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# Rank those three in order from smallest to biggest.

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4489
Rank those three in order from smallest to biggest.  [#permalink]

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27 Sep 2016, 16:20
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:41) correct 38% (01:35) wrong based on 153 sessions

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Attachment:

three roots.png [ 34.21 KiB | Viewed 1443 times ]

Rank those three in order from smallest to biggest.

(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, II, I

This problem involves a bit of number sense. For a discussion of this skill, as well as the OE for this particular question, see:
Number Sense for the GMAT

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Joined: 05 Jun 2015
Posts: 82
Location: United States
WE: Engineering (Transportation)
Re: Rank those three in order from smallest to biggest.  [#permalink]

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27 Sep 2016, 17:45
We can write all the terms with the same exponent
$$\sqrt{5}$$ , $$\sqrt[3]{2}$$, $$\sqrt[4]{401}$$
$$\sqrt[3]{5^6}$$, $$\sqrt[3]{2^4}$$, $$\sqrt[4]{401^3}$$

We know $$2^4$$ < $$5^6$$, so II < I

$$5^6$$ = $$125^3$$ <$$401^3$$
So I < III

II < I < III
Option C
Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: Rank those three in order from smallest to biggest.  [#permalink]

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27 Sep 2016, 18:44
1
2
mikemcgarry wrote:
Attachment:
three roots.png

Rank those three in order from smallest to biggest.
(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, II, I

This problem involves a bit of number sense. For a discussion of this skill, as well as the OE for this particular question, see:
Number Sense for the GMAT

Mike

Get them in same roots..
I. 2√5= √(2*2*5)=√20= 4th root of 20*20 or 4th root of 400
II. 3√2=√3*3*2=√18 ---- so LESS than I

Let's check III now
III. 4th root of 401-------- so GREATER than I.. therefore the greatest

So smallest to largest ----- II, I, III

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Manager
Joined: 24 Oct 2013
Posts: 136
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: Rank those three in order from smallest to biggest.  [#permalink]

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27 Sep 2016, 19:55
for expressions like this we need to take lcm of the roots of the expressions

on taking lcm, these terms can be written as 5^6 , 2^4, 401^3

now its clear which one is smallest and which one is biggest term

2^4 < 5^6 < 401^3

Option C
Senior Manager
Joined: 02 Apr 2014
Posts: 473
GMAT 1: 700 Q50 V34
Re: Rank those three in order from smallest to biggest.  [#permalink]

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24 Dec 2017, 06:02
1
1
Raising the power of all the options to power 4, will help rank easily

1. $$(2 * \sqrt{5})^4$$ = $$2^4 * 5^2$$ = 400
2. $$(3 * \sqrt{2}) ^ 4$$ = $$3^4 * 2 ^ 2$$ = 81 * 4 = 324
3. $$(401 ^ {1/4})^4$$ = 401

Rank from smallest to biggest : 2, 1, 3

Re: Rank those three in order from smallest to biggest. &nbs [#permalink] 24 Dec 2017, 06:02
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