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.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
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
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
16 Sep 2014, 01:07
Kudos
Bookmarks
If \(x = 10^{10}\), \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}\) is closest to:
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)
16 Sep 2014, 01:07
Kudos
Bookmarks
Official Solution:
If \(x = 10^{10}\), \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}\) is closest to:
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)
Reduce by \(x^2\) to get \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200} = \frac{1 + \frac{2}{x} + \frac{7}{x^2} }{3 - \frac{10}{x} + \frac{200}{x^2} }\).
For large \(x\), such as \(10^{10}\), terms like \(\frac{2}{x}\), \(\frac{7}{x^2}\), \(\frac{10}{x}\), and \(\frac{200}{x^2}\) become significantly small and approach 0. As a result, the fraction approximates \(\frac{1}{3}\).
Alternative Explanation
Substitute: \(x = 10^{10}\):
\(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}=\)
\(=\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200}\).
Note that we are asked to find an approximate value of the expression. Now, observe that \(10^{20}\) is a significantly larger number than \(2*10^{10} + 7\), which makes \(2*10^{10} + 7\) negligible in comparison. Likewise, \(3*10^{20}\) is much larger than \(-10*10^{10} + 200\), rendering \(-10*10^{10} + 200\) also negligible.
Therefore, \(\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200} \approx \frac{10^{20} }{3*10^{20} }=\frac{1}{3}\).
Answer: B
If \(x = 10^{10}\), \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}\) is closest to:
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)
Reduce by \(x^2\) to get \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200} = \frac{1 + \frac{2}{x} + \frac{7}{x^2} }{3 - \frac{10}{x} + \frac{200}{x^2} }\).
For large \(x\), such as \(10^{10}\), terms like \(\frac{2}{x}\), \(\frac{7}{x^2}\), \(\frac{10}{x}\), and \(\frac{200}{x^2}\) become significantly small and approach 0. As a result, the fraction approximates \(\frac{1}{3}\).
Alternative Explanation
Substitute: \(x = 10^{10}\):
\(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}=\)
\(=\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200}\).
Note that we are asked to find an approximate value of the expression. Now, observe that \(10^{20}\) is a significantly larger number than \(2*10^{10} + 7\), which makes \(2*10^{10} + 7\) negligible in comparison. Likewise, \(3*10^{20}\) is much larger than \(-10*10^{10} + 200\), rendering \(-10*10^{10} + 200\) also negligible.
Therefore, \(\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200} \approx \frac{10^{20} }{3*10^{20} }=\frac{1}{3}\).
Answer: B
General Discussion
11 Sep 2015, 14:52
Kudos
Bookmarks
I think this is a high-quality question and I agree with explanation.
