NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 21:43 It is currently 25 Apr 2024, 21:43
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Which of the following has the greatest value?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
rahulms
Intern
Intern
Joined: 17 Jan 2010
Posts: 17
Own Kudos [?]: 134 [54]
Given Kudos: 8
Send PM
Which of the following has the greatest value? [#permalink] New post   25 Jan 2010, 00:20
3
Kudos
51
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

56% (01:59) correct 44% (01:58) wrong based on 542 sessions
Hide Show timer Statistics
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) \(1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}\)
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11667 [12]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   07 Mar 2015, 17:37
7
Kudos
5
Bookmarks
Expert Reply
Hi All,

Certain questions on the GMAT can be solved rather quickly if you spot the Number Properties involved and you have the ability to pattern-match.

The 'key' to answering this question quickly is the knowledge that 'squaring a positive fraction makes the fraction SMALLER, while square-rooting a positive fraction makes the fraction BIGGER.'

Here is the proof:

(1/2)^2 = (1/2)(1/2) = 1/4

Squaring the positive fraction made the fraction SMALLER.

Root(1/4) = Root(1)/Root(4) = 1/2

Square-rooting the positive fraction made the fraction BIGGER.

With that knowledge, take a look at the first 3 answer choices to this question. The prompt asks which of the 5 answers is biggest (and we'll get to all of the answers in a moment). Which of the first 3 answer choices is biggest? Notice how all 3 have the same fractions - one answer square-roots them all, one leaves them as is, and one squares them all. You should be able to say definitively that Answer A is the largest of those 3.

Next, a bit of estimation will come in handy. Notice how Answer A ADDS 4 fractions that are all fairly close to 1.... so that total has to be a little less than 4.....

What do Answers D and E do....? Without doing the calculation, you should notice how BOTH answers subtract at least one fraction; by extension, there's no way that those 2 totals are close to 4.

Final Answer:
Show Spoiler
A


GMAT assassins aren't born, they're made,
Rich
General Discussion
User avatar
gurpreetsingh
SVP
SVP
Joined: 12 Oct 2009
Status:<strong>Nothing comes easy: neither do I want.</strong>
Posts: 2279
Own Kudos [?]: 3594 [1]
Given Kudos: 235
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Send PM
Reviews Badge
Re: Which of the following has the greatest value? [#permalink] New post   25 Jan 2010, 06:19
1
Bookmarks
x^m is greater when

M is more if X >1
M is less if X <1

in this case out of a b c , a will hav max value.

option E > D clearly

in E . 3/4 is greater than 1/3

that means E is at most 1+4/5 = 9/5

now in option 1... \sqrt{2}/\sqrt{3} is smallest .

Thus sum of option 1 is atleast 4*\sqrt{2}/\sqrt{3} which comes more than 2

and 9/5 is less than 2.

lol this method seems to be weird but i calculated it in dat way only
User avatar
Bullet
Intern
Intern
Joined: 17 Nov 2009
Posts: 21
Own Kudos [?]: 168 [3]
Given Kudos: 9
Concentration: General Business Administration
Schools:University of Toronto, Mcgill, Queens
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   14 Feb 2010, 01:53
2
Kudos
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) \(1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}\)

Show Spoiler
A


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
User avatar
prashantbacchewar
Manager
Manager
Joined: 20 Apr 2010
Posts: 154
Own Kudos [?]: 248 [0]
Given Kudos: 28
Concentration: Finacee, General Management
Schools:ISB, HEC, Said
 Q48  V28
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   21 Sep 2010, 05:17
It seems to be easy but time consuming. What is the source of this problem.
User avatar
prashantbacchewar
Manager
Manager
Joined: 20 Apr 2010
Posts: 154
Own Kudos [?]: 248 [0]
Given Kudos: 28
Concentration: Finacee, General Management
Schools:ISB, HEC, Said
 Q48  V28
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   21 Sep 2010, 05:19
This seems to be simple but time consuming problem what is the source?
User avatar
onedayill
Manager
Manager
Joined: 25 Feb 2010
Posts: 208
Own Kudos [?]: 320 [1]
Given Kudos: 10
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   21 Sep 2010, 06:01
prashantbacchewar wrote:
This seems to be simple but time consuming problem what is the source?


