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Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4485
Rank those three in order from smallest to biggest.  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 60% (01:34) correct 40% (01:39) wrong based on 135 sessions

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Attachment: three roots.png [ 34.21 KiB | Viewed 2029 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 _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Math Expert V
Joined: 02 Aug 2009
Posts: 8602
Re: Rank those three in order from smallest to biggest.  [#permalink]

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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
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Senior Manager  P
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Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: Rank those three in order from smallest to biggest.  [#permalink]

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1
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

Manager  Joined: 05 Jun 2015
Posts: 69
Location: United States
WE: Engineering (Transportation)
Re: Rank those three in order from smallest to biggest.  [#permalink]

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We can write all the terms with the same exponent
$$\sqrt{5}$$ , $$\sqrt{2}$$, $$\sqrt{401}$$
$$\sqrt{5^6}$$, $$\sqrt{2^4}$$, $$\sqrt{401^3}$$

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

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

II < I < III
Option C
Manager  S
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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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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
Intern  B
Joined: 10 Jun 2019
Posts: 9
Re: Rank those three in order from smallest to biggest.  [#permalink]

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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.   [#permalink] 20 Jun 2019, 23:38

# Rank those three in order from smallest to biggest.  