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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
First of all, clearly \(\sqrt{2/3}=\sqrt{\frac{4}{9}}<\sqrt{\frac{5}{9}}\)
So, II is bigger than I. Now, what about III? When we take higher order roots, the values move closer to one. If the number starts larger than one, then higher and higher roots make it smaller, closer to one. If the number starts between 0 and 1, then higher and higher roots make it larger, closer to one. Therefore, III is larger than II. From smallest to biggest, I, II, III.
Re: Rank the following quantities in order, from smallest to biggest.
[#permalink]
Show Tags
13 Mar 2015, 08:10
2
2
Bunuel wrote:
Rank the following quantities in order, from smallest to biggest.
I. 2/3
II. \(\sqrt{\frac{5}{9}}\)
III. \(\sqrt[5]{\frac{5}{9}}\)
(A) I, II, III (B) I, III, II (C) II, I, III (D) III, I, II (E) III, II, I
Kudos for a correct solution.
in positive numbers , we should remember that square root of a fraction is always greater than the fraction...that is \(\sqrt{x/y}\)> \(x/y\), where x<y.... and square or higher power of a fraction will keep reducing the value with higher powers... \(2/3\)=\(\sqrt{4/9}\)<\(\sqrt{5/9}\)<5\(\sqrt{4/9}\) so ans A..l,ll,lll
_________________
Re: Rank the following quantities in order, from smallest to biggest.
[#permalink]
Show Tags
09 Apr 2015, 17:07
well to figure out the first two expresion it is easy to determine that II > I, so since it is asked to make smalest to bigest, we can conclude that I needs to be before II, looking in the answer choices only A has I before II so safely we can pick A as final answer. Im sure if the answer choices had different setup the outcome would be much harder to determine if we are not sure how to evaulate III.
Re: Rank the following quantities in order, from smallest to biggest.
[#permalink]
Show Tags
10 Apr 2015, 15:14
HI Naina1, you are totlay correct, I didnt see that one , I guess was just lucky to get the correct answer, I was doing it fast, and I do understant the concept behind the root fraction. I hope to be lucky on the D-day
From Stmnt 1 & 2 when we compare the numerator of fraction then \(\sqrt{5}\) > 2. However, \(\sqrt{5/9}\) can be written as \(\sqrt{5}\)/3 or \(\sqrt{5}\) / -3 when base is +ve \(\sqrt{5}/\) 3 > 2/3 but when base is -ve \(\sqrt{5}/\) -3 < 2/3.
Please advise how do we decide on the base of \(\sqrt{5/9}\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
From Stmnt 1 & 2 when we compare the numerator of fraction then \(\sqrt{5}\) > 2. However, \(\sqrt{5/9}\)can be written as \([fraction]5[/fraction]\)/ 3 or \(\sqrt{5}\) / -3 when base is +ve \(\sqrt{5}/\) 3 > 2/3 but when base is -ve \(\sqrt{5}/\) -3 < 2/3.
Please advise how do we decide on the base of \sqrt{5/9}
Hi.. Square root is always positive.. So √9= 3 only.. But square is where you look at both + & - X^2=9.. x=3 or -3
_________________
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Rank the following quantities in order, from smallest to biggest.
[#permalink]
Show Tags
21 Apr 2018, 23:56
Bunuel wrote:
Rank the following quantities in order, from smallest to biggest.
I. 2/3
II. \(\sqrt{\frac{5}{9}}\)
III. \(\sqrt[5]{\frac{5}{9}}\)
(A) I, II, III (B) I, III, II (C) II, I, III (D) III, I, II (E) III, II, I
Kudos for a correct solution.
2/3 = \(\sqrt{\frac{4}{9}}\) <\(\sqrt{\frac{5}{9}}\) So, I < II
Now since 0<5/9<1.. So powers will reduce its value and roots will increase its value. Square root will be lees than cube root will be less than 4th root will be less than 5th root.. and so on.. Th value will keep on increasing towards 1.
close
48% (01:30) correct 