If its taking more time then try this:

Try to find out the option which has the lowest denominator so it will result in greater value.
User avatar
shrouded1
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2931 [2]
Given Kudos: 25
Location: London
 Q51  V41
Send PM
GMAT ToolKit User Reviews Badge
Re: Which of the following has the greatest value? [#permalink] New post   21 Sep 2010, 06:08
2
Kudos
prashantbacchewar wrote:
This seems to be simple but time consuming problem what is the source?


I really think this is one of those problems which can throw you off because it seems complicated, but I do believe its one of those questions you can easily do in less than 30 secs ... and its this kind of stuff that will make you save time in the real GMAT

Between A,B,C --> A is clearly the biggest

D is clearly less than B, it has the same terms some positive and some negative

E is also less than B : 4/5 - 3/4 + 2/3 + 2/3 which is less than 2/3-3/4+4/5+5/6, which has to be less than B

No calculations, just a quick manipulation mentally is sufficient
User avatar
prashantbacchewar
Manager
Manager
Joined: 20 Apr 2010
Posts: 154
Own Kudos [?]: 248 [0]
Given Kudos: 28
Concentration: Finacee, General Management
Schools:ISB, HEC, Said
 Q48  V28
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   21 Sep 2010, 06:44
shrouded1

Thanks for sharing approach +1 to you
User avatar
metallicafan
Retired Moderator
Joined: 04 Oct 2009
Status:2000 posts! I don't know whether I should feel great or sad about it! LOL
Posts: 767
Own Kudos [?]: 3947 [0]
Given Kudos: 109
Location: Peru
Concentration: Finance, SMEs, Developing countries, Public sector and non profit organizations
Schools:Harvard, Stanford, Wharton, MIT &amp; HKS (Government)
GPA: 4.0
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   21 Sep 2010, 14:21
+1 A

I think that here is not necessary to make many calculations.
You can eliminate some options with just watching.
User avatar
P
chesstitans
VP
VP
Joined: 12 Dec 2016
Posts: 1030
Own Kudos [?]: 1779 [0]
Given Kudos: 2562
Location: United States
Schools: Stanford '19 Carroll '19 LBS '19
GMAT 1: 700 Q49 V33
GPA: 3.64
Send PM
GMAT ToolKit User
Re: Which of the following has the greatest value? [#permalink] New post   17 Apr 2017, 17:31
E is less than B because E = 1/4 + 1/3 + 4/5 < 2/3 + 4/5 => E <B
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64925 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   27 Jul 2018, 01:34
2
Kudos
1
Bookmarks
Expert Reply
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) \(1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}\)



All terms of each option are 1 or less than 1. Options (D) and (E) have negative terms and a quick look shows that they will certainly be less than the other 3 options. So ignore them.

Out of (B) and (C), compare first terms of each: 2/3 (= 6/9) of option (B) is more than 4/9 of option (C). All other terms will follow the same pattern so (B) is greater than (C)

Now compare the first terms of options (A) and (B): \(\sqrt{2}/\sqrt{3} ( = \sqrt{6}/3\) = 2.something / 3) while first term of option (B) is just 2/3. So the first term of option (A) is greater. All other terms will follow the same pattern.

Hence option (A) is greatest.
User avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1720
Own Kudos [?]: 1344 [0]
Given Kudos: 607
Location: United States
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   20 Nov 2019, 07:46
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) \(1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}\)


D vs. E: E > D
\(-\frac{1}{3}+ \frac{4}{5}<\frac{4}{5} + \frac{1}{3}\)

B vs. E: B > E
\(\frac{2}{3} + \frac{3}{4} + \frac{4}{5}>\frac{4}{5} + \frac{1}{3} + \frac{1}{4}\)

B vs. C: B > C
A proper fraction raised to a positive number gets smaller.

B vs. A: A > B
When we take the root of a proper fraction it gets larger.

Ans (A)
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32681
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Which of the following has the greatest value? [#permalink] New post   30 May 2023, 13:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Which of the following has the greatest value? [#permalink]
30 May 2023, 13:08
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions