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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## integer problem, plz help! tagged by: ##### This topic has 1 expert reply and 2 member replies will really appreciate if anyone can explain the following question Thanks! Q. If a,b,k are positive integers is a^k a factor of b^m? 1. a is a factor of b 2. k<= m (k is equal to or smaller than m) The answer is C. GMAT Instructor Joined 01 May 2008 Posted: 189 messages Followed by: 1 members Upvotes: 25 Test Date: 2/18/2006 GMAT Score: 750+ We can write the question mathematically like so: Does there exist an integer x, such that: x(a^k) = b^m? (You get this from the definition of a factor. For$ to be a factor of #, there is some integer such that $*integer = #.) Now let's take a look at what statement 1 tells us. "a is a factor of b." Thus, there is some integer y such that ay = b. Plugging that into the equation given by the question, we have: xa^k = b^m xa^k = (ay)^m xa^k = (a^m)*(y^m). Now, y^m is just some integer, so we can cut down on confusion by calling that z. xa^k = za^m Dividing both sides by a^k gives us: x = za^(k-m) Now, the question is still, is x an integer? x will be an integer if k>=m, because then a^(k-m) will be an integer, and z is an integer. However, if k=m, we do not have enough information and statement 1 is not sufficient. Considering statement 2, we have: xa^k = b^m, and k<=m. We can express x as: x = (b^m)/(a^k). We could have a,b,m, and k such that: x=(3^2)/(2^1) = 9/2 (not an integer) Or, we could have a,b,m, and k such that: x=(4^2)/(2^1)=16/2=8 (an integer) So, statement 2 doesn't give us enough information to determine if x is an integer. Combining the statements, we find that we had reduced statement 1 to "x will be an integer if k>=m." Statement 2 gives us this very piece of information. So, put together we have sufficient information and the answer is C. _________________ Tatiana Becker | GMAT Instructor | Veritas Prep Senior | Next Rank: 100 Posts Joined 06 Jul 2008 Posted: 95 messages Upvotes: 2 Test Date: Aug 23 Hi , Am i missing something.. In this statement xa^k = za^m Dividing both sides by a^k gives us: x = za^(k-m) when we divide will it not be x=za^(m-k). Please let me know.. thanks in advance . ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2327 messages Followed by: 348 members Upvotes: 1090 GMAT Score: 780 crave165 wrote: will really appreciate if anyone can explain the following question Thanks! Q. If a,b,k are positive integers is a^k a factor of b^m? 1. a is a factor of b 2. k<= m (k is equal to or smaller than m) The answer is C. I hope it's clear that neither statement is sufficient on its own (for (1): 2 is a factor of 2, but 2^10 is not a factor of 2^2; for (2), 3^1 is not a factor of 2^2.) If we use both: a is a factor of b: thus b = ca, where c is an integer. Thus, b^m = (ca)^m = (c^m)(a^m). Is this divisible by a^k? Yes, as long as k <= m. If that's not clear, do the division: (b^m)/(a^k) = (c^m)(a^m)/(a^k) = (c^m)*(a^(m-k)) which is an integer as long as m - k is greater than or equal to 0. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT 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 • Award-winning private GMAT tutoring Register now and save up to$200

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