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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: 4675
Rank those three in order from smallest to biggest. [#permalink]

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27 Sep 2016, 17:20
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45% (medium)

Question Stats:

61% (01:06) correct 39% (01:01) wrong based on 129 sessions

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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
[Reveal] Spoiler: OA

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Manager
Joined: 05 Jun 2015
Posts: 84
Location: United States
WE: Engineering (Transportation)
Re: Rank those three in order from smallest to biggest. [#permalink]

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27 Sep 2016, 18:45
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
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Posts: 5776
Re: Rank those three in order from smallest to biggest. [#permalink]

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27 Sep 2016, 19:44
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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
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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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Location: India
Concentration: General Management, Strategy
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Re: Rank those three in order from smallest to biggest. [#permalink]

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27 Sep 2016, 20:55
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
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Posts: 471
Re: Rank those three in order from smallest to biggest. [#permalink]

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24 Dec 2017, 07:02
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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.   [#permalink] 24 Dec 2017, 07:02
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