GRE Prep 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.
For which of the integers n, where 10 < n < 20, (n 1)! is not divisi
[#permalink]
16 Nov 2023, 02:27
16 Nov 2023, 02:27
Expert Reply
2
Bookmarks
00:00
Question Stats:
100% (01:21) correct
0% (00:00) wrong based on 5 sessions
Hide Show timer Statistics
For which of the integers n, where 10 < n < 20, (n − 1)! is not divisible by n.
Indicate all such values.
(A) 11
(B) 12
(C) 13
(D) 15
(E) 16
(F) 17
(G) 19
Indicate all such values.
(A) 11
(B) 12
(C) 13
(D) 15
(E) 16
(F) 17
(G) 19
Part of the project: The Butler-GRE Daily New Quant and Verbal Questions to Practice (2023) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
ShowHide Answer
Official Answer
A,C,F,G
Manager
Joined: 11 Nov 2023
Posts: 207
Given Kudos: 76
WE:Business Development (Advertising and PR)
For which of the integers n, where 10 < n < 20, (n 1)! is not divisi
[#permalink]
01 Dec 2023, 17:02
01 Dec 2023, 17:02
1
In order for (n-1)! to be divisible by n, there must be a combination of factors within (n-1)! that is a factor of n. Since (n-1)! is a product of all of the integers less than n, the only solutions are when n is a prime number.
To illustrate, let's look at option A, n = 11.
\(\frac{(11-1)!}{11} = \frac{10*9*8*7*6*5*4*3*2*1}{11}\)
There are no common factors between 10! and 11. Thus, A is an answer.
Option B, n = 12.
\(\frac{(12-1)!}{12} = \frac{11*10*9*8*7*6*5*4*3*2*1}{12}\)
Since 6*2 = 12, we know that (12-1)! is divisible by 12. Thus, B is NOT an answer.
Ideally you would see the pattern by now, but to test a few more:
Option C, n = 13
\(\frac{(13-1)!}{13} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{13}\)
Since 13 is a prime, there's aren't any factors other than itself and 1. Thus, C is an answer.
Option D, n = 14.
\(\frac{(14-1)!}{14} = \frac{13*12*11*10*9*8*7*6*5*4*3*2*1}{14}\)
Since 7*2 = 14, we know that (12-1)! is divisible by 14. Thus, B is NOT an answer.
To illustrate, let's look at option A, n = 11.
\(\frac{(11-1)!}{11} = \frac{10*9*8*7*6*5*4*3*2*1}{11}\)
There are no common factors between 10! and 11. Thus, A is an answer.
Option B, n = 12.
\(\frac{(12-1)!}{12} = \frac{11*10*9*8*7*6*5*4*3*2*1}{12}\)
Since 6*2 = 12, we know that (12-1)! is divisible by 12. Thus, B is NOT an answer.
Ideally you would see the pattern by now, but to test a few more:
Option C, n = 13
\(\frac{(13-1)!}{13} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{13}\)
Since 13 is a prime, there's aren't any factors other than itself and 1. Thus, C is an answer.
Option D, n = 14.
\(\frac{(14-1)!}{14} = \frac{13*12*11*10*9*8*7*6*5*4*3*2*1}{14}\)
Since 7*2 = 14, we know that (12-1)! is divisible by 14. Thus, B is NOT an answer.
gmatclubot
For which of the integers n, where 10 < n < 20, (n 1)! is not divisi [#permalink]
01 Dec 2023, 17:02
Moderators:
