What is the value of x^2 – y^2?

Question

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

chetan2u · Answer

Hi,
firstlwhat 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 either we know the values of the difference and sum of two numbers or the values of x and y..
lets see the statements.
1)x+ y= 66.... we are yet to know x-y.. insuff
2)xy=9.. again nothing what we are looking for..

combined it gives  an imaginary number..  different values of x and y, which will not give you a unique answer..
E
you may search for DS and you will get a way to move around these type of Qs..best of luck

porvakanti · Answer

Thanks Chetan.
So the answer is C - Neither 1 or 2 is sufficient ?

Bunuel · Answer

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

chetan2u · Answer

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 be square root of a negat.... ,
 after writing till here, i realize ofcourse it will be positive,... an oversight 
thanks

chetan2u · Answer

Hi since none are sufficient and combined too they are not suff,
answer will be E,
answer will be C, when you get a certain answer after you have combine the info provided by the two statement

vbandyo · Answer

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

umodi · Answer

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.

chetan2u · Answer

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

harikrish · Answer

Can you provide a solution  pushpitkc

pushpitkc · Answer

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)

Bismarck · Answer

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

bumpbot · Answer

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What is the value of x^2 – y^2?

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