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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Unable to understand this DS problem ##### This topic has 1 expert reply and 5 member replies ## Unable to understand this DS problem If P has a total of 8 positive factors, including 1 and P, what is the value of P? Positive integer P has 2 positive prime factors, 5 and 11. 1. 125 is a factor of P. 2. 121 is not a factor of P. I can understand that statement 1 is sufficient to answer the question because we can determine the 8 positive factors as follows : statement 1: 125 can be written as 5^3 .So 5^2 ,5 ,11,11*5,11*5^2,11*5^3,1 are all factors of P.Since p is a factor of itself P=11*5^3. But the answer says that statement 2 is also sufficient.How to determine that? Thanks for your help. Last edited by manjus_mailme on Wed Apr 14, 2010 12:22 pm; edited 1 time in total Master | Next Rank: 500 Posts Joined 15 Mar 2010 Posted: 435 messages Followed by: 1 members Upvotes: 32 Target GMAT Score: 750+ manjus_mailme wrote: If P has a total of 8 positive factors,..... P has exactly 2 positive prime factors, 5 and 11. Please correct the question _________________ Whether you think you can or can't, you're right. - Henry Ford Senior | Next Rank: 100 Posts Joined 02 Feb 2010 Posted: 37 messages eaakbari wrote: manjus_mailme wrote: If P has a total of 8 positive factors,..... P has exactly 2 positive prime factors, 5 and 11. Please correct the question Does the question make sense now.The question from the source itself was wrong.I edited it as it is now. ### GMAT/MBA Expert GMAT Instructor Joined 08 Jan 2008 Posted: 3225 messages Followed by: 611 members Upvotes: 1710 GMAT Score: 800 Let's start by fixing up the problem: Quote: If P has a total of 8 positive factors, including 1 and P, what is the value of P? Positive integer P has 2 positive prime factors, 5 and 11. becomes: Quote: Positive integer P has only 2 distinct prime factors, 5 and 11. If P has a total of 8 positive factors, what's the value of P? Step 1 of the Kaplan Method for DS: Analyze the stem We know that 4 of the factors of P are 1, 5, 11 and P. We also know that P has no other primes factors other than 5 and 11; what we don't know is how many 5s and 11s P contains. Step 2 of the Kaplan Method for DS: Evaluate the Statements (1) 125 is a factor of P. Therefore, P has at least 3 "5"s among it's primes. So, we have 1, 5, 11, 25, 55, 125, 25*11, 125*11 as our 8 factors. Therefore, P = 125*11... sufficient. (2) 121 is NOT a factor of P. Therefore, P has exactly 1 factor of 11; the other factors all have to be 5s. Well, the only way to generate 8 factors for P is if we have 3 "5"s among the factors; as above, P = 125*11... sufficient. Each of (1) and (2) is sufficient alone, choose (D). Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today! Legendary Member Joined 15 Jan 2010 Posted: 610 messages Followed by: 2 members Upvotes: 47 P has 8 factors 1, 5 , 11 , a, b, c , d, P (1) 125 is a factor of P. so a, b, c or d can be 125 so possible values of a,b and c are 25, 55, 125, 25*11 ( but does it have to be 55 or 25*11 can it not be 121 ) since there are 4 more factors a to d, does it restrict the existence of 11*11 as one of the factors till (2) 121 is NOT a factor of P clears the air. and if it does restrict the existence of 121 then is (2) really necessary. What am I missing ? Senior | Next Rank: 100 Posts Joined 13 Jul 2009 Posted: 51 messages Upvotes: 1 If a Number P is factorized in the format P= a^m * b^n. and a , b are two prime factors of a number, then the number of factors is given by = (m+1)*(n+1). For example, No of factors of 6 = 2^1*3^1 = (1+1)*(1+1)=2*2=4 ----> 1,2,3,6. From the Question, we have 5 and 11 as prime factors.... 5^m * 11^n ... And Number of factors=8 From (i) 125 is factor of P---> 125=5^3 and P=5^3 * 11^n Number of factors = (3+1)*(n+1)=8---> n=1. S(i) is Sufficient. From (ii) 121 is not a factor of P. Only possibility=5^3*11---> Sufficient. Hence D. Thx Stuart. Senior | Next Rank: 100 Posts Joined 02 Feb 2010 Posted: 37 messages Thank you so much for explaning the problem .It was very helpful. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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