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 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
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
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
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.
08 Nov 2009, 16:34
Kudos
Bookmarks
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:18) correct
0%
(00:00)
wrong
based on 5
sessions
History
Date
Time
Result
Not Attempted Yet
There must be an easier way?
Q: Positive integer P has exactly 2 positive prime factors, 5 and 11. If P has a total of 8 positive factors, including 1 and P, what is the value of P?
S1. 125 is a factor of P.
S2. 121 is not a factor of P.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
OA: D
OE: We know that positive integer P has exactly 2 positive prime factors, 5 and 11, and that P has a total of 8 positive factors, including 1 and P. From these two facts, we can deduce that:
P has 6 factors that are neither 1 nor P.
Since a product's factors are necessarily composed of its prime factors, all factors of P, including P, are of the form 5x11y, where x and y are non-negative integers.
The question asks us to determine the value of P.
Statement 1 tells us that P is divisible by 125. Since the prompt is concerned with the prime factors of P, it will help to rewrite 125 as 53. Since P is divisible by 53, it is also divisible by 52 and 5. Similarly, since 11 is a factor of P, 11 × 53, 11 × 52, 11 × 5, and 11 are factors of P. At this point, we have all 8 of P's factors: 1, 5, 52, 53, 11, 11 × 5, 11 × 52, and 11 × 53. Since P is a factor of itself, we know that the largest of these 8 factors, 11 × 53, must be equal to P. Statement 1 is sufficient.
Statement 2 tells us that P is not divisible by 121, which we can write as 112. Since P's only prime factors are 5 and 11, and since 112 is not a factor of P, we know that the remaining factors must either have only 5 as a prime factor or else be the product of 11 and a number that has only 5 as a prime factor. We can list these factors easily: 5 × 11, 52, 52 × 11, 53, 53 × 11. If we now include 1, 5, and 11, we see that we have identified exactly 8 factors. Again, the largest factor, 53 × 11, must be equal to P. Statement 2 is also sufficient.
Since each statement alone is sufficient, answer choice D is correct.
Struggling! Thanks for any help.
PS. Would this be considered 600-700 level problem or is way easier than I am making it out to be?
Q: Positive integer P has exactly 2 positive prime factors, 5 and 11. If P has a total of 8 positive factors, including 1 and P, what is the value of P?
S1. 125 is a factor of P.
S2. 121 is not a factor of P.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
OA: D
OE: We know that positive integer P has exactly 2 positive prime factors, 5 and 11, and that P has a total of 8 positive factors, including 1 and P. From these two facts, we can deduce that:
P has 6 factors that are neither 1 nor P.
Since a product's factors are necessarily composed of its prime factors, all factors of P, including P, are of the form 5x11y, where x and y are non-negative integers.
The question asks us to determine the value of P.
Statement 1 tells us that P is divisible by 125. Since the prompt is concerned with the prime factors of P, it will help to rewrite 125 as 53. Since P is divisible by 53, it is also divisible by 52 and 5. Similarly, since 11 is a factor of P, 11 × 53, 11 × 52, 11 × 5, and 11 are factors of P. At this point, we have all 8 of P's factors: 1, 5, 52, 53, 11, 11 × 5, 11 × 52, and 11 × 53. Since P is a factor of itself, we know that the largest of these 8 factors, 11 × 53, must be equal to P. Statement 1 is sufficient.
Statement 2 tells us that P is not divisible by 121, which we can write as 112. Since P's only prime factors are 5 and 11, and since 112 is not a factor of P, we know that the remaining factors must either have only 5 as a prime factor or else be the product of 11 and a number that has only 5 as a prime factor. We can list these factors easily: 5 × 11, 52, 52 × 11, 53, 53 × 11. If we now include 1, 5, and 11, we see that we have identified exactly 8 factors. Again, the largest factor, 53 × 11, must be equal to P. Statement 2 is also sufficient.
Since each statement alone is sufficient, answer choice D is correct.
Struggling! Thanks for any help.
PS. Would this be considered 600-700 level problem or is way easier than I am making it out to be?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
08 Nov 2009, 17:09
Kudos
Bookmarks
Finding the number of factors of an integer N:
First make prime factorization of an integer \(N=a^p*b^q*c^r\); a, b, and c are prime factors of N and p, q, and r are their powers.
The number of factors of N will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE this will include 1 and N itself.)
e.g. Finding the number of all factors of 450:
\(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
Back to original question:
P has exactly 2 positive prime factors, 5 and 11: \(P=5^x*11^y\) x>=1 and y>=1.
P has a total of 8 positive factors, including 1 and P: (x+1)*(y+1)=8
NOTE: that according to this max value of x and y are 3. Which means that 5 and 11 have max power of 3. (if x or y >3 then (x+1)*(y+1) will be more than 8)
(1) 125 is a factor of P: \(P=125*n=5^3*n\) which means that P must have at least 3 power of 5 to be the multiple of 125. As max value of x is also 3, hence x=3, --> y=1. P=5^x*11^y=5^3*11^1. Sufficient.
(2) 121=11^2 is not a factor of P. Means that the power of 11 in P is 1, y=1, x=3 --> P=5^x*11^y=5^3*11^1. Sufficient.
Answer: D.
First make prime factorization of an integer \(N=a^p*b^q*c^r\); a, b, and c are prime factors of N and p, q, and r are their powers.
The number of factors of N will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE this will include 1 and N itself.)
e.g. Finding the number of all factors of 450:
\(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
Back to original question:
P has exactly 2 positive prime factors, 5 and 11: \(P=5^x*11^y\) x>=1 and y>=1.
P has a total of 8 positive factors, including 1 and P: (x+1)*(y+1)=8
NOTE: that according to this max value of x and y are 3. Which means that 5 and 11 have max power of 3. (if x or y >3 then (x+1)*(y+1) will be more than 8)
(1) 125 is a factor of P: \(P=125*n=5^3*n\) which means that P must have at least 3 power of 5 to be the multiple of 125. As max value of x is also 3, hence x=3, --> y=1. P=5^x*11^y=5^3*11^1. Sufficient.
(2) 121=11^2 is not a factor of P. Means that the power of 11 in P is 1, y=1, x=3 --> P=5^x*11^y=5^3*11^1. Sufficient.
Answer: D.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderators:
