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.
Jun 0210:00 AM PDT
-11:00 AM PDT
Probability is one of the most important GMAT Quant topics because it often combines logic, counting, set theory, and permutations & combinations. Many students try to solve probability questions by listing every possible case, but GMAT probability...- Jun 03
08:30 AM PDT
-09:30 AM PDT
In Episode 7 of our GMAT Ninja CR series, we are rounding up the oddballs, the misfits, and the format-benders: EXCEPT, Fill-In-The-Blanks, and other unusual Critical Reasoning question types. When you see a question that ends with a literal blank line 
May 2910:00 AM IST
-11:00 PM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.- Jun 04
08:30 AM PDT
-09:30 AM PDT
For most test takers, Data Insights is the most challenging section on the GMAT, with test takers scoring several points lower on average on DI than on Quant or Verbal and completing the section with less time to spare. - 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..
23 Jan 2024, 02:55
Kudos
Bookmarks
For how many integer values of \(n\) is \(\frac{n^2 + 6n + 24}{n + 3}\) an integer?
A. 1
B. 2
C. 4
D. 6
E. 8
A. 1
B. 2
C. 4
D. 6
E. 8
23 Jan 2024, 02:55
Kudos
Bookmarks
Official Solution:
For how many integer values of \(n\) is \(\frac{n^2 + 6n + 24}{n + 3}\) an integer?
A. 1
B. 2
C. 4
D. 6
E. 8
Start with completing the square in the numerator:
Split the fraction:
Since \(n + 3\) is an integer, the whole expression will be an integer whenever \(\frac{15}{n + 3}\) is an integer.
For \(\frac{15}{n + 3}\), the denominator, \(n+3\), must be a divisor of 15. Since \(15 = 3*5\), it has \((1 + 1)(1 + 1) = 4\) positive divisors and 4 negative ones: 1, 3, 5, 15, -1, -3, -5, and -15. Therefore, \(n\) can take a total of 8 values: -2, 0, 2, 12, -4, -6, -8, and -18, respectively.
Answer: E
For how many integer values of \(n\) is \(\frac{n^2 + 6n + 24}{n + 3}\) an integer?
A. 1
B. 2
C. 4
D. 6
E. 8
Start with completing the square in the numerator:
\(\frac{n^2 + 6n + 24}{n + 3} = \frac{n^2 + 6n + 9 + 15}{n + 3} = \frac{(n + 3)^2 + 15}{n + 3}\).
Split the fraction:
\(\frac{(n + 3)^2 + 15}{n + 3} = \frac{(n + 3)^2}{n + 3} + \frac{15}{n + 3} = n + 3 + \frac{15}{n + 3}\).
Since \(n + 3\) is an integer, the whole expression will be an integer whenever \(\frac{15}{n + 3}\) is an integer.
For \(\frac{15}{n + 3}\), the denominator, \(n+3\), must be a divisor of 15. Since \(15 = 3*5\), it has \((1 + 1)(1 + 1) = 4\) positive divisors and 4 negative ones: 1, 3, 5, 15, -1, -3, -5, and -15. Therefore, \(n\) can take a total of 8 values: -2, 0, 2, 12, -4, -6, -8, and -18, respectively.
Answer: E
18 Jan 2025, 01:13
Kudos
Bookmarks
I like the solution - it’s helpful.
