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# Rank the following quantities in order, from smallest to biggest. I 2

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4675
Rank the following quantities in order, from smallest to biggest. I 2 [#permalink]

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05 Jan 2015, 15:46
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Difficulty:

95% (hard)

Question Stats:

38% (01:14) correct 62% (01:18) wrong based on 147 sessions

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Rank the following quantities in order, from smallest to biggest.

I. $$2^{120}$$

II. $$3^{72}$$

III. $$17^{30}$$

(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) III, I, II
(E) III, II, I

For the OE for this problem, as well as a 11 other challenging problems in exponents & powers & roots, see:
http://magoosh.com/gmat/2014/challengin ... and-roots/

Mike
[Reveal] Spoiler: OA

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Magoosh Test Prep

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Joined: 13 May 2011
Posts: 201
Concentration: Strategy, Technology
GMAT 1: 750 Q49 V42
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WE: Accounting (Consulting)
Rank the following quantities in order, from smallest to biggest. I 2 [#permalink]

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11 Jun 2015, 03:15
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I. $$2^{120}$$

II. $$3^{72}$$

III. $$17^{30}$$

Let's simplify!
We can't uniform the bases, but it's obvious that exponents can be simplified (they are all multiples of 6).

First,
$$2^{120} = (2^{20})^6$$
$$3^{72}=(3^{12})^6$$
$$17^{30}=(17^5)^6$$

ok, this didn't help much, but let's try to compare only 2 at a time:

$$2^{120} = (2^{20})^6 = (2^{5})^{24} = 32^{24}$$
$$3^{72}=(3^{12})^6 = (3^{3})^{24} = 27^{24}$$

Clearly, I > II

Great! Now, lets compare first and third (120 and 30 are easier).

$$2^{120} = (2^{4})^{30} = 16^{30}$$, clearly < $$17^{30}$$

Hence, III > I > II. Answer:
[Reveal] Spoiler:
C

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Manager
Joined: 05 Jun 2015
Posts: 84
Location: United States
WE: Engineering (Transportation)
Re: Rank the following quantities in order, from smallest to biggest. I 2 [#permalink]

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17 Sep 2016, 20:22
We need to compare $$2^{12}$$, $$3^{72}$$ and $$17^{30}$$

The exponents 120, 72 and 30 have 6 as common factor.

rewriting, $$(2^{20}){6}$$, $$(2^{12}){6}$$, $$(17^{5}){6}$$

the last term: $$(2^4 +1 )^{5}){6}$$
$$(2^{20} + 5 *2^{14} +......){6}$$
This is definitely greater than the first term..Second term is the smallest.

Hence, III > I > II
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Re: Rank the following quantities in order, from smallest to biggest. I 2 [#permalink]

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10 Dec 2017, 13:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Rank the following quantities in order, from smallest to biggest. I 2   [#permalink] 10 Dec 2017, 13:15
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