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
Which of the following is the greatest? (A) 1/√2+1/√4+1/
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 157
- Joined: Sat Nov 19, 2016 5:34 am
- Thanked: 2 times
- Followed by:4 members
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
For a number greater than 1, say 'a,'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
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
_________________
Manhattan Review GMAT Prep
Locations: New York | Vienna | Kuala Lumpur | Sydney | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
To make it easier to compare the fractions, replace the denominators (2, 4, 6, 8) with PERFECT SQUARES 4, 9, 16, 25.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
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
(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.