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.
k is a positive integer and 225 and 216 are both divisors of
[#permalink]
Updated on: 02 Feb 2020, 13:29
Updated on: 02 Feb 2020, 13:29
5
1
Expert Reply
4
Bookmarks
00:00
Question Stats:
68% (02:04) correct
31% (01:58) wrong based on 297 sessions
Hide Show timer Statistics
k is a positive integer and 225 and 216 are both divisors of k. If \(k = 2^a \times 3^b \times 5^c\), where a, b and are positive integers, what is the least possible value of \(a + b + c\)?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Kudos for the right answer and explanation
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Kudos for the right answer and explanation
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Given Kudos: 0
GPA: 3.72
Re: k is a positive integer and 225 and 216 are both divisors of
[#permalink]
02 Feb 2020, 11:19
02 Feb 2020, 11:19
9
2
Bookmarks
Carcass wrote:
k is a positive integer and 225 and 216 are both divisors of k. If \(k - 2^a \times 3^b \times 5^c\), where a, b and are positive integers, what is the least possible value of \(a + b + c\)?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Kudos for the right answer and explanation
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Kudos for the right answer and explanation
\(225 = 5^2 * 3^2\) and \(216 = 2^3 * 3^3\)
Since 225 and 216 are both divisors of \(k\), it must be that \(k\) is a multiple of the LCM of 225 and 216
=> \(k\) = Multiple of \(5^2 * 3^3 * 2^3\)
Since \(k = 2^a \times 3^b \times 5^c\), and we need the minimum values of \(a, b, c\), we take:
=> \(k\) = \(5^2 * 3^3 * 2^3\) = \(5^c * 3^b * 2^a\)
=> \(a = 3\), \(b = 3\), \(c = 2\)
=> \(a + b + c = 8\)
Answer E
General Discussion
Re: k is a positive integer and 225 and 216 are both divisors of
[#permalink]
26 Jul 2021, 06:00
26 Jul 2021, 06:00
3
Easiest way to solve this question is to do the prime factorization of both 225 and 216.
225: (3)^2 (5)^1
216:(3)^3 * (2)^3 * (5)^2
The least common multiple is therefore a = 3, b =3, c = 2.
Finally, 3 + 3 + 2 = 8.
B.O.L
225: (3)^2 (5)^1
216:(3)^3 * (2)^3 * (5)^2
The least common multiple is therefore a = 3, b =3, c = 2.
Finally, 3 + 3 + 2 = 8.
B.O.L
