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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 ## The number 75 can be written as the sum of the squares of... tagged by: swerve ##### This topic has 4 expert replies and 1 member reply ### Top Member ## The number 75 can be written as the sum of the squares of... The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? A. 17 B. 16 C. 15 D. 14 E. 13 The OA is E. I guessed this right - but is there an algebraic way to do this PS question? Please, can any expert explain it? I need your help. Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12422 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 swerve wrote: The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? A. 17 B. 16 C. 15 D. 14 E. 13 We're looking for 3 DIFFERENT squares that add to 75 Here are the only squares we need to consider: 1, 4, 9, 16, 25, 36, 49, 64 Can you find 3 that add to 75? After some fiddling, we may notice that 1 + 25 + 49 In other words, 1Â˛ + 5Â˛ + 7Â˛ = 75 We want the SUM of 1 + 5 + 7, which is 13 Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12422 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 swerve wrote: I guessed this right - but is there an algebraic way to do this PS question? Please, can any expert explain it? I need your help. Thanks. No, there's no straightforward algebraic solution. Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9942 messages Followed by: 492 members Upvotes: 2867 GMAT Score: 800 Hi swerve, This question can be solved with a bit of 'brute force' arithmetic, but the speed with which you solve it will likely depend on how quickly you can write everything down and how you do the work. We're asked to find the three positive integers, whose squares add up to 75. To start, we should write down the list of possible squares: 1 4 9 16 25 36 49 64 We're limited to these 8 numbers. To work efficiently, we should work from 'greatest to least'.. If we use 64, then the other two numbers have to add up to 11....but there's NO WAY to make that happen (so 64 is NOT one of the numbers we need). Next, let's try 49... then the other two numbers have to add up to 26....25 and 1 'fit', so the three numbers are 49, 25 and 1 (7, 5 and 1 --> that sum = 13). Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com Legendary Member Joined 07 Sep 2017 Posted: 808 messages Followed by: 3 members Upvotes: 6 The way I solved it was as follows: $$75=49+25+1\ =\ 7^2+5^2+1.$$ Hence, the numbers are 1, 5 and 7. Therefore, $$7+5+1=13.$$ Therefore, the answer is E=13. ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 swerve wrote: The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? A. 17 B. 16 C. 15 D. 14 E. 13 If the sum of 3 different perfect squares is 75, each must be less than 75. So, we want to start by writing out the perfect squares that are less than 75: 1, 4, 9, 16, 25, 36, 49, 64 In this problem, there is no shortcut for determining which 3 squares add up to 75; however, it is strategic to start with the largest one, 64, and move down the list if it doesnâ€™t work: 64 + 11 = 75 There is no way 11 can be written as a sum of two squares. So, we move down to 49: 49 + 26 = 75 We see that 26 can be written as the sum of 25 and 1; that is: 49 + 25 + 1 = 75 We have found the three perfect squares that sum to 75. In other words: 7^2 + 5^2 + 1^2 = 75 The sum of 7, 5, and 1 is 7 + 5 + 1 = 13. Answer: E _________________ Jeffrey Miller Head of GMAT Instruction • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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