BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If x>0 and √5x = √3x+1, what is the value of 4x^2?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: Sun Apr 17, 2011 4:27 am
Location: India
Thanked: 6 times
Followed by:2 members
GMAT Score:620

If x>0 and √5x = √3x+1, what is the value of 4x^2?

by vinni.k » Sun Mar 11, 2018 10:06 am
If x>0 and √5x = √3x+1, what is the value of 4x^2?

A. 1/2
B. 1
C. 4x−1
D. 10x−1
E. 16x−1

OA is E

How to approach this question ?

My approach:-
√5x = √3x+1
Squaring both the sides we get :
5x = 3x + 1 + 2√3x
2x = 1 + 2√3x
Squaring both sides again
4x^2 = 1 + 12x + 4√3x
I am getting stuck here. Any other better approach? Can I plug numbers for x ? The two approaches that are coming into my mind are algebra and number plugging, but both of them seem to be not working at the moment.

Thanks
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Mar 11, 2018 10:17 am
vinni.k wrote:If x>0 and √5x = √3x+1, what is the value of 4x^2?

A. 1/2
B. 1
C. 4x−1
D. 10x−1
E. 16x−1
Since none of the answer choices contains a √, perform algebra that will clear the √ symbols:

√(5x) = √(3x) + 1

[√(5x)]² = ((√3x) + 1)²

5x = 3x + 2√(3x) + 1

2x - 1 = 2√(3x)

(2x - 1)² = (2√(3x))²

4x² - 4x + 1 = 4(3x)

4x² - 4x + 1 = 12x

4x² = 16x - 1.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: Sun Apr 17, 2011 4:27 am
Location: India
Thanked: 6 times
Followed by:2 members
GMAT Score:620

by vinni.k » Sun Mar 11, 2018 11:05 am
Thanks Mitch,

I was trying to understand the difference between my approach and your approach. I got stuck with the square roots, but you just got rid of the square roots, after checking the answer choices. I could have got it.

I just want to understand a bit more clearly. In case, if i see a similar kind of question in the test, and the answer choices do contain or don't contain the square roots, then my approach or strategy should be based on what is given in the answer choice.

What if the there were a square root, then my approach could have been right.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Mar 12, 2018 2:44 am
vinni.k wrote:Thanks Mitch,

I was trying to understand the difference between my approach and your approach. I got stuck with the square roots, but you just got rid of the square roots, after checking the answer choices. I could have got it.

I just want to understand a bit more clearly. In case, if i see a similar kind of question in the test, and the answer choices do contain or don't contain the square roots, then my approach or strategy should be based on what is given in the answer choice.

What if the there were a square root, then my approach could have been right.
We should ALWAYS keep our eyes on the answer choices.
In the posted problem, none of the answers include √, so we should perform algebra that will eliminate this symbol.
vinni.k wrote:2x = 1 + 2√3x
Squaring both sides again
4x^2 = 1 + 12x + 4√3x
Squaring the equation in red will not eliminate the √ from the right side.
Before squaring, we should isolate the term with √ on the right side, as follows:
2x - 1 = 2√(3x).
Squaring the equation in blue will eliminate the √, leading us to the correct answer.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Sun Mar 18, 2018 10:12 am
$$Given\ that\ x>0\ \left(i.e\ x\ is\ positive\right)$$
$$\sqrt{5x}=\sqrt{3x+1}$$
$$Square\ both\ sides,$$
$$\left(\sqrt{5x}\right)^2=\left(\sqrt{3x+1}\right)^2$$
$$5x=3x+1$$
$$5x-3x=1$$
$$2x=1,\ hence\ x=\frac{1}{2}\ \left[x\ is\ positive\right]$$
$$Now,\ 4x^2=4\left(\frac{1}{2}\right)^2=4\left(\frac{1}{4}\right)=1\ \left(option\ B\right)$$
Top
Post new topic Post Reply
• Page 1 of 1