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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 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). _________________ Stuart Kovinsky | Kaplan GMAT Faculty | Toronto Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount 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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