GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Feb 2019, 12:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53020
If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

### Show Tags

31 May 2017, 00:38
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:17) correct 18% (02:35) wrong based on 104 sessions

### HideShow timer Statistics

If $$x^2 + y^2 = 2ab$$ and $$2xy = a^2 + b^2$$, with a, b, x, y > 0, then x + y =

(A) ab

(B) a – b

(C) a + b

(D) $$\sqrt{a^2 + b^2}$$

(E) $$\sqrt{a^2 − b^2}$$

_________________
Intern
Joined: 26 Jul 2016
Posts: 41
Location: India
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

### Show Tags

31 May 2017, 01:38
1
1
x^2 + y^2 = 2ab-------- (1)
2xy = a^2 + b^2-------- (2)
(1)+(2) => x^2 + y^2 +2xy = a^2 + b^2+2ab
(x+y)^2=(a+b)^2
(x+y)=(a+b)
Director
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

### Show Tags

31 May 2017, 15:02
1
1
Bunuel wrote:
If $$x^2 + y^2 = 2ab$$ and $$2xy = a^2 + b^2$$, with a, b, x, y > 0, then x + y =

(A) ab

(B) a – b

(C) a + b

(D) $$\sqrt{a^2 + b^2}$$

(E) $$\sqrt{a^2 − b^2}$$

$$x^2 + y^2 = 2ab$$ -------------(i)
$$2xy = a^2 + b^2$$ -------------(ii)

We get;

$$x^2 + y^2 +2xy = a^2+b^2+2ab$$
$$(x+y)^2 = (a+b)^2$$

Therefore; x+y = a+b
Intern
Joined: 25 Apr 2016
Posts: 25
Concentration: Entrepreneurship, Marketing
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

### Show Tags

31 May 2017, 18:45

Given:- x^2 + y^2 = 2ab
and 2xy = a^2 + b^2

(x+y)^2 = x^2 + y^2 + 2xy (standard formula)

Substituting:-

a^2 + b^2 +2ab = (x+y)^2
or x+y = a+b
Non-Human User
Joined: 09 Sep 2013
Posts: 9863
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

### Show Tags

05 Sep 2018, 08:30
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^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +   [#permalink] 05 Sep 2018, 08:30
Display posts from previous: Sort by