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27 Sep 2016, 17:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:40) correct
37%
(01:53)
wrong
based on 551
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
three roots.png [ 34.21 KiB | Viewed 7127 times ]
(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
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
Answer (C)
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)
General Discussion
27 Sep 2016, 18:45
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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
\(\sqrt{5}\) , \(\sqrt[3]{2}\), \(\sqrt[4]{401}\)
\(\sqrt[3]{5^6}\), \(\sqrt[3]{2^4}\), \(\sqrt[4]{401^3}\)
We know \(2^4\) < \(5^6\), so II < I
\(5^6\) = \(125^3\) <\(401^3\)
So I < III
II < I < III
Option C
