Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 13:52 ### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

1
7 00:00

Difficulty:   85% (hard)

Question Stats: 47% (01:30) correct 53% (01:33) wrong based on 331 sessions

### HideShow timer Statistics Rank the following quantities in order, from smallest to biggest.

I. 2/3

II. $$\sqrt{\frac{5}{9}}$$

III. $$\sqrt{\frac{5}{9}}$$

(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.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

1
4
Bunuel wrote:
Rank the following quantities in order, from smallest to biggest.

I. 2/3

II. $$\sqrt{\frac{5}{9}}$$

III. $$\sqrt{\frac{5}{9}}$$

(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.

_________________
##### General Discussion
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

2
2
Bunuel wrote:
Rank the following quantities in order, from smallest to biggest.

I. 2/3

II. $$\sqrt{\frac{5}{9}}$$

III. $$\sqrt{\frac{5}{9}}$$

(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
_________________
Intern  Joined: 06 Jun 2014
Posts: 45
Re: Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

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.
Manager  Joined: 05 Feb 2015
Posts: 50
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

Hi Kzivrev

choice D also have I before II
Intern  Joined: 06 Jun 2014
Posts: 45
Re: Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

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 Director  P
Joined: 31 Jul 2017
Posts: 515
Location: Malaysia
GMAT 1: 700 Q50 V33 GPA: 3.95
WE: Consulting (Energy and Utilities)
Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

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

I. 2/3

II. $$\sqrt{\frac{5}{9}}$$

III. $$\sqrt{\frac{5}{9}}$$

(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

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.. !!
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Rank the following quantities in order, from smallest to biggest.  [#permalink]

### Show Tags

1
rahul16singh28 wrote:
Bunuel wrote:
Rank the following quantities in order, from smallest to biggest.

I. 2/3

II. $$\sqrt{\frac{5}{9}}$$

III. $$\sqrt{\frac{5}{9}}$$

(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

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.

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
_________________
Director  D
Joined: 13 Mar 2017
Posts: 731
Location: India
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

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

I. 2/3

II. $$\sqrt{\frac{5}{9}}$$

III. $$\sqrt{\frac{5}{9}}$$

(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.

Hence, $$\sqrt{\frac{5}{9}}$$ < $$\sqrt{\frac{5}{9}}$$

So, II < III

Hence, I < II < III.
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish". Re: Rank the following quantities in order, from smallest to biggest.   [#permalink] 22 Apr 2018, 00:56
Display posts from previous: Sort by

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