Around the World in 80 Questions (Day 4): Does xy = x^2 ?

Question

Does  xy = x^2  ?

(1)  xy = y^2

(2)  x^2 = y^2

NiranjanaV · Answer

Does xy = x^2?
Does xy - x^2 = 0?
Does x(y-x) = 0?

1) xy = y^2
=> y(x-y) = 0
=> y = 0 or (x-y) = 0 ---> NOT SUFFICIENT

2) x^2 = y^2
=> (x+y)(x-y) = 0
=> x = y or x=-y ----> NOT SUFFICIENT

Combine: xy = x^2 = y^2 ---> SUFFICIENT

Archit3110 · Answer

target is
xy=x^2
x(y-x)=0
x=0 ; x=y
#1
 xy = y^2 
y(x-y)=0
y=0 ,x=y
insufficient
#2
  x^2 = y^2 
x & y can be of same sign or opposite sign or can be 0
insufficient
from 1 &2
we can say that x=y=0
  OPTION C is correct

missionmba2025 · Answer

xy = x^2

xy - x^2 = 0

x(y-x) = 0

x = 0  or  x = y

(1)  xy = y^2

xy - y^2 = 0

y(x - y) = 0

Two possibilities, x = y or y = 0.

If x = y, Does  xy = x^2  ? is yes

If y = 0 and x = 4, Does  xy = x^2  ? is no

Not sufficient.

(2)  x^2 = y^2

x^2 - y^2 = 0

(x+y)(x - y) = 0

Two possibilities, x = y or x = -y.

If x = y, Does  xy = x^2  ? is yes

If y = 3 and x = -3, Does  xy = x^2  ? is no

Not sufficient.

Combined

The common term in both (1) and (2) is x = y.

The statements combined tell us  xy = x^2 . The answer is Yes.

IMO C

$!vakumar.m · Answer

Does xy=x^2 ?
the above equation can be rewritten as : x^2 - xy =0
x(x-y) = 0=> x = 0 or x =y

(1) xy=y^2
=> y(y-x) = 0
=> y = 0 (for y = 0 we can't determine value of x and hence check the condition) or x =y (the given condition is true)
Not sufficient

(2) x^2=y^2
=>x^2 - y^2 =0
=> (x-y)*(x+y) =0
=> x = y (condition is true) or x = -y (on solving we get y =0, hence can't find the value of x)
Not sufficient 
Statement 1 and 2 together
subtract both equations we get : x^2 - xy = 0
or x^2 = xy - True
Sufficient
Answer C

BottomJee · Answer

LHS = xy
RHS =  x^2 
We need to find our whether LHS = RHS.

Using Statement 1, we get
x = y 
or y = 0
if x = y then xy =  x^2  is possible
But if y = 0, then we cannot determine whether xy =  x^2  as x can be 0 or it can be any other number.
Hence, Statement 1 is not sufficient.

Using Statement 2, we get
x = y or x = -y
If x = y, then  xy = x^2  is possible
But if x = -y, then xy is not equal to  x^2  because in the LHS we will have -y * y and in RHS we will have y*y
Hence, Statement 2 is not sufficient.

Considering both the statements together, we get
x = y (common condition from both the statements)
Then, LHS = x*y = x*x
RHS =  x^2  = x * x
LHS = RHS.

IMO OA should be C.

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Around the World in 80 Questions (Day 4): Does xy = x^2 ?

Prep Toolkit

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