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Which is greater: 10^7 or 7^10?
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26 Oct 2017, 23:42
26 Oct 2017, 23:42
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Question Stats:
64% (00:56) correct
36% (00:47) wrong based on 100 sessions
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Quantity A |
Quantity B |
\(10^7\) |
\(7^{10}\) |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Kudos for correct solution.
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Joined: 10 Apr 2015
Posts: 6218
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Re: Which is greater: 10^7 or 7^10?
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30 Oct 2017, 14:43
30 Oct 2017, 14:43
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Bunuel wrote:
Quantity A |
Quantity B |
10^7 |
7^10 |
We can solve this question using matching operations
Given:
Quantity A: 10^7
Quantity B: 7^10
Divide both quantities by 7^7 to get;
Quantity A: (10^7)/(7^7)
Quantity B: (7^10)/(7^7)
Simplify to get;
Quantity A: (10/7)^7
Quantity B: 7^3
ASIDE: If you're wondering how I got (10/7)^7 for Quantity A, I used a nice rule that says (b^x)/c^x) = (b/c)^x
Evaluate 7^3 to get;
Quantity A: (10/7)^7
Quantity B: 343
First recognize that 2^7 = 128
Since 10/7 is LESS THAN 2, we can conclude that (10/7)^7 is some number less than 128
So we have:
Quantity A: some number less than 128
Quantity B: 343
Answer: B
Cheers,
Brent
General Discussion
Re: Which is greater: 10^7 or 7^10?
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27 Oct 2017, 02:35
27 Oct 2017, 02:35
2
One way to solve it could be to rewrite \(7^10 = 7^7 7^3\) and divide both sides by \(7^7\). Thus, we have to compare \(\frac{10}{7}^7\) and \(7^3\). Given that 10/7 is roughly 1.5, it is easy to notice that quantity B is greater. Answer B
