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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 sum of the squares of three numbers is 138, while the tagged by: nkmungila1 ##### This topic has 5 expert replies and 0 member replies ## The sum of the squares of three numbers is 138, while the The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. 20 B. 30 C. 40 D. 50 E. 60 ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 nkmungila1 wrote: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. 20 B. 30 C. 40 D. 50 E. 60 This is kind of an odd question. You could mix and match perfect squares until you find numbers that work. 8^2 + 7^2 + 5^2 = 64 + 49 + 25 = 138. There's actually no reason to use the second piece of information here (which could have been worded a bit more clearly), but if we took 8, 7, and 5, there are three products we can generate by selecting two of the three numbers and then multiplying them: 8*7, 8*5, and 7*5, or 56, 40, and 35. These do, in fact, sum to 131. 8+7+5 =20. And the answer is A. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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nkmungila1 wrote:
The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

A. 20
B. 30
C. 40
D. 50
E. 60
(Worth noting that 11^2 + 4^2 + 1^2 would also get us to 138, but because 11 + 4 + 1 = 16 isn't an option, we can discard this possibility without testing to see if the second condition would be met.)

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Save $100 off any live Veritas Prep GMAT Course Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 nkmungila1 wrote: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. 20 B. 30 C. 40 D. 50 E. 60 Hi nkmungila1, Let's take a look at your question. This is a very easy algebraic question if we just take a closer look at it. Let the three numbers be x, y and z. The question states that, "The sum of the squares of three numbers is 138." x^2 + y^2 + z^2 = 138 ---- (i) "The sum of their products taken two at a time is 131." xy + yz + zx = 131 --- (ii) We are asked to find the sum of the numbers. x + y + z = ? We will use the following polynomial identity to solve this problem. (x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + zx) Plugin the known values from (i) and (ii) (x + y + z)^2 = 138 + 2(131) (x + y + z)^2 = 138 + 262 (x + y + z)^2 = 400 Taking square root on both sides, x + y + z = âˆš400 x + y + z = 20 The sum of the numbers is 20. Therefore, Option A is true. I am available if you'd like any followup. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 116 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 DavidG@VeritasPrep wrote: nkmungila1 wrote: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. 20 B. 30 C. 40 D. 50 E. 60 (Worth noting that 11^2 + 4^2 + 1^2 would also get us to 138, but because 11 + 4 + 1 = 16 isn't an option, we can discard this possibility without testing to see if the second condition would be met.) Those were the first squares that popped into my head - I was pretty surprised that there was another set of three squares that sums to 138! (which, apropos of nothing, has been a favorite number of mine ever since I heard that Misfits song about it 20 years ago ...) Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Matt@VeritasPrep wrote: DavidG@VeritasPrep wrote: nkmungila1 wrote: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. 20 B. 30 C. 40 D. 50 E. 60 (Worth noting that 11^2 + 4^2 + 1^2 would also get us to 138, but because 11 + 4 + 1 = 16 isn't an option, we can discard this possibility without testing to see if the second condition would be met.) Those were the first squares that popped into my head - I was pretty surprised that there was another set of three squares that sums to 138! (which, apropos of nothing, has been a favorite number of mine ever since I heard that Misfits song about it 20 years ago ...) I'm making an official request that we all make a more concerted effort to make more GMAT-Misfit connections on these boards _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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