Around the World in 80 Questions (Day 9): Is x^3 - y^3 = 0 ?

Is x^3−y^3=0
the question is (x-y)(x^2+xy+y^2)=0?
(1) xy<0
since xy<0 then x is not equal y therefore x^3-y^3 is not equal to 0. Hence it is sufficient. only A and D are left
(2) x−y=11
since x is not equal to y then 2 is sufficient
The answer is D

Q: Is x^3 - y^3 = 0?
Q: Is x^3 = y^3 ?

1) xy < 0
=> One is +ve number and the other is - ve number
=> x^3 - y^3 is not equal to zero ---> SUFFICIENT

2) x - y = 11
=> x = 11 + y
Q: Is (11 + y)^3 = y^3 ?
Cube root both sides => Is 11 + y = y ? No ---> SUFFICIENT

Answer - [D]

My Answer: D, both statements alone are sufficient.

For x^3-y^3 = 0, either x=y or x=y=0.

Statement (1): If xy<0, one of the numbers is positive and the other is negative. So x is not equal to y. Also, it is not possible for x=y=0 because 0 is not less than 0. Hence, sufficient.
Statement (2): If x-y=11, it can be concluded that neither is x=y nor is x=y=0. So, also sufficient.

the given target condition of \(x^3 - y^3 = 0\)
will be possible only when both x & y are same and of same sign i.e. both are +ve or both are -ve

#1
\(xy < 0\)
for this to be true both x & y have to be of opposite sign
the condition of \(x^3 - y^3 = 0\) will not be true
sufficient
#2
\(x - y = 11\)
case 1
x& y are both +ve
14-3 =11
case 2
x & y are of opposite sign
8-(-3)=11
case 3
c & y are both -ve
-3-(-14) = 11
also for x-y = 11
one has to be odd and other number even so therefore answer to target x^3-y^3 will be always no
sufficient
OPTION D

Is x3−y3=0
(1) xy<0
(2) x−y=11

The question is asking whether x3=y3 or x=0 and y=0.
(1) xy<0 means xy= negative number, which shows either x= negative number or y= negative number. sufficient to answer.
(2) x-y=11 means x is greater than y by 11 meaning it is not equal or equal to each other. Sufficient to answer.
Answer is (D)

answer is D.

STATEMENT 1 : xy<0
x and y are of opposite signs. so x^3 and y^3 will be of opposite signs. in such a case x^3 can never be equal to y^3. so x^3 - y^3 is NOT equal to zero. so, this statement is sufficient

STATEMENT 2 : x-y=11
x^3 - y^3 = (x-y)(x^2 + y^2 - xy) = (x-y)*((x-y)^2 + xy) . This can be zero only is xy = -((x-y)^2) i.e., xy = -121 when x-y=11. there exists no such solution. so x^3 - y^3 is NOT equal to zero. so, this statement is sufficient

Therefore each option is sufficient. thus answer is D

\(x^3-y^3=(x-y)(x^2+y^2+xy); x^2+y^2+xy\) is always \(>=0\)

S1) \(xy<0 \) means \(x\) & \(y \) are of opp signs hence term is never \(0\) (Suff)
S2) \(x-y=11\) means, expression is \(11(y^2+11y+121)\).This has a discriminant \(<0\). hence always \(>0\) (suff)

Hence D)

The question asks if x=y

(1) xy<0 -> One must be positive and the other is negative -> x=\=y -> Sufficient

(2) x-y=11 -> x=11+y -> x=\=y -> Sufficient

Answer D

Is x^3−y^3=0
x^3=y^3
x=y

Statement (1) xy<0
means x not equal to y
x & y are of opposite signs
Hence x^3−y^3=0 is not true
Statement 1 is sufficient

(2) x−y=11
x=y+11
x is not equal to y
hence x^3−y^3=0 is not true
Statement 2 is sufficient

Option D is Correct

Excellent question! Kudos to the amazing brain who designed it.
So we need to see if \(x^3 - y^3 = 0\).
That means, (x-y)(x^2+y^2+xy)=0
Hence, either we need x=y or we need x^2+y^2+xy=0
The second case is not possible as you will need imaginary roots to make x^2+y^2+xy=0.
Hence, we need to see of x=y.
(1) xy<0: if x=y, xy will never be less than 0. Hence, sufficient.
(2) x=y+11. Hence, x is not equal to y. Sufficient.

Hence, D is the answer.

Is \(x^3 - y^3 = 0\) ?

(1) \(xy < 0\)

(2) \(x - y = 11\)

Case I: xy <0
what it says is if x >0, y <0 or vice-versa
lets say if x = 2, y = -3
and hence x^3- y^3 is not equal to 0
if x =2 and y = -2
then x^3 -y^3 = 16
so for all the different values the expression x^3 -y^3 is not equal to 0
hence this is sufficient

Case II: x-y =11
x^ - y^3 = (x-y) (x^2+ y^2 +xy)
=(x-y) ((x-y)^2 + 3xy)
= 11 *(121 + 3xy)
again if x and y are both >0 or both <0, then the above expression will be positive and not equal to 0
if x and y are opposite xy<0
in order for the above expression to be 0, 3xy =-121 and x - y =11
i.e 3(11+y) y = -121
3y^2 +33y +121=0
here(33)^2- 4*3*121 = 1089 - 1452 <0
so it will have imaginary

hence there won't be any value of x and y where this expression will be 0
so this is sufficient

D is the answer

Is x^3−y^3=0
on solving we get is x=y?


(1) xy<0
this says that x and y has opposite signs, so x cannot equal to y, hence sufficient.


(2) x−y=11
difference of x and y =11, so x cannot equal to y, hence sufficient.

Hence my pick will be D, either of (1) or (2) can solve the question.

Q:- Is x^3 - y^3 = 0
or, Is x = y ?

S1:- xy<0, in this condition x can never be equal to y as one of the values have to be negative and other one have to be positive.

So, S1 is sufficient.

S2:- x - y = 11

Again in this condition x can never be equal to y.

So, S2 is sufficient

Hence, D is correct choice.

To find : If \(x^3 - y^3 = 0\)

i.e \(x^3 = y^3 \)

It can only be true when x=y.

(1) \(xy < 0\)

That means one of x and y is positive and other is negative.
i.e x and y are not equal.

Sufficient.

(2) \(x - y = 11\)

That means x and y are not equal.
Sufficient.

Answer : D

Is x^3−y^3=0
Is x^3 = y^3

Statement 1: xy<0
In this signs of x and y are opposite. So x^3 = y^3 is not equal. Sufficient

Statement 2: x−y=11
x = y+11 ,it is equal when x = 5.5 and y = -5.5.In this also signs of x and y are opposite. So x^3 = y^3 is not equal.
Sufficient

Answer is D

whether X^3 - Y^3 = 0,

Statement 1: X.Y<0 , gives X and Y both are non-Zero, and either of X or Y is +ve and other is necessarily negative. so lets assume X is positive and the Y is negative would mean X^3 - y^3 can not be zero. Conversely if X is negative and Y is positive so again answer will be a non-Zero. Sufficient

Statement 2: x−y=11 or X= Y+11 so putting it in Equation (Y+11)^3 - Y^3 will always be a +ve number so it can be confidentally answered as non -Zero. So Sufficient.

Answer is D.

Given x^3 - y^ 3 = 0 i.e. x^3 = y^3
Taking cube roots on both sides, x=y

Statment 1
xy<0
This means that x and y are of opposite sides. Hence x=y not possible. Clear answer

SUFFICIENT

Statement 2
x-y=11
i.e. x = y+11
Hence x=y not possible. Clear answer

SUFFICIENT