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.
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.
May 1501:00 PM IST
-11:00 AM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.
May 1810:00 AM PDT
-11:00 AM PDT
Join us in a live GMAT practice session and solve 25 challenging GMAT questions with other test takers in timed conditions, covering GMAT Quant, Data Sufficiency, Data Insights, Reading Comprehension, and Critical Reasoning questions.- May 19
12:00 PM PDT
-01:00 PM PDT
Scoring 329 on the GRE is not always about using more books, more courses, or a longer study plan. In this episode of GRE Success Talks, Ashutosh shares his GRE preparation strategy, study plan, and test-day experience, explaining how he kept his prep.... - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
26 Apr 2023, 02:46
Kudos
Bookmarks
If \(m \neq 0\) and \(\frac{m^4}{|m|} < \sqrt{m^2}\), then which of the following must be true?
I. \(m < \pi\)
II. \(m^2 < 1\)
III. \(m^3 > -8\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. \(m < \pi\)
II. \(m^2 < 1\)
III. \(m^3 > -8\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
26 Apr 2023, 02:46
Kudos
Bookmarks
Official Solution:
If \(m \neq 0\) and \(\frac{m^4}{|m|} < \sqrt{m^2}\), then which of the following must be true?
I. \(m < \pi\)
II. \(m^2 < 1\)
III. \(m^3 > -8\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Since \(\sqrt{m^2} = |m|\), we have \(\frac{m^4}{|m|} < |m|\).
Multiplying both sides by \(|m|\), we get \(m^4 < m^2\).
Dividing both sides by \(m^2\), we have \(m^2 < 1\).
This inequality implies that \(-1 < m < 1\).
So, essentially, the question asks: Given that \(-1 < m < 1\), which of the following statements must be true?
I. \(m < \pi\). Since \(-1 < m < 1\), it is correct to say that for any \(m\) from this range, \(m < \pi\).
II. \(m^2 < 1\). This statement is already established to be true from our earlier steps. So, this statement is always true.
III. \(m^3 > -8\). This inequality implies that \(m > -2\). Since \(-1 < m < 1\), it is true for all values of \(m\) in this range that \(m > -2\).
Answer: E
If \(m \neq 0\) and \(\frac{m^4}{|m|} < \sqrt{m^2}\), then which of the following must be true?
I. \(m < \pi\)
II. \(m^2 < 1\)
III. \(m^3 > -8\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Since \(\sqrt{m^2} = |m|\), we have \(\frac{m^4}{|m|} < |m|\).
Multiplying both sides by \(|m|\), we get \(m^4 < m^2\).
Dividing both sides by \(m^2\), we have \(m^2 < 1\).
This inequality implies that \(-1 < m < 1\).
So, essentially, the question asks: Given that \(-1 < m < 1\), which of the following statements must be true?
I. \(m < \pi\). Since \(-1 < m < 1\), it is correct to say that for any \(m\) from this range, \(m < \pi\).
II. \(m^2 < 1\). This statement is already established to be true from our earlier steps. So, this statement is always true.
III. \(m^3 > -8\). This inequality implies that \(m > -2\). Since \(-1 < m < 1\), it is true for all values of \(m\) in this range that \(m > -2\).
Answer: E
23 Jan 2025, 12:30
Kudos
Bookmarks
Bunuel Thanks for the explanation.
However , since its a must be true question, Incase of X<pie, how will x satisfy for -3 and -2
Similarly for option 3, x will not satisfy.
Can you please explain?
However , since its a must be true question, Incase of X<pie, how will x satisfy for -3 and -2
Similarly for option 3, x will not satisfy.
Can you please explain?
