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 0808:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
09 Oct 2023, 09:38
Kudos
Bookmarks
For how many integer values of \(n\) does the expression \(\frac{100}{n - 7}\) yield an integer?
A. 4
B. 9
C. 12
D. 16
E. 18
A. 4
B. 9
C. 12
D. 16
E. 18
09 Oct 2023, 09:38
Kudos
Bookmarks
Official Solution:
For how many integer values of \(n\) does the expression \(\frac{100}{n - 7}\) yield an integer?
A. 4
B. 9
C. 12
D. 16
E. 18
Given that \(n\) is an integer, \(\frac{100}{n - 7}\) will be an integer if \(n-7\) is a divisor of 100. Upon factorizing 100, we find \(100 = 2^2*5^2\). Thus, 100 has \((2+1)(2+1) = 9\) positive divisor. However, there are an equal number of negative divisors. Therefore, \(\frac{100}{n - 7}\) will be an integer for 18 values of \(n-7\), and consequently for 18 values of \(n\).
Answer: E
For how many integer values of \(n\) does the expression \(\frac{100}{n - 7}\) yield an integer?
A. 4
B. 9
C. 12
D. 16
E. 18
Given that \(n\) is an integer, \(\frac{100}{n - 7}\) will be an integer if \(n-7\) is a divisor of 100. Upon factorizing 100, we find \(100 = 2^2*5^2\). Thus, 100 has \((2+1)(2+1) = 9\) positive divisor. However, there are an equal number of negative divisors. Therefore, \(\frac{100}{n - 7}\) will be an integer for 18 values of \(n-7\), and consequently for 18 values of \(n\).
Answer: E
General Discussion
miag
Expert
Verbal Forum Moderator
Joined: 10 Dec 2023
Last visit: 01 May 2026
Posts: 404
Own Kudos:
Given Kudos: 737
Location: India
Concentration: Marketing, Sustainability
Schools: Anderson '26 (A) Haas '26 (A) Kellogg '26 (A)
GMAT Focus 1: 675 Q87 V83 DI80 
GPA: 3.2/4
Products:
Expert reply
Schools: Anderson '26 (A) Haas '26 (A) Kellogg '26 (A)
GMAT Focus 1: 675 Q87 V83 DI80
Posts: 404
Kudos:
160
15 Apr 2025, 08:56
Kudos
Bookmarks
this was a great question!
