Last visit was: 10 Sep 2024, 17:53 It is currently 10 Sep 2024, 17:53
Toolkit
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 0 < x <= y , what is the value of x?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 95423
Own Kudos [?]: 657417 [7]
Given Kudos: 87231
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2583 [3]
Given Kudos: 459
Location: India
Director
Joined: 02 Oct 2017
Posts: 548
Own Kudos [?]: 503 [0]
Given Kudos: 14
Manager
Joined: 07 Apr 2018
Posts: 82
Own Kudos [?]: 119 [0]
Given Kudos: 61
Location: India
Re: If 0 < x <= y , what is the value of x? [#permalink]
Given: x>0, y>0, 0<x<=y
To find- x

1) x^2+2xy=12y+36
Adding y^2 to both sides, we get x^2 +2xy+ y^2 = y^2 + 12y+ 36
(x+y)^2 = (y+6)^2
As x and y are positive, x=6
Sufficient

2) y(x^3−216)=0
Either y=0 or (x^3-216)=0
y can't be zero, so (x^3-216)=0
=> x=6
Sufficient

Manager
Joined: 02 Dec 2018
Posts: 245
Own Kudos [?]: 34 [0]
Given Kudos: 70
Re: If 0 < x <= y , what is the value of x? [#permalink]
amanvermagmat wrote:
Bunuel wrote:
If $$0 < x \leq y$$ , what is the value of x?

(1) $$x^2 + 2xy = 12y + 36$$

(2) $$y(x^3 - 216) = 0$$

(1) Lets add y^2 to both sides, we get:
x^2 + 2xy + y^2 = y^2 + 12y + 36. Now LHS is the square of (x+y) and RHS can be factorised. Doing so, we get:
(y+x)^2 = (y+6)^2
Since we are given that both x and y are positive, we know that (y+x) will also be positive, and (y+6) will also be positive. So we can be sure that in the above equation, both sides we have squares of positive quantities only. Thus we can conclude that:
y+x = y+6 or x = 6. Sufficient.

(2) This means that either y = 0 or (x^3 - 216) = 0. But since both x and y are positive given, y cannot be 0. So we must have x^3 - 216 = 0 or x^3 = 216 or x = 6. Sufficient.

Understood the method. But the answer can only be arrived if we add y square both sides. What would give us a hint to add and check?
Non-Human User
Joined: 09 Sep 2013
Posts: 34812
Own Kudos [?]: 876 [0]
Given Kudos: 0
Re: If 0 < x <= y , what is the value of x? [#permalink]
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 0 < x <= y , what is the value of x? [#permalink]
Moderator:
Math Expert
95423 posts