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16 Sep 2014, 00:14
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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
28 Dec 2016, 16:06
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CircleOfLife
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.
