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25 Jul 2024, 01:17
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
100% (00:30) wrong based on 2 sessions
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26 Aug 2024, 12:27
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Official Explanation
In this question, you are asked to compare the quantity 950^2000 with the quantity 10^6000. Note that both quantities are written in the form “base to a power.” If the bases were equal, you would be able to compare the quantities by comparing the powers. Because powers of 10 are easier to work with than powers of 950, it is reasonable to try to compare the quantities by rewriting the quantity 950^2000 as a power of 10. Unfortunately, there is no obvious way to do that. However, if you can approximate 950 by a power of 10, you may then be able to use the approximation to compare the quantity 950^2000 with the quantity 10^6000.
Note that 950 is close to, but a little less than, 1,000, or 10^3. Raising both sides of the inequality 950<10^3 to the power 2,000 gives the inequality 950<10^3 < [(10)^3]^2000 = 10^6000. Since [(10)^3]^2000, you can conclude that 950^2000<10^6000. Thus, Quantity A is less than Quantity B, and the correct answer is Choice B.
In this question, you are asked to compare the quantity 950^2000 with the quantity 10^6000. Note that both quantities are written in the form “base to a power.” If the bases were equal, you would be able to compare the quantities by comparing the powers. Because powers of 10 are easier to work with than powers of 950, it is reasonable to try to compare the quantities by rewriting the quantity 950^2000 as a power of 10. Unfortunately, there is no obvious way to do that. However, if you can approximate 950 by a power of 10, you may then be able to use the approximation to compare the quantity 950^2000 with the quantity 10^6000.
Note that 950 is close to, but a little less than, 1,000, or 10^3. Raising both sides of the inequality 950<10^3 to the power 2,000 gives the inequality 950<10^3 < [(10)^3]^2000 = 10^6000. Since [(10)^3]^2000, you can conclude that 950^2000<10^6000. Thus, Quantity A is less than Quantity B, and the correct answer is Choice B.
