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

 It is currently 12 Dec 2019, 19:10

### 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

# If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

### Show Tags

08 Apr 2019, 14:42
1
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:24) correct 47% (03:08) wrong based on 36 sessions

### HideShow timer Statistics

If $$x + y = 30$$ and $$x^3 + y^3=8100$$, what is the value of $$x^2+y^2$$?

A. $$480$$
B. $$(15 + \sqrt{15})^2$$
C. $$420$$
D. $$880$$
E. Information is not sufficient to answer
Manager
Joined: 07 Apr 2018
Posts: 100
Location: United States
Concentration: General Management, Marketing
GMAT 1: 600 Q45 V28
GPA: 3.8
Re: If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

### Show Tags

08 Apr 2019, 19:05
(x+y)^3= x^3 + y^3 + 3xy(x+y)
hence xy= 210
(x+y)2=x^2+y^2 -2xy
x^2+y^2=480
Senior Manager
Joined: 12 Sep 2017
Posts: 308
If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

### Show Tags

09 Apr 2019, 17:17
1
$$x + y = 30$$
$$x^3 + y^3 = 8100$$
$$x^2 + y^2 = ?$$

$$(x + y)^2 = x^2 + 2xy + y^2 = 900$$

$$x^2 + y^2 = 900 -2xy$$

and

$$(x^2 + y^2)(x + y) = x^3 + x^2y + xy^2 + y^3$$

$$(x^2 + y^2)(x + y) = (x^3 + y^3) + xy(x+y)$$

So combining both

$$(900 - 2xy)(30) = (8100) + xy(30)$$

$$27,000 - 60xy = 8100 + 30xy$$

$$xy = 210$$

$$x^2 + y^2 = 900 -2(210)$$

$$x^2 + y^2 =480$$

A
If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?   [#permalink] 09 Apr 2019, 17:17
Display posts from previous: Sort by