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, 00:11
Kudos
Bookmarks
Is \(k\) a positive number?
(1) \(|k^3| + 1 > k\)
(2) \(k + 1 > |k^3|\)
(1) \(|k^3| + 1 > k\)
(2) \(k + 1 > |k^3|\)
16 Sep 2014, 00:12
Kudos
Bookmarks
Official Solution:
Is \(k\) a positive number?
(1) \(|k^3| + 1 > k\)
Test values:
If \(k\) is positive, then \(|k^3| =k^3\). In this case, we'd have \(k^3 + 1 > k\), and regardless of whether \(k\) is less than 1 or greater than or equal to 1, \(k^3 + 1\) will always be greater than \(k\). For example, consider 1/2, 2, ... ;
If \(k\) is 0, \(|k^3| + 1 > k\) is also true;
If \(k\) is negative, then the left-hand side, \(|k^3| + 1\), is positive, while the right-hand side, \(k\), is negative. Therefore, \(|k^3| + 1 > k\) holds for all negative values of \(k\).
Thus, we can conclude that \(|k^3| + 1 > k\) is true for all values of \(k\). As a result, this statement is completely useless in determining whether \(k\) is positive or not.
(2) \(k + 1 > |k^3|\)
Test some usual suspects:
Both \(k = 0\), giving a NO answer to the question, as well as \(k = 1\), giving an YES answer to the question, satisfy this statement. Not sufficient.
(1)+(2) Since the first statement does not limit the values of \(k\) and the second statement is not sufficient on its own, we cannot determine whether \(k\) is positive or not even when we combine the two statements. Not sufficient.
Answer: E
Is \(k\) a positive number?
(1) \(|k^3| + 1 > k\)
Test values:
If \(k\) is positive, then \(|k^3| =k^3\). In this case, we'd have \(k^3 + 1 > k\), and regardless of whether \(k\) is less than 1 or greater than or equal to 1, \(k^3 + 1\) will always be greater than \(k\). For example, consider 1/2, 2, ... ;
If \(k\) is 0, \(|k^3| + 1 > k\) is also true;
If \(k\) is negative, then the left-hand side, \(|k^3| + 1\), is positive, while the right-hand side, \(k\), is negative. Therefore, \(|k^3| + 1 > k\) holds for all negative values of \(k\).
Thus, we can conclude that \(|k^3| + 1 > k\) is true for all values of \(k\). As a result, this statement is completely useless in determining whether \(k\) is positive or not.
(2) \(k + 1 > |k^3|\)
Test some usual suspects:
Both \(k = 0\), giving a NO answer to the question, as well as \(k = 1\), giving an YES answer to the question, satisfy this statement. Not sufficient.
(1)+(2) Since the first statement does not limit the values of \(k\) and the second statement is not sufficient on its own, we cannot determine whether \(k\) is positive or not even when we combine the two statements. Not sufficient.
Answer: E
17 Jan 2018, 12:34
Kudos
Bookmarks
Hi everyone,
After demonstrating that each statement alone is not sufficient (by plugging in numbers), I proved that E is the correct answer by adding the two inequalities together:
(1) |K^3|+1>K
(2) K+1>|K^3|
Added together: |K^3|+ K+ 2 > |K^3| + K
After substracting (|K^3| + K) from both sides we get: 2 > 0, which is always true; therefore K can be any number, not only a positive one - the statements taken together are still not sufficent
After demonstrating that each statement alone is not sufficient (by plugging in numbers), I proved that E is the correct answer by adding the two inequalities together:
(1) |K^3|+1>K
(2) K+1>|K^3|
Added together: |K^3|+ K+ 2 > |K^3| + K
After substracting (|K^3| + K) from both sides we get: 2 > 0, which is always true; therefore K can be any number, not only a positive one - the statements taken together are still not sufficent
