Is x^2 equal to xy

[MarsAlien]

Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)

(2) x = y

[ravindra_iit]

'B'

 

stem asks for is x^2 = xy => is x=0 or x=y!

 

(1) Insuff

(2) Suff

[MarsAlien]

does (1) not show that x=y=5 ??

I had chosen the option D.

[thankont]

I think it is --b-- since we could have

x=-5 and y=5 so x^2=25 but xy=-25

[Krissy Sh]

I think the answer is "either of them is sufficiant" because 1) means x^2=xy, so x*x=x*y, or x=y which is 2). If we replace them we get x=y=5 or x=y=-5.

[AsterixCyprus]

Imo B.

[gmatgoal]

Since we need to prove that x^2=xy, we need to find if x=y

A seems to be the answer, but I wanted to find out whats wrong with my calculation.

(1) x^2 – y^2 = (x + 5)(y - 5)

(x+y)(x-y) = (x + 5)(y - 5) =(y - 5)(x + 5)=(- 5 + y)(x -(-5))

(x+y)(x-y) =(- 5 + y)(x -(-5))

Hence x=y=-5

Why is the ans not D

[cinghal1]

Krissy Sh I COMPLETELY AGREE WITH YOU...ans could be either x=y=5 or x=y=-5 and in both cases, we get xy=x2. ans is D!

 

Though i have one doubt - can you please explain ow you got the soln x=y=+5? was it by trial and error or did you solve the equation? pl explain. thanks!

[surya167]

Why is some one not coming out with the Official Answer - The OA!

Then we will keep discussing in vain till we dont confirm whats the answer!

[winjeemat]

Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)

(2) x = y

 

is x^2 = xy ? ........(1)

=> Is x = 0 OR x = y ?

This is basically equation of pair of two lines x = 0 & x = y.

 

St 1

x^2 – y^2 = (x + 5)(y - 5) ......(2)

 

Let us identify the sol set of eq (1) & (2).

 

When x = 0 solutions are (0, 5/2(-1+sqrt(5))) & (0, 5/2(-1-sqrt(5))).

 

When x = y solutions are (5,5), (-5,-5).

 

Thus for the range of values of x & y of eq (2) the given inequality (1) will be satisfied only for the above four solutions otherwise not. Hence INSUFF

 

St 2

SUFF

 

Ans B

 

PS: the line of reasonong given in St 1 is important because if eq (1) & (2) has no solution set then the given inequality will be false & St 1 will be sufficient. [For eg consider the eq x^2 + y^2 = (x + 5)(y - 5)]

[samwisegamji]

in stmt 1 we have

 

x^2 – y^2 = (x + 5)(y - 5)

 

or x^2 - y^2 = xy -5x + 5y - 25

 

so if x^2 =xy then we have

 

y^2 = 5x - 5y + 25

 

this may not be the case alawys so INSUFF

 

B SUFF

[shsingh]

Since we need to prove that x^2=xy, we need to find if x=y

A seems to be the answer, but I wanted to find out whats wrong with my calculation.

(1) x^2 – y^2 = (x + 5)(y - 5)

(x+y)(x-y) = (x + 5)(y - 5) =(y - 5)(x + 5)=(- 5 + y)(x -(-5))

(x+y)(x-y) =(- 5 + y)(x -(-5))

Hence x=y=-5

Why is the ans not D

 

 

Hi the answer here is not D because x and y are not necessarily intergers.

 

lets simplify A to y^2 = 5x-5y+25

 

so this can have many variations of x and y values satisfying it but not necessarily x^2 = xy

[borntorun]

IMo B

 

Is X^2 = xy ?

 

X^2 could be equal to xy only when either x=0 or x=y

 

from 1) we can't say safely either x = 0 or x=y

 

from 2 ) x=y ---sufficient