The Question has been edited
from x2-y2 => x^2 – y^2
————————————–
Is x^2 – y^2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
B
A
The answer is A.
C
Reasoning:
consider A:
x-y is a positive number:
let x = 8, y = -10 then x2 – y2 results in a -ve number
x = 2, y = 1 then x2 – y2 results in a +ve number
So, A alone cannot be the answer
consider B:
x+y is a positive number:
let x = 2, y = 1 then x2-y2 results in a +ve number
x = 3, y = 4 then x2 – y2 results in a -ve number
So, B alone cannot be the answer
combining both A and B :
x2-y2 = (x+y)(x-y)
from option A and option B :
x2-y2 = (positive)(positive) = positive
Therefore, C is the option
My bad… answer should be C only…
C should be the ans
c
the answer is E
take the ezampla of -4 and -3
the answer is E
take the example of -4 and -3
The answer is C .
@Cyril,
in case of -4,-3 none of the statements (either A or B) would satisfy the conditions. Neither x-y is positive nor x+y is positive. So we cant take this condtion.
The ans for sure is C
C is the answer.
Vamsi’s explination is apt.
A
I might be reading this wrong…is the question “Is x2 – y2 a positive number?” read as “Is x squared minus x squared a positive number?” or is it read like “Is x times 2 minus y times 2 a positive number?”
C
1st statement says x – y is a positive number,
this means that x is greater then y,
so a commen multiple (2 ) will not change the sing thus A sufficient
2nd statement says x + y is a positive number.
cant say anything firmly weather X is greater or Y .
so the answer is A
C
A. Agree with kapil.
Actually, I read it wrong. If the coefficients are squared (x^2), not doubled (2x), I agree with Vamsi Krishna Kanuri’s answer
I guess the question seems to confusing as it is not clear what (x2 – y2) denotes. Assuming it is [(square of x) - (square of y)], in its proper format; The answer should be C.
A is wrong reason is x-y is + means x>y but take this example
3>-4 here x>y but x2-y2 will be negative
now take 3>2 here x>y in this case x2-y2 is negative
ans should be C
Agree with Vamsi Krishna Kanuri’s explanation. The only possible answer is C.
PS: To the people who writes an answer try to explain it, not just mention it….. so everybody can share and learn with the explanation.
the ans is A
reason being 2 datas r given —-x-y=positive and x+y=positive
ans stands true if the case is 1—but need not be true if the case is 2
kindly give attention dear Vamsi Krishna Kanuri
YOU SAYS THAT
let x = 8, y = -10 then x2 – y2 results in a -ve number
my point is this will not be negative just check this
(2*8)-(2*-10)=16-(-20)=16+20=36
thus answer is A because we can firmly say that x>y as per statement 1
cyril,
Answer is c.
(X2 – Y2) = (X+Y) (X-Y)
Condn1.
IF X-Y is positive then X2-Y2 is +ve or -ve that depends upon X+Y,so we can’t come to an solution.
condn2.
IF X+Y is positive then X2-Y2 is +ve or -ve that depends upon X-Y,so we can’t come to an solution.
If we use both the statements we can give an definite answer.
So answer is C.
There needs to be more clarity on whether it is X squared minus Y squared or if it is X*2 – Y*2. Depending on this the answers could vary.
In this case we can assume that it should be read as Xsquared minus Ysquared as if it were a second multiple of X,Y, it could have been simply written as 2X-2Y which is the conventional way of writing it.
Now we are given that X-Y is a positive no. For this to be true, x>Y always and will work for any of the following possible values of X and Y
1) X = 4, Y=3 : x>y therefore X -Y is positive
2) X= -4, Y= -8 : x>Y therefore x-y is positive
3) X= 8, Y = -4 : X>Y therefore x-y is positive.
When we square these values we get the following:
1) 16 – 9 : this is a positive number
2) 16 – 64 : this is a negative number
3) 64 – 16 : this is again a positive number.
Hence we cannot have a definite “YES” or a “NO” to the question stem. Therefore we cannot have option A as the answer.
When we take the second statement X + Y is positive if X Y there can be positive or negative answers. So therefore the second option B cannot hold good.
If we consider both the options then we can safely conclude that they will be true only if X>Y which is possible in both cases.
Hence “C” will be the correct answer!
Ans: c
x2-y2=(x+y)(x-y)
and +ve x +ve is always positive…
The correct answer is C
I feel “C” is correct
Answer is C
the x2 and y2 mentioned here in the question is interpreted as x^2 and y^2.
This question in DS is a very common question and answer to this question is “C”.
C is be the ans