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.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
26 May 2017, 04:42
Kudos
Bookmarks
If \(n\) is a positive integer, is \(361\) a factor of \(n\)?
(1) \(76\) is the greatest common divisor of \(380\) and \(n\)
(2) \(5,776\) is the least common multiple of \(304\) and \(n\)
(1) \(76\) is the greatest common divisor of \(380\) and \(n\)
(2) \(5,776\) is the least common multiple of \(304\) and \(n\)
26 May 2017, 04:42
Kudos
Bookmarks
Official Solution:
The greatest common divisor of the integers is the least value of the exponents, and the least common multiple of the integers is the maximum value of the quotients.
Since there is 1 variable \((n)\) in the original condition, D is most likely to be the answer.
In the case of con 1), from \(361 = 19^{2}, 76 = 2^{2}19\), and \(380=2^{2}(5)(19)\), the greatest common divisor of \(380\) and \(n\) is \(76\). Since the greatest common divisor of the integers is the least value of the exponents, \(n = 2^{2}19, 2^{2}(3)(19),\ldots\) , hence it is not unique, and not sufficient.
In the case of con 2), from \(5,776 = 2^{4}19^{2}, 304 = 2^{4}19\), the least common multiple of \(n\) and \(2^{4}19\) is \(2^{4}19^{2}\). Since the least common multiple of the integers is the maximum value of the exponents, \(n\) should always have \(19^{2}\), hence always yes, and it is sufficient. Therefore, the answer is B.
Answer: B
The greatest common divisor of the integers is the least value of the exponents, and the least common multiple of the integers is the maximum value of the quotients.
Since there is 1 variable \((n)\) in the original condition, D is most likely to be the answer.
In the case of con 1), from \(361 = 19^{2}, 76 = 2^{2}19\), and \(380=2^{2}(5)(19)\), the greatest common divisor of \(380\) and \(n\) is \(76\). Since the greatest common divisor of the integers is the least value of the exponents, \(n = 2^{2}19, 2^{2}(3)(19),\ldots\) , hence it is not unique, and not sufficient.
In the case of con 2), from \(5,776 = 2^{4}19^{2}, 304 = 2^{4}19\), the least common multiple of \(n\) and \(2^{4}19\) is \(2^{4}19^{2}\). Since the least common multiple of the integers is the maximum value of the exponents, \(n\) should always have \(19^{2}\), hence always yes, and it is sufficient. Therefore, the answer is B.
Answer: B
Moderator:
