GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 13:13 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61283
If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

### Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 75% (01:32) correct 25% (01:12) wrong based on 81 sessions

### HideShow timer Statistics

If $$4x^2 + 9y^2 = 100$$ and $$(2x + 3y)^2 = 150$$, then what is the value of $$6xy$$?

(A) 5(2 + √6 )

(B) 10√6

(C) 25

(D) 50

(E) 100

_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4329
If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

### Show Tags

Top Contributor
Bunuel wrote:
If $$4x^2 + 9y^2 = 100$$ and $$(2x + 3y)^2 = 150$$, then what is the value of $$6xy$$?

(A) 5(2 + √6 )

(B) 10√6

(C) 25

(D) 50

(E) 100

GIVEN: $$(2x + 3y)^2 = 150$$

Expand and simplify to get: $$4x^2+12xy+9y^2 = 150$$
We're also given the equation: $$4x^2 + 9y^2 = 100$$

Subtract the bottom equation from the top equation to get: $$12xy = 50$$
Divide both sides by 2 to get: $$6xy = 25$$

Cheers,
Brent
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9426
Location: United States (CA)
Re: If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

### Show Tags

Bunuel wrote:
If $$4x^2 + 9y^2 = 100$$ and $$(2x + 3y)^2 = 150$$, then what is the value of $$6xy$$?

(A) 5(2 + √6 )

(B) 10√6

(C) 25

(D) 50

(E) 100

FOILing the left hand side of the second equation, we have:

4x^2 + 9y^2 + 12xy = 150

Subtracting the first equation 4x^2 + 9y^2 = 100 from the equation above, we have:

12xy = 50

Dividing both sides of the equation by 2, we have:

6xy = 25

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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. Re: If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of   [#permalink] 01 Jan 2020, 18:35
Display posts from previous: Sort by

# If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  