Events & Promotions
|
|
GMAT 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.
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
07 Mar 2024, 00:56
Kudos
Bookmarks
The value of \(\frac{7^{5} - 10^{20}}{5^{20} - 3^{5}}\) is
A. less than \(-10^6\)
B. greater than \(-10^6\) and less than \(-10^4\)
C. greater than \(-10^4\) and less than \(-10^2\)
D. greater than \(-10^2\) and less than \(0\)
E. greater than \(0\)
A. less than \(-10^6\)
B. greater than \(-10^6\) and less than \(-10^4\)
C. greater than \(-10^4\) and less than \(-10^2\)
D. greater than \(-10^2\) and less than \(0\)
E. greater than \(0\)
07 Mar 2024, 00:56
Kudos
Bookmarks
Official Solution:
The value of \(\frac{7^{5} - 10^{20}}{5^{20} - 3^{5}}\) is
A. less than \(-10^6\)
B. greater than \(-10^6\) and less than \(-10^4\)
C. greater than \(-10^4\) and less than \(-10^2\)
D. greater than \(-10^2\) and less than \(0\)
E. greater than \(0\)
Expressions both in the numerator and denominator are quite ugly and do not factor nicely. However, looking at the answer options, we see that they are well spread, which should be a hint that we should approximate.
Observe that \(10^{20}\) is a significantly larger number than \(7^{5}\), which makes \(7^{5}\) negligible in comparison. Likewise, \(5^{20}\) is much, much larger than \(3^{5}\), making \(3^{5}\) also negligible. Therefore:
The above expression will be less than -1,000,000, which is \(-10^6\).
Answer: A
The value of \(\frac{7^{5} - 10^{20}}{5^{20} - 3^{5}}\) is
A. less than \(-10^6\)
B. greater than \(-10^6\) and less than \(-10^4\)
C. greater than \(-10^4\) and less than \(-10^2\)
D. greater than \(-10^2\) and less than \(0\)
E. greater than \(0\)
Expressions both in the numerator and denominator are quite ugly and do not factor nicely. However, looking at the answer options, we see that they are well spread, which should be a hint that we should approximate.
Observe that \(10^{20}\) is a significantly larger number than \(7^{5}\), which makes \(7^{5}\) negligible in comparison. Likewise, \(5^{20}\) is much, much larger than \(3^{5}\), making \(3^{5}\) also negligible. Therefore:
\(\frac{7^{5} - 10^{20}}{5^{20} - 3^{5}} \approx \)
\(\approx\frac{-10^{20}}{5^{20}} = \)
\(=\frac{-2^{20}5^{20}}{5^{20}} = \)
\(=-2^{20} = \)
\(=-2^{10} 2^{10} \approx \)
\(\approx- 1,024*1,024\)
\(\approx\frac{-10^{20}}{5^{20}} = \)
\(=\frac{-2^{20}5^{20}}{5^{20}} = \)
\(=-2^{20} = \)
\(=-2^{10} 2^{10} \approx \)
\(\approx- 1,024*1,024\)
The above expression will be less than -1,000,000, which is \(-10^6\).
Answer: A
