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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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Rank those three in order from smallest to biggest.
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27 Sep 2016, 16:20
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60% (01:34) correct 40% (01:39) wrong based on 135 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, IThis 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 GMATMike
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Re: Rank those three in order from smallest to biggest.
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27 Sep 2016, 18:44
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, IThis 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 GMATMike 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.
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24 Dec 2017, 06:02
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.
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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



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Re: Rank those three in order from smallest to biggest.
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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



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Re: Rank those three in order from smallest to biggest.
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20 Jun 2019, 23:38
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.




Re: Rank those three in order from smallest to biggest.
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20 Jun 2019, 23:38




