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 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
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.
22 Jan 2012, 16:44
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
36% (02:04) correct
64%
(02:06)
wrong
based on 641
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive integer, is x – 1 a factor of 104?
(1) x is divisible by 3.
(2) 27 is divisible by x.
(1) x is divisible by 3.
(2) 27 is divisible by x.
22 Jan 2012, 16:59
Kudos
Bookmarks
enigma123
If x is a positive integer, is x – 1 a factor of 104?
(1) x is divisible by 3 --> well, this one is clearly insufficient, as x can be 3, x-1=2 and the answer would be YES but if x is 3,000 then the answer would be NO.
(2) 27 is divisible by x --> factors of 27 are: 1, 3, 9, and 27. Now, if x is 3, 9, or 27 then the answer would be YES (as 2, 8, and 26 are factors of 104) BUT if x=1 then x-1=0 and zero is not a factor of ANY integer (zero is a multiple of every integer and factor of none of the integer). Not sufficient.
(1)+(2) As from (1) x is a multiple of 3 then taking into account (2) it can only be 3, 9, or 27. For all these values x-1 is a factor of 104. Sufficient.
Answer: C.
22 Apr 2015, 23:12
Kudos
Bookmarks
Hi Guys,
The question deals with the concepts of factors and multiples of a number. Its important to analyze the information given in the question first before preceding to the statements. Please find below the detailed solution:
Step-I: Understanding the Question
The question tells us that \(x\) is a positive integer and asks us to find if \(x-1\) is a factor of 104
Step-II: Draw Inferences from the question statement
Since \(x\) is a +ve integer, we can write \(x>0\). The question talks about the factors of 104. Let's list out the factors of 104.
\(104 = 13 * 2^3\). So, factors of 104 are {1,2,4,8,13,26,52,104}, a total of 8 factors.
If \(x-1\) is to be a factor of 104, \(2<=x<=105\). With these constraints in mind lets move ahead to the analysis of the statements.
Step-III: Analyze Statement-I independently
St-I tells us that \(x\) is divisible by 3. This would mean that \(x\) can take a value of any multiple of 3. Now, all the multiples of 3 are not factors of 104. So, we can't say for sure if \(x-1\) is a factor of 104. Hence, statement-I alone is not sufficient to answer the question.
Step-IV: Analyze Statement-II independently
St-II tells us that 27 is divisible by \(x\) i.e. \(x\) is a factor of 27. Let's list out the factors of 27 - {1,3,9,27}. But, we know that for \(x-1\) to be a factor of 104, \(2<=x<=105\). We see from the values of factors of 27, \(x\) can either be less than 2(i.e. 1) or greater than 2 (i.e. 3,9 & 27). Hence, statement-II alone is not sufficient to answer the question.
Step-V: Analyze both statements together
St-I tells us that \(x\) is a multiple of 3 and St-II tells us that \(x\) can take a value of {1, 3, 9, 27}. Combining these 2 statements we can eliminate \(x=1\) from the values which \(x\) can take. So, \(x\)={ 3, 9, 27} and \(x-1\) = {2, 8, 26}. We observe that all the values which \(x-1\) can take is a factor of 104. Hence, combining st-I & II is sufficient to answer our question.
Answer: Option C
Takeaway
Analyze the information given in the question statement properly before proceeding for analysis of the statements. Had we not put constraints on the values of x, we would not have been able to eliminate x=1 from st-II analysis.
Hope it helps!
Regards
Harsh
The question deals with the concepts of factors and multiples of a number. Its important to analyze the information given in the question first before preceding to the statements. Please find below the detailed solution:
Step-I: Understanding the Question
The question tells us that \(x\) is a positive integer and asks us to find if \(x-1\) is a factor of 104
Step-II: Draw Inferences from the question statement
Since \(x\) is a +ve integer, we can write \(x>0\). The question talks about the factors of 104. Let's list out the factors of 104.
\(104 = 13 * 2^3\). So, factors of 104 are {1,2,4,8,13,26,52,104}, a total of 8 factors.
If \(x-1\) is to be a factor of 104, \(2<=x<=105\). With these constraints in mind lets move ahead to the analysis of the statements.
Step-III: Analyze Statement-I independently
St-I tells us that \(x\) is divisible by 3. This would mean that \(x\) can take a value of any multiple of 3. Now, all the multiples of 3 are not factors of 104. So, we can't say for sure if \(x-1\) is a factor of 104. Hence, statement-I alone is not sufficient to answer the question.
Step-IV: Analyze Statement-II independently
St-II tells us that 27 is divisible by \(x\) i.e. \(x\) is a factor of 27. Let's list out the factors of 27 - {1,3,9,27}. But, we know that for \(x-1\) to be a factor of 104, \(2<=x<=105\). We see from the values of factors of 27, \(x\) can either be less than 2(i.e. 1) or greater than 2 (i.e. 3,9 & 27). Hence, statement-II alone is not sufficient to answer the question.
Step-V: Analyze both statements together
St-I tells us that \(x\) is a multiple of 3 and St-II tells us that \(x\) can take a value of {1, 3, 9, 27}. Combining these 2 statements we can eliminate \(x=1\) from the values which \(x\) can take. So, \(x\)={ 3, 9, 27} and \(x-1\) = {2, 8, 26}. We observe that all the values which \(x-1\) can take is a factor of 104. Hence, combining st-I & II is sufficient to answer our question.
Answer: Option C
Takeaway
Analyze the information given in the question statement properly before proceeding for analysis of the statements. Had we not put constraints on the values of x, we would not have been able to eliminate x=1 from st-II analysis.
Hope it helps!
Regards
Harsh
