|
|
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.
14 May 2018, 01:58
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (01:46) correct
38%
(01:45)
wrong
based on 407
sessions
History
Date
Time
Result
Not Attempted Yet
GMAT CLUB'S FRESH QUESTION
Is a positive integer x odd?
(1) The greatest common factor of the smallest positive factor of x and the largest positive factor of x is odd
(2) The least common multiple of the smallest positive factor of x and the largest positive factor of x is even
M36-26
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
11 Oct 2021, 08:07
Kudos
Bookmarks
Bunuel
Official Solution:
Is a positive integer \(x\) odd?
(1) The greatest common factor of the smallest positive factor of \(x\) and the largest positive factor of \(x\) is odd
The smallest positive factor of any positive integer is 1 and the largest positive factor of any positive integer is the integer itself. So, we are given that the greatest common factor of 1 and \(x\) is odd. This is true for any positive integer \(x\) because the greatest common factor of 1 and \(x\) is always 1, which is odd. So, \(x\) could be any positive even or any positive odd number. Not sufficient.
(2) The least common multiple of the smallest positive factor of \(x\) and the largest positive factor of \(x\) is even
The smallest positive factor of any positive integer is 1 and the largest positive factor of any positive integer is the integer itself. So, we are given that the least common multiple 1 and \(x\) is even. Since the least common multiple 1 and \(x\) is \(x\) itself, then we are basically told that \(x\) is even. Sufficient.
Answer: B
General Discussion
14 May 2018, 02:56
Kudos
Bookmarks
Solution
Given:
• x is a positive integer
To find:
• Is the value of x odd?
Approach and Working:
As x is a positive integer,
• The smallest positive factor of x = 1
• The largest positive factor of x = x
Analysing Statement 1
• As per the information provided in Statement 1, the GCF of the smallest positive factor of x and the largest positive factor of x is odd
- o Or, GCF (1, x) = odd
- o Hence, we cannot say anything about the nature of the number x
Analysing Statement 2
• As per the information provided in Statement 2, the LCM of the smallest positive factor of x and the largest positive factor of x is even
- o Or, LCM (1, x) = even
- o Hence, we can say that the number x is an even number
Hence, the correct answer is option B.
Answer: B
