If 0

Question

If  0 < x \leq y  , what is the value of x?

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

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

amanvermagmat · Answer

(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.

Hence  D answer

push12345 · Answer

I) put x=y in eqn
3y^2=12(y+3)
Solving we get x=6 or x=-2
But x>0 given
So x=6 
Sufficient

II) either y=0 or x^3-216=0
Y cannot be zero as y>0 so x^3=216
So x=6 as x>0
Sufficient

D is answer

Posted from my mobile device

PP777 · Answer

Given: x>0, y>0, 0 x=6 Sufficient Correct answer- D

shanks2020 · Answer

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?

bumpbot · Answer

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If 0 < x <= y , what is the value of x?

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