May 20 10:00 PM PDT  11:00 PM PDT Practice the one most important Quant section  Integer Properties, and rapidly improve your skills. May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day!
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 837
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
14 Jun 2015, 05:01
Question Stats:
60% (01:44) correct 40% (01:40) wrong based on 269 sessions
HideShow timer Statistics
If x and y are positive and \(x^2+y^2\)=100, then for which of the following is the value of x+y greatest? A. x=10 B. x=9 C. x=8 D. x=7 E. x=6
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.




Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
14 Jun 2015, 11:47
reto wrote: If x and y are positive and \(x^2+y^2\)=100, then for which of the following is the value of x+y greatest?
A. x=10 B. x=9 C. x=8 D. x=7 E. x=6 \(x^2 + y^2 = 100\) > \((x+y)^22xy=100\) > \((x+y)^2=100+2xy\) > \(x+y=\sqrt{100+2xy}\). We need to maximize \(x+y\), thus we need to maximize \(\sqrt{100+2xy}\). To maximize \(\sqrt{100+2xy}\) we need to maximize \(xy\). Now, for given sum of two numbers, their product is maximized when they are equal, hence from \(x^2 + y^2 = 100\) we'll have that \(x^2y^2\) (or which is the same xy) is maximized when \(x^2=y^2\). In this case \(x^2 + x^2 = 100\) > \(x=\sqrt{50}\approx{7}\). Answer: D.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
14 Jun 2015, 11:51
Bunuel wrote: reto wrote: If x and y are positive and \(x^2+y^2\)=100, then for which of the following is the value of x+y greatest?
A. x=10 B. x=9 C. x=8 D. x=7 E. x=6 \(x^2 + y^2 = 100\) > \((x+y)^22xy=100\) > \((x+y)^2=100+2xy\) > \(x+y=\sqrt{100+2xy}\). We need to maximize \(x+y\), thus we need to maximize \(\sqrt{100+2xy}\). To maximize \(\sqrt{100+2xy}\) we need to maximize \(xy\). Now, for given sum of two numbers, their product is maximized when they are equal, hence from \(x^2 + y^2 = 100\) we'll have that \(x^2y^2\) (or which is the same xy) is maximized when \(x^2=y^2\). In this case \(x^2 + x^2 = 100\) > \(x=\sqrt{50}\approx{7}\). Answer: D. Questions about this concept: ifx2y2100andx0andy0themaximumvalueofx147064.htmlifthepopulationofcityaisincreasedbyainyear130222.htmlthelengthsofthetwoshorterlegsofarighttriangleaddupto40u128319.htmlwhatisthegreatestpossibleareaofatriangularregion91398.htmlm05183677.htmlgiventhatabcdisarectangleistheareaoftriangleabe127051.htmlHope it helps.
_________________



Manager
Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
Schools: Kellogg 1YR '17, Booth '16, McCombs '18, Tepper '18, INSEAD Jan '17, ISB '17, NUS '18, IIMA , IIMB, IIMC , IIML '15

If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
14 Jun 2015, 12:17
Bunuel wrote: reto wrote: If x and y are positive and \(x^2+y^2\)=100, then for which of the following is the value of x+y greatest?
A. x=10 B. x=9 C. x=8 D. x=7 E. x=6 \(x^2 + y^2 = 100\) > \((x+y)^22xy=100\) > \((x+y)^2=100+2xy\) > \(x+y=\sqrt{100+2xy}\). We need to maximize \(x+y\), thus we need to maximize \(\sqrt{100+2xy}\). To maximize \(\sqrt{100+2xy}\) we need to maximize \(xy\). Now, for given sum of two numbers, their product is maximized when they are equal, hence from \(x^2 + y^2 = 100\) we'll have that \(x^2y^2\) (or which is the same xy) is maximized when \(x^2=y^2\). In this case \(x^2 + x^2 = 100\) > \(x=\sqrt{50}\approx{7}\). Answer: D. I did this by plugging nos. \(x^2 + y^2 = 100\) => \(y^2 = 100  x^2\) => \(y = \sqrt{(10 + x)(10  x)}\) (didn't consider the negative value after taking sqrt as x & y are +ve) Hence, \(x + y = x + \sqrt{(10 + x)(10  x)}\) Now plugging values, A. \(x = 10 => x + y = \sqrt{(10 + 10)(10  10)} + 10 = 10\) B. \(x = 9 => x + y = \sqrt{(10 + 9)(10  9)} + 9 = \sqrt{19} + 9 = 13.5(roughly)\) C. \(x = 8 => x + y = \sqrt{(10 + 8)(10  8)} + 8 = \sqrt{36} + 8 = 14\) D. \(x = 7 => x + y = \sqrt{(10 + 7)(10  7)} + 7 = \sqrt{51} + 7 = 14.1(roughly)\)(slightly over 14) E. \(x = 6 => x + y = \sqrt{(10 + 6)(10  6)} + 6 = \sqrt{64} + 6 = 14\) Hence answer is D



Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 729

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
15 Sep 2016, 15:10
I plugged in the answer choices. Whoever wrote this problem deliberately made the answer choices easy to plug in  the solution is pretty elegant! (A) x = 10 gives y = 0, for a sum of 10. For (C) and (E), notice that this is basically the Pythagorean theorem written out! (6,8,10) is a Pythagorean triple. So, if x = 6, y = 8, and vice versa. Both (C) and (E) give us a sum of 6 + 8 = 14. You can conclude that neither of these can be the answer, since if one of them was right, the other one would also have to be right. Also, since 14 is greater than 10, (A) can't be the right answer. Our only two contenders are (B) and (D). At this point, consider guessing. IF you keep working: (B) gives a sum of 9 + sqrt(100  81) = 9 + sqrt(19). (D) gives a sum of 7 + sqrt(100  49) = 7 + sqrt(51). Which of those is greater? sqrt(19) is definitely less than 5, so (B) is definitely less than 14. (B) can't be right, and you can stop here. To prove (D) is correct, notice that sqrt(51) is more than 7, so (D) is definitely more than 14 and is the largest value.
_________________



Current Student
Joined: 24 Jul 2016
Posts: 78
Location: United States (MI)
GPA: 3.6

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
15 Sep 2016, 17:16
Answer is D, since square root of 50 is not there in the options Sent from my iPhone using GMAT Club Forum mobile app



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9224
Location: Pune, India

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
15 Sep 2016, 22:31
reto wrote: If x and y are positive and \(x^2+y^2\)=100, then for which of the following is the value of x+y greatest?
A. x=10 B. x=9 C. x=8 D. x=7 E. x=6 Maximum/minimum values often occur at extremes/transition points. For the maximum value of x + y, there are two extremes:  x and y are as far apart as possible (x is slightly less than 10 and y is slightly more than 0. Here x+y = about 10)  x and y are as close as possible (\(x = \sqrt{50} = 7.something\). Here x + y = 7.something + 7.something = 14.something) Answer (D)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 17 Aug 2015
Posts: 99

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
28 Nov 2016, 21:22
Although I first solved it by simply walking over choices (first saw 10 and then went to 8..then went to 6 and understood the answer is 7).
Another interpretation could be that if x and y are sides of a triangle and there is a third side that is root of (x^2+ y^2) then that must be the hypotenuse. Note that the hypotenuse has to be 10. So let us maximize the perimeter of this triangle keeping one side fixed. It is quick to see that this will happen if the sides x and y are closest to each other. In choice A and B, one side is extreme. In C, D and E choices, choice D has most balance . If I have one side as 7 then other side is root(51) which is close to 7. This is our answer



Current Student
Joined: 12 Aug 2015
Posts: 2616

If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
19 Jan 2017, 13:09
This is such a great Question. I actually used Brute force here. We can use estimation to check the values of x+y in each option.
Option 1> x=10 => y=0 > Not allowed as y>0 Option 2> x=9=> y=4.something => x+y=> 13.something Option 3> x=8=> y=6 =>x+y=14 Option 4> x=7 => y=7.something => x+y=14.something Option 5=> x=6=>y=8=> x+y=14
Hence clearly Option 4 will give us the greatest value of x+y Hence D.
_________________



Intern
Status: casado
Joined: 26 Jan 2010
Posts: 16
Location: chile

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
21 Jan 2017, 14:13
The statement does not affirm that X and Y are positive integers, only affirms that they are positive numbers. But if we consider positive integers we would have two correct alternatives C and E. Therefore the criterion is not correct. If the values for X, Y must be positive numbers, then the closer these numbers are, the greater their sum. X = 7 and Y = sqr (51), then X + Y> 14 Answer C @
_________________
claudio hurtado maturana Private lessons GMAT QUANT GRE QUANT SAT QUANT Classes group of 6 students GMAT QUANT GRE QUANT SAT QUANT Distance learning courses GMAT QUANT GRE QUANT SAT QUANT Website http://www.gmatchile.clWhatsapp +56999410328 Email clasesgmatchile@gmail.com Skype: clasesgmatchile@gmail.com Address Avenida Hernando de Aguirre 128 Of 904, Tobalaba Metro Station, Santiago Chile.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6160
Location: United States (CA)

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
28 Feb 2018, 11:24
reto wrote: If x and y are positive and \(x^2+y^2\)=100, then for which of the following is the value of x+y greatest?
A. x=10 B. x=9 C. x=8 D. x=7 E. x=6 Let’s analyze each answer choice: A) When x = 10, y = 0 and x + y = 10. B) When x = 9, y = √19 ≈ 4.4 and x + y ≈ 13.4. C) When x = 8, y = 6 and x + y = 14. D) When x = 7, y = √51 ≈ 7.2 and x + y ≈ 14.2. E) When x = 6, y = 8 and x + y = 14. We see that the sum of x and y will be the greatest when x = 7. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



NonHuman User
Joined: 09 Sep 2013
Posts: 10958

Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
Show Tags
25 Mar 2019, 14:46
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: If x and y are positive and x^2+y^2=100, then for which of the followi
[#permalink]
25 Mar 2019, 14:46






