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.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
If n is a positive integer and the product of all integers from 1 to n
[#permalink]
24 Feb 2023, 08:36
24 Feb 2023, 08:36
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
100% (01:10) correct
0% (00:00) wrong based on 4 sessions
Hide Show timer Statistics
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A. 10
B. 11
C. 12
D. 13
E. 14
A. 10
B. 11
C. 12
D. 13
E. 14
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If n is a positive integer and the product of all integers from 1 to n
[#permalink]
27 Feb 2023, 02:15
27 Feb 2023, 02:15
1
Expert Reply
To solve this problem, we need to consider the prime factorization of 990, which is 2 × 3^2 × 5 × 11. The product of all integers from 1 to n can be written as n!, the factorial of n. To ensure that n! is a multiple of 990, n! must have at least one factor of 2, two factors of 3, one factor of 5, and one factor of 11.
The smallest integer that satisfies these conditions is 11, because:
The factors of 2 in 11! are: 2, 4, 6, 8, and 10.
The factors of 3 in 11! are: 3, 6, and 9.
The factors of 5 in 11! are: 5 and 10.
The factors of 11 in 11! is: 11.
Thus, the least possible value of n is 11, and the answer is (B).
The smallest integer that satisfies these conditions is 11, because:
The factors of 2 in 11! are: 2, 4, 6, 8, and 10.
The factors of 3 in 11! are: 3, 6, and 9.
The factors of 5 in 11! are: 5 and 10.
The factors of 11 in 11! is: 11.
Thus, the least possible value of n is 11, and the answer is (B).
gmatclubot
Re: If n is a positive integer and the product of all integers from 1 to n [#permalink]
27 Feb 2023, 02:15
Moderators:
