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Rank the following quantities in order, from smallest to biggest.

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Rank the following quantities in order, from smallest to biggest. [#permalink]

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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.
[Reveal] Spoiler: OA

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Re: Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 13 Mar 2015, 09:10
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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
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Expert Post
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Posts: 44599
Re: Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 15 Mar 2015, 22:08
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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.


MAGOOSH OFFICIAL SOLUTION:

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.

Answer = (A).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 09 Apr 2015, 18:07
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.
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Re: Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 09 Apr 2015, 22:33
Hi Kzivrev

choice D also have I before II
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Re: Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 10 Apr 2015, 16:14
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 :)
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Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 11 Dec 2017, 20:39
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.


Hi Bunuel

Can you please help me to clarify the doubt.

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 \(\sqrt{5/9}\)
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Re: Rank the following quantities in order, from smallest to biggest. [#permalink]

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New post 11 Dec 2017, 20:49
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rahul16singh28 wrote:
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.


Hi Bunuel

Can you please help me to clarify the doubt.

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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: Rank the following quantities in order, from smallest to biggest.   [#permalink] 11 Dec 2017, 20:49
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