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.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
16 Sep 2014, 01:20
Kudos
Bookmarks
If \(x\) is a positive integer, \(f(x)\) is defined as the number of positive integers smaller than \(x\) that share no common factors with \(x\) other than 1. If \(x\) is a prime number, what is the value of \(f(x)\) in terms of \(x\)?
A. \(x - 2\)
B. \(x - 1\)
C. \(\frac{(x + 1)}{2}\)
D. \(\frac{(x - 1)}{2}\)
E. 2
A. \(x - 2\)
B. \(x - 1\)
C. \(\frac{(x + 1)}{2}\)
D. \(\frac{(x - 1)}{2}\)
E. 2
16 Sep 2014, 01:20
Kudos
Bookmarks
Official Solution:
If \(x\) is a positive integer, \(f(x)\) is defined as the number of positive integers smaller than \(x\) that share no common factors with \(x\) other than 1. If \(x\) is a prime number, what is the value of \(f(x)\) in terms of \(x\)?
A. \(x - 2\)
B. \(x - 1\)
C. \(\frac{(x + 1)}{2}\)
D. \(\frac{(x - 1)}{2}\)
E. 2
The question is essentially asking how many positive integers smaller than a given prime number \(x\) have no factors in common with \(x\), except for 1.
Since \(x\) is a prime number, it only has two distinct factors: 1 and itself. As a result, any positive integer smaller than \(x\) will not share any factors with \(x\) other than 1. Therefore, there will be \(x-1\) positive integers smaller than \(x\) that meet this criterion.
For example, consider the prime number \(x=7\). The positive integers smaller than 7 that have no factors in common with 7, except for 1, are: 1, 2, 3, 4, 5, and 6. Thus, the value of \(f(x)\) for \(x=7\) is \(7-1=6\).
Answer: B
If \(x\) is a positive integer, \(f(x)\) is defined as the number of positive integers smaller than \(x\) that share no common factors with \(x\) other than 1. If \(x\) is a prime number, what is the value of \(f(x)\) in terms of \(x\)?
A. \(x - 2\)
B. \(x - 1\)
C. \(\frac{(x + 1)}{2}\)
D. \(\frac{(x - 1)}{2}\)
E. 2
The question is essentially asking how many positive integers smaller than a given prime number \(x\) have no factors in common with \(x\), except for 1.
Since \(x\) is a prime number, it only has two distinct factors: 1 and itself. As a result, any positive integer smaller than \(x\) will not share any factors with \(x\) other than 1. Therefore, there will be \(x-1\) positive integers smaller than \(x\) that meet this criterion.
For example, consider the prime number \(x=7\). The positive integers smaller than 7 that have no factors in common with 7, except for 1, are: 1, 2, 3, 4, 5, and 6. Thus, the value of \(f(x)\) for \(x=7\) is \(7-1=6\).
Answer: B
General Discussion
21 Oct 2016, 21:22
Kudos
Bookmarks
I think this is a very good GMAT like 'convoluted' question. The controversy related to 1 is actually because of the confusing language the question stem uses. Let me try and put it in another way:
...and do not have a common factor with \(x\) other than 1
The above statement only says that 1 is a factor of numbers less than \(x\) and not that 1 should be excluded from the set of number less than \(x\)
Lets take \(x = 7\). Below is the set of \(x\) according to question stem
6 - Less than 7, and does not have a common factor with 7 other than 1
5 - Less than 7, and does not have a common factor with 7 other than 1
4 - Less than 7, and does not have a common factor with 7 other than 1
3 - Less than 7, and does not have a common factor with 7 other than 1
2 - Less than 7, and does not have a common factor with 7 other than 1
1 - Less than 7, and does not have a common factor with 7 other than 1
Hence, 1 has to be in the set!
Total elements: 6
\(x-1\)
Option B
...and do not have a common factor with \(x\) other than 1
The above statement only says that 1 is a factor of numbers less than \(x\) and not that 1 should be excluded from the set of number less than \(x\)
Lets take \(x = 7\). Below is the set of \(x\) according to question stem
6 - Less than 7, and does not have a common factor with 7 other than 1
5 - Less than 7, and does not have a common factor with 7 other than 1
4 - Less than 7, and does not have a common factor with 7 other than 1
3 - Less than 7, and does not have a common factor with 7 other than 1
2 - Less than 7, and does not have a common factor with 7 other than 1
1 - Less than 7, and does not have a common factor with 7 other than 1
Hence, 1 has to be in the set!
Total elements: 6
\(x-1\)
Option B
