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Rank those three in order from smallest to biggest.

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Magoosh GMAT Instructor
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Rank those three in order from smallest to biggest.  [#permalink]

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New post 27 Sep 2016, 17:20
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:37) correct 40% (01:41) wrong based on 127 sessions

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Attachment:
three roots.png
three roots.png [ 34.21 KiB | Viewed 1829 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
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Re: Rank those three in order from smallest to biggest.  [#permalink]

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New post 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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Re: Rank those three in order from smallest to biggest.  [#permalink]

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New post 24 Dec 2017, 07:02
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2
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

Answer (C)
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Re: Rank those three in order from smallest to biggest.  [#permalink]

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New post 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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Re: Rank those three in order from smallest to biggest.  [#permalink]

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New post 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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Re: Rank those three in order from smallest to biggest.  [#permalink]

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New post 21 Jun 2019, 00:38
Approached the question by trying to find the 4th power of all the choices so as to eliminate the 4th root of 401 in Choice III. In doing so, we get
Choice I - 400
Choice II - 324
Choice III - 401

So arranging from smallest to largest, we get II < I < III. Hence, Option C is the right answer.
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Re: Rank those three in order from smallest to biggest.   [#permalink] 21 Jun 2019, 00:38
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