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16 Sep 2014, 00:14
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Difficulty:
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64% (01:01) correct
36%
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Which of the following expressions has the greatest value?
A. \(1^{999}\)
B. \(2^{300}\)
C. \(3^{200}\)
D. \(4^{100}\)
E. \(16^{50}\)
A. \(1^{999}\)
B. \(2^{300}\)
C. \(3^{200}\)
D. \(4^{100}\)
E. \(16^{50}\)
16 Sep 2014, 00:14
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Official Solution:
Which of the following expressions has the greatest value?
A. \(1^{999}\)
B. \(2^{300}\)
C. \(3^{200}\)
D. \(4^{100}\)
E. \(16^{50}\)
To compare the given expressions effectively, consider a common base or power. Observe that all expressions can be expressed as some power of 100:
A. \(1^{999}\). Taking 1 to any power is still 1. If the base were a different number, then we could approximate the answer by using a power of 1,000.
B. \(2^{300} = 2^{3*100}=(2^3)^{100} = 8^{100}\).
C. \(3^{200} =3^{2*100} = (3^2)^{100} = 9^{100}\).
D. \(4^{100} = 4^{100}\).
E. \(16^{50} = (4^2)^{50} = 4^{100}\).
Therefore, option C, \(3^{200}\), has the greatest value.
Answer: C
Which of the following expressions has the greatest value?
A. \(1^{999}\)
B. \(2^{300}\)
C. \(3^{200}\)
D. \(4^{100}\)
E. \(16^{50}\)
To compare the given expressions effectively, consider a common base or power. Observe that all expressions can be expressed as some power of 100:
A. \(1^{999}\). Taking 1 to any power is still 1. If the base were a different number, then we could approximate the answer by using a power of 1,000.
B. \(2^{300} = 2^{3*100}=(2^3)^{100} = 8^{100}\).
C. \(3^{200} =3^{2*100} = (3^2)^{100} = 9^{100}\).
D. \(4^{100} = 4^{100}\).
E. \(16^{50} = (4^2)^{50} = 4^{100}\).
Therefore, option C, \(3^{200}\), has the greatest value.
Answer: C
General Discussion
iamgregmaicher
Joined: 11 Aug 2016
Last visit: 02 Feb 2023
Posts: 6
Own Kudos:
Given Kudos: 14
Location: United States (PA)
Concentration: Finance, General Management
Schools: UNC Kenan-Flagler (II)
GMAT 1: 710 Q48 V40
GPA: 2.42
WE:Other (Mutual Funds and Brokerage)
23 Sep 2016, 18:31
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I think this is a high-quality question and I agree with explanation. Fantastic solution. So simple!
