If $$4x^2+9y^2=100$$
and $$(2x+3y)^2=150$$
then what is the value of 6xy?
$$(A)\ 5(2+\sqrt{6})$$
$$(B)\ 10\sqrt{6}$$
$$(C)\ 25$$
$$(D)\ 50$$
$$(E)\ 100$$
The OA is C.
I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is...
This topic has expert replies
-
- Moderator
- Posts: 2205
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
- EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hi LUANDATO,If $$4x^2+9y^2=100$$
and $$(2x+3y)^2=150$$
then what is the value of 6xy?
$$(A)\ 5(2+\sqrt{6})$$
$$(B)\ 10\sqrt{6}$$
$$(C)\ 25$$
$$(D)\ 50$$
$$(E)\ 100$$
The OA is C.
I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Let's take a look at your question.
We will be solving this question using the following polynomial identity.
$$\left(a+b\right)^2=a^2+b^2+2ab$$
We are given with:
$$\left(2x+3y\right)^2=150$$
Evaluate the LHS using the polynomial identity (a+b)^2 = a^2 + b^2 + 2ab, we get:
$$\left(2x\right)^2+\left(3y\right)^2+2\left(2x\right)\left(3y\right)=150$$
$$4x^2+9y^2+2\left(6xy\right)=150...(i)$$
Also it is given in the question that:
$$4x^2+9y^2=100$$
Plugging in the value in eq(i), we get:
$$100+2\left(6xy\right)=150$$
$$2\left(6xy\right)=150-100$$
$$2\left(6xy\right)=50$$
$$\left(6xy\right)=\frac{50}{2}$$
$$6xy=25$$
Therefore value of 6xy is 25. Option C is correct.
Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Foiling the second equation, we have:BTGmoderatorLU wrote:If $$4x^2+9y^2=100$$
and $$(2x+3y)^2=150$$
then what is the value of 6xy?
$$(A)\ 5(2+\sqrt{6})$$
$$(B)\ 10\sqrt{6}$$
$$(C)\ 25$$
$$(D)\ 50$$
$$(E)\ 100$$
The OA is C.
I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
4x^2 + 9y^2 + 12xy = 150
Subtracting the first equation 4x^2 + 9y^2 = 100 from the equation above, we have:
12xy = 50
6xy = 25
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews