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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
07 Mar 2024, 00:58
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:05) correct
46%
(02:26)
wrong
based on 399
sessions
History
Date
Time
Result
Not Attempted Yet
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 \(0\)
15 Mar 2024, 14:00
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
General Discussion
07 Mar 2024, 01:10
Kudos
Bookmarks
Bunuel
We can approximate the values
\(\frac{7^{5} - 10^{20}}{5^{20} - 3^{5}} \approx \frac{- 10^{20}}{5^{20}}\)
\(\approx - 2^{20} \approx - 2^{10} * 2^{10} \)
\(\approx - 1024 * 1024 \)
\(\approx -10^6 *\) Some Value
Hence the final value will be less than \(-10^6\)
Option A
