by hazelnut01 » Sun May 07, 2017 5:36 am

Which of the following is the greatest?

(A) (1/âˆš2)+(1/âˆš4)+(1/âˆš6)+(1/âˆš8)

(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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Source: Beat The GMAT — Problem Solving | Sun May 07, 2017 5:36 am

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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?

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

Contact Rich at [email protected]

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun May 07, 2017 8:48 pm

ziyuenlau wrote:Which of the following is the greatest?

(A) (1/âˆš2)+(1/âˆš4)+(1/âˆš6)+(1/âˆš8)

(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/âˆša > 1/a > 1/a^2;

For example, say a = 2, then 1/2 = 0.5; 1/âˆš2 = 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/âˆš2)+(1/âˆš4)+(1/âˆš6)+(1/âˆš8): It can be greatest as the four terms are of form 1/âˆša.

(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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon May 08, 2017 3:18 am

ziyuenlau wrote:Which of the following is the greatest?

(A) (1/âˆš2)+(1/âˆš4)+(1/âˆš6)+(1/âˆš8)

(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/âˆš4)+(1/âˆš9)+(1/âˆš16)+(1/âˆš25) = 1/2 + 1/3 + 1/4 + 1/5 = 3/4 + 1/3 + 1/5.

B --> (1/4Â²)+(1/9Â²)+(1/16Â²)+(1/25Â²) = 1/2â�´ + 1/3â�´ + 1/4â�´ + 1/5â�´ = less than A.

C --> 1/2â�´ + 1/2â�¹ + 1/2Â¹â�¶ + 1/2Â²â�µ = 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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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

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/âˆš2 is bigger than 1/2 and 1/âˆš4 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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