|
|
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.
05 Jan 2023, 11:15
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (02:48) correct
45%
(02:17)
wrong
based on 49
sessions
History
Date
Time
Result
Not Attempted Yet
If positive integer \(A = m^3n^2\), where m and n are distinct prime numbers, is 54 a factor of A?
(1) 25mn is the least common multiple of 15 and 50
(2) The greatest common factor of \(15m^3\) and \(14n^2\) is 6
(1) 25mn is the least common multiple of 15 and 50
(2) The greatest common factor of \(15m^3\) and \(14n^2\) is 6
05 Jan 2023, 13:27
Kudos
Bookmarks
Bunuel
Given: \(A = m^3n^2\) ; m and n are distinct prime numbers
\(54 = 2 * 27 = 2 * 3^3\)
Given: Does A consist of \(2 * 3^3\)
In other words, we want to know if m = 3 and n = 2
Statement 1
(1) 25mn is the least common multiple of 15 and 50
LCM of 15 and 50 = \(5^2 * 3 * 2\)
We know the product of \(5^2 * m * n\) equals to \(5^2 * 3 * 2\), however we do not know if m = 2 and n = 3 or vice versa.
Depending on the values of m and n, the response to the question will change. Hence this statement is not sufficient. Eliminate A and D.
Statement 2
The greatest common factor of \(15m^3\) and \(14n^2\) is 6
GCD or (\(5*3*m^3\) , \(2*7*n^2\)) = 2 * 3
This means both terms \(5*3*m^3\) and \(2*7*n^2\) consist of 2 * 3.
Thus we can conclude that m = 2 and n = 3
This is sufficient to answer our question.
Option B
Moderators:
