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# M01-08

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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15 Sep 2014, 23:14
1
10
00:00

Difficulty:

25% (medium)

Question Stats:

66% (00:34) correct 34% (00:36) wrong based on 179 sessions

### HideShow timer Statistics

Which expression has the greatest value?

A. $$1^{999}$$
B. $$2^{300}$$
C. $$3^{200}$$
D. $$4^{100}$$
E. $$16^{50}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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15 Sep 2014, 23:14
3
1
Official Solution:

Which expression has the greatest value?

A. $$1^{999}$$
B. $$2^{300}$$
C. $$3^{200}$$
D. $$4^{100}$$
E. $$16^{50}$$

Find a common base or a common power to compare the statements. Use 100 as a common power, because all expressions are more or less divisible by 100:
1. $$1^{999} = 1^{100}$$

Taking 1 to any power is still 1. If the base was a different number, then we could approximate the answer by using a power of 1,000.
2. $$2^{300} = (2^3)^{100} = 8^{100}$$
3. $$3^{200} = (3^2)^{100} = 9^{100}$$
4. $$4^{100} = 4^{100}$$
5. $$16^{50} = (4^2)^{50} = 4^{100}$$

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Intern
Joined: 11 Aug 2016
Posts: 9
Location: United States (PA)
Concentration: Finance, General Management
GMAT 1: 710 Q48 V40
GPA: 2.42
WE: Other (Mutual Funds and Brokerage)

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23 Sep 2016, 17:31
I think this is a high-quality question and I agree with explanation. Fantastic solution. So simple!
Intern
Joined: 18 Nov 2011
Posts: 4

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28 Dec 2016, 14:35
Since this is a PS question. shouldn't the answer choices be either ascending or descending?
Founder
Joined: 04 Dec 2002
Posts: 17239
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5

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28 Dec 2016, 15:06
2
CircleOfLife wrote:
Since this is a PS question. shouldn't the answer choices be either ascending or descending?

You mean to make it easier for you to answer the question?
Good try....

P.S. On the GMAT if a question asks for the largest/smallest value, the answer choices do NOT follow a pattern.
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Joined: 26 Feb 2018
Posts: 53
Location: India
GMAT 1: 560 Q41 V27
WE: Web Development (Computer Software)

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04 Apr 2018, 11:49
I think this is a high-quality question and I agree with explanation. A good question with a little trick to follow.
Intern
Joined: 14 Jun 2018
Posts: 47
Location: India

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03 Sep 2018, 02:10
Intern
Joined: 01 Aug 2018
Posts: 2
Location: United Arab Emirates
GPA: 3.32
WE: Analyst (Commercial Banking)

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26 Sep 2018, 05:20
Why wasn't choice E's 4^2 changed into 16^100?
Intern
Joined: 01 Aug 2018
Posts: 2
Location: United Arab Emirates
GPA: 3.32
WE: Analyst (Commercial Banking)

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26 Sep 2018, 05:21
Nevermind my question. Took me two seconds
Re: M01-08   [#permalink] 26 Sep 2018, 05:21
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# M01-08

Moderators: chetan2u, Bunuel

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