GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Which is greater: 10^7 or 7^10?
[#permalink]
26 Oct 2017, 23:42
26 Oct 2017, 23:42
9
Bookmarks
00:00
Question Stats:
63% (00:56) correct
36% (00:47) wrong based on 98 sessions
Hide Show timer Statistics
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which is greater: 10^7 or 7^10?
[#permalink]
30 Oct 2017, 14:43
30 Oct 2017, 14:43
5
1
Bookmarks
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?
[#permalink]
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
