|
|
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.
16 Sep 2014, 01:22
Kudos
Bookmarks
How many positive factors does positive integer \(n\) have?
(1) The difference between the largest and the smallest positive factors of \(n\) is 21
(2) \(n+1\) has positive 2 factors
(1) The difference between the largest and the smallest positive factors of \(n\) is 21
(2) \(n+1\) has positive 2 factors
16 Sep 2014, 01:22
Kudos
Bookmarks
Official Solution:
How many positive factors does positive integer \(n\) have?
(1) The difference between the largest and the smallest positive factors of \(n\) is 21.
For any integer, its largest factor is the integer itself, and the smallest factor is 1. Given this, \(n - 1 = 21\), which implies \(n = 22\). The number 22 has 4 factors: 1, 2, 11, and 22. Sufficient.
(2) \(n+1\) has positive 2 factors.
This statement simply implies that \(n+1\) is a prime number. For example, \(n\) can be 2 (\(2+1=3=prime\)) with 2 factors or 6 (\(6+1=7=prime\)) with 4 factors. Not sufficient.
Answer: A
How many positive factors does positive integer \(n\) have?
(1) The difference between the largest and the smallest positive factors of \(n\) is 21.
For any integer, its largest factor is the integer itself, and the smallest factor is 1. Given this, \(n - 1 = 21\), which implies \(n = 22\). The number 22 has 4 factors: 1, 2, 11, and 22. Sufficient.
(2) \(n+1\) has positive 2 factors.
This statement simply implies that \(n+1\) is a prime number. For example, \(n\) can be 2 (\(2+1=3=prime\)) with 2 factors or 6 (\(6+1=7=prime\)) with 4 factors. Not sufficient.
Answer: A
27 May 2018, 07:46
Kudos
Bookmarks
i thought i was pretty thorough with number thoery until i saw this question. chose E. only after reading the explanation from Bunuel was i able to understand. hope such things strike my mind during the exam.
