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# What is the value of x^2 – y^2?

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Re: What is the value of x^2 – y^2? [#permalink]
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chetan2u wrote:
porvakanti wrote:
Hi,
I'm new here. I'd like to know how to solve the below problem:

What is the value of x2 – y2?
I) x+ y= 66
II) xy = 9
A] I alone is sufficient while II alone is not sufficient
B] II alone is sufficient while I alone is not sufficient
C] Neither I nor II is sufficient
D] Both I and II together are sufficient

A brief approach to solve would be very helful.

Hi,
firstly the Q does not seem to be a correct one..
what is DS..
you have a statement,.."What is the value of x2 – y2?..
can this be answered by any of the statement?" is what you have to look for..
what is x^2-y^2? (x-y)(x+y)...
so elther we know teh values of the difference and sum of two numbers or thevalues of x and y..
lets see the statements.
1)x+ y= 66.... we rae yet to know x-y.. insuff
2)xy=9.. again nothing what we are looking for..

combined it gives an imaginary number..

you may search for DS and you will get a way to move around these type of Qs..best of luck

According to my calculation the system of equation does not give imaginary numbers. Can you please check again?
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Re: What is the value of x^2 – y^2? [#permalink]
Bunuel wrote:
chetan2u wrote:
porvakanti wrote:
Hi,
I'm new here. I'd like to know how to solve the below problem:

What is the value of x2 – y2?
I) x+ y= 66
II) xy = 9

According to my calculation the system of equation does not give imaginary numbers. Can you please check again?

hi Bunuel,
I have the two statements which give me teh sum of the roots and product of the roots..
with these info , I can make the Quad eq as.
x^2-66x+9=0...
Also by substituting the value of y obtained from stat II, I would get the same eq..
in the eq above, if I find the Discriminant..
D=$$\sqrt{(b^2-4ac)}$$....
which is $$\sqrt{(66^2-4*9)}$$, which is going to besquare root of a negat....,
after writing till here, i realize ofcourse it will be positive,... an oversight
thanks
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Re: What is the value of x^2 – y^2? [#permalink]
porvakanti wrote:
Thanks Chetan.
So the answer is C - Neither 1 or 2 is sufficient ?

Hi since none are sufficient and combined too they are not suff,
answer will be C, when you get a certain answer after you have combine the info provided by the two statement
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Re: What is the value of x^2 – y^2? [#permalink]
According to Question: value of x^2-y^2 ?

Statement 1: x+y=66
x^2-y^2=(x+y)(x-y)==>(66)(x-y)==> No value . NOT SUFF

Statement 2: xy=9
x^2-y^2=(x+y)(x-y)==> no meaning of xy=9. No value . NOT SUFF

Combining (1)+(2) , no ans, no value. NOT SUFF

ANS: E
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Re: What is the value of x^2 – y^2? [#permalink]
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porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

x^2-y^2 = (x+y)(x-y)

Using (1) and (2) this question can be solved by using the following formula:
(x+y)^2 = (x-y)^2 + 4xy.

By (1) we have the value of (x+y) and by (2) we have the value of xy.
Putting them both in the above equation will help us get (x-y).
So we have the values of (x+y) as well as (x-y).

Thus C.
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Re: What is the value of x^2 – y^2? [#permalink]
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umodi wrote:
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

x^2-y^2 = (x+y)(x-y)

Using (1) and (2) this question can be solved by using the following formula:
(x+y)^2 = (x-y)^2 + 4xy.

By (1) we have the value of (x+y) and by (2) we have the value of xy.
Putting them both in the above equation will help us get (x-y).
So we have the values of (x+y) as well as (x-y).

Thus C.

Hi,
a good approach to the Q but the last step is not correct..
what you finally get is the value of (x-y)^2...
and this will give you two answers for x-y, one positive and one negative..
here (x+y)^2 = (x-y)^2 + 4xy...
(66)^2 = (x-y)^2 + 4*9..
so .(x-y)^2=66^2-36..
so x-y= $$\sqrt{66^2-36}$$ or -$$\sqrt{66^2-36}$$..
so insuff..hope it helped
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Re: What is the value of x^2 – y^2? [#permalink]
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

Can you provide a solution pushpitkc
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Re: What is the value of x^2 – y^2? [#permalink]
harikrish wrote:
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

Can you provide a solution pushpitkc

The individual statements are not enough. But when we combine the
information in both the statements, we know that the quadratic equation
will be x^2 - (sum of roots)x + product of roots = 0 -> x^2 -66x + 9=0

The roots of this equation are
$$\frac{66 + \sqrt4320}{2} = 33 + 32.86 = 65.86$$ (approximately)
$$\frac{66 - \sqrt4320}{2} = 33 - 32.86 = 0.14$$ (approximately)

If there are two roots, the value of x^2 - y^2 will not be unique. (Insufficient - Option E)
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What is the value of x^2 – y^2? [#permalink]
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

OA:E
What is the value of $$x^2 – y^2$$ or $$(x-y)(x+y)$$?

(1) $$x + y = 66$$
We are given the value of $$x + y$$, and not given the value of $$x-y$$
So Statement 1 alone is not sufficient.

(2) $$xy = 9$$
The product of $$xy$$ is given but we cannot find either individual value of $$x$$ and $$y$$ or value of expression of $$x^2 – y^2$$ or $$(x-y)(x+y)$$
So Statement 2 alone is not sufficient.

Combining 1 and 2, we get

$$x + y = 66$$
$$(x-y)^2 =(x + y)^2-4xy$$
$$(x-y)^2=(66)^2-4*9=(66)^2-(6)^2 =(66+6)(66-6)=72*60=2^1*3^1*5^1*12^2$$
$$x-y = ±12\sqrt{30}$$
So Expression $$x^2 – y^2$$ can have 2 values : $$12*66*\sqrt{30}$$ or $$-12*66*\sqrt{30}$$
Combining (1) and (2) will also not give unique value of expression $$x^2 – y^2$$
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Re: What is the value of x^2 – y^2? [#permalink]
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Re: What is the value of x^2 – y^2? [#permalink]
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