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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 ## GMAT Prpe ##### This topic has 11 member replies ## GMAT Prpe I dont know what is the component I should be focussing on while doing this problem If n and y are positive integers and 450y=n^3, which of the following must be an integer?? I.y/3*2^2*5 II.y/3^2*2*5 III.y/3*2*5^2 Thanks _________________ Maxx Legendary Member Joined 05 Sep 2007 Posted: 645 messages Followed by: 5 members Upvotes: 34 moneyman wrote: I dont know what is the component I should be focussing on while doing this problem If n and y are positive integers and 450y=n^3, which of the following must be an integer?? I.y/3*2^2*5 II.y/3^2*2*5 III.y/3*2*5^2 Thanks 450 = 2 x 5^2 x 3^2 Now 2 x 5^2 x 3^2 x y = n^3 So at minimum, y = 2^2 x 5 x 3 So y/3*2^2*5 is the minimum value which will always be integer. Got me, Max? _________________ Correct me If I am wrong Regards, Amitava Master | Next Rank: 500 Posts Joined 03 Mar 2007 Posted: 468 messages Upvotes: 5 Got it Amitava..But I really could not figure out the approach..now its clear..Thanks _________________ Maxx Legendary Member Joined 06 May 2007 Posted: 789 messages Followed by: 6 members Upvotes: 15 Target GMAT Score: 710 i tried to push numbers out for this and wound up with n=10 and y=2.2 when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer. I tried to break this up into primes but then got lost. can someone explain this to me in baby steps and please give qa. thanks folks! _________________ Appetite for 700 and I scraped my plate! Senior | Next Rank: 100 Posts Joined 10 Mar 2008 Posted: 72 messages Upvotes: 25 Test Date: April 19, 2008 Target GMAT Score: 730 Enginpasa1 wrote: i tried to push numbers out for this and wound up with n=10 and y=2.2 when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer. I tried to break this up into primes but then got lost. can someone explain this to me in baby steps and please give qa. thanks folks! Step by step: Find the prime factors of 450. 450 ->45*10 ->9*5*2*5 -->3*3*5*2*5 --->2*3*3*5*5 The question states that 450y = n^3. Since y and n are both positive integers, this means that 450y must be a perfect cube. In order for 450y to be a perfect cube, we look at our current prime factors of 450: (2) (3*3) (5*5) Therefore, in order for 450y to be a perfect cube, we need an additional 5, an additional 3, and two additional 2's. (2) (3*3) (5*5) * y ->(2) (3*3) (5*5) * [(2*2) (3) (5)] -->(2*2*2) (3*3*3) (5*5*5) = perfect cube Thus, at minimum, y must be [(2*2) (3) (5)] or 2^2 * 3 * 5. We look at our answer choices and plug in for y. I) y/3*2^2*5 -> (2^2 * 3 * 5) / 3*2^2*5 = 1 (integer) II) y/3^2*2*5 -> (2^2 * 3 * 5) / 3^2*2*5 = 2/3 (not an integer) III) y/3*2*5^2 -> (2^2 * 3 * 5) / 3*2*5^2 = 2/5 (not an integer) Legendary Member Joined 06 May 2007 Posted: 789 messages Followed by: 6 members Upvotes: 15 Target GMAT Score: 710 Is there a way to approach this problem and not go through all of your steps. Can we force a value for y and n and then test each roman numeral? _________________ Appetite for 700 and I scraped my plate! Senior | Next Rank: 100 Posts Joined 10 Mar 2008 Posted: 72 messages Upvotes: 25 Test Date: April 19, 2008 Target GMAT Score: 730 Enginpasa1 wrote: Is there a way to approach this problem and not go through all of your steps. Can we force a value for y and n and then test each roman numeral? To me, this approach makes the most sense, and like camitava showed, it is pretty straightforward. I would not go through my step by step method on paper; rather, a lot of it would be mental. The underlying process is quite simple: 1. Recognize that 450y must be a perfect cube. 2. Break 450 into its prime factors and see what y at minimum must be to create a perfect cube. 3. Glance at I, II, and III to see if this minimum value of y can cancel all the denominator values. Legendary Member Joined 06 May 2007 Posted: 789 messages Followed by: 6 members Upvotes: 15 Target GMAT Score: 710 i guess the answer hinges on seeing that 450y must be a perfect cube. NOw I get it! thanks _________________ Appetite for 700 and I scraped my plate! Junior | Next Rank: 30 Posts Joined 10 Apr 2008 Posted: 27 messages Upvotes: 1 Great solution. Senior | Next Rank: 100 Posts Joined 10 Apr 2008 Posted: 93 messages Upvotes: 20 Test Date: Soon enough Enginpasa1 wrote: i tried to push numbers out for this and wound up with n=10 and y=2.2 when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer. I tried to break this up into primes but then got lost. can someone explain this to me in baby steps and please give qa. thanks folks! A quick suggestion Enginpasa: On the GMAT, more often than not, there is as much information in the options and the other parts of the question as the actual question itself. The 3 Roman Numeral statements are CLEAR indicators that Prime factorisation is in some way or the other involved. Any method that takes us away from that will be longer and relatively more cumbersome. _________________ For love, not money. Junior | Next Rank: 30 Posts Joined 24 Jul 2009 Posted: 18 messages Upvotes: 2 Thank you very much Junior | Next Rank: 30 Posts Joined 24 Jul 2009 Posted: 18 messages Upvotes: 2 tmmyc wrote: Enginpasa1 wrote: i tried to push numbers out for this and wound up with n=10 and y=2.2 when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer. I tried to break this up into primes but then got lost. can someone explain this to me in baby steps and please give qa. thanks folks! Step by step: Find the prime factors of 450. 450 ->45*10 ->9*5*2*5 -->3*3*5*2*5 --->2*3*3*5*5 The question states that 450y = n^3. Since y and n are both positive integers, this means that 450y must be a perfect cube. In order for 450y to be a perfect cube, we look at our current prime factors of 450: (2) (3*3) (5*5) Therefore, in order for 450y to be a perfect cube, we need an additional 5, an additional 3, and two additional 2's. (2) (3*3) (5*5) * y ->(2) (3*3) (5*5) * [(2*2) (3) (5)] -->(2*2*2) (3*3*3) (5*5*5) = perfect cube Thus, at minimum, y must be [(2*2) (3) (5)] or 2^2 * 3 * 5. We look at our answer choices and plug in for y. I) y/3*2^2*5 -> (2^2 * 3 * 5) / 3*2^2*5 = 1 (integer) II) y/3^2*2*5 -> (2^2 * 3 * 5) / 3^2*2*5 = 2/3 (not an integer) III) y/3*2*5^2 -> (2^2 * 3 * 5) / 3*2*5^2 = 2/5 (not an integer) thank you very much, I was surfing the web looking for such a good explanation. Good luck mat • Award-winning private GMAT tutoring Register now and save up to$200

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