If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y

[zealous87]

I found this DS question while giving the CAT

If x2/9 - 4/y2 = 12, what is the value of x?

(1) x/3 + 2/y = 6

(2) x/3 - 2/y = 2


The OE given is based on the formula:
x^2-y^2 = (x+y)(x-y)

where the author assumes x = x/3 and y = 2/y.

I reasoned that in this case, x could also be x/-3 and y could be-2/y also. This made me mark the choice as C rather than D.

I would be grateful if someones explains this.

[gokul_nair1984]

You are right in your approach,
I do understand that you can get x=x/-3 but y cannot be
-2/y..It has to be 2/y

Only then you will get (x/-3)^2-(2/y)^2 as x2/9 - 4/y2 .

Now even if x=-x/3, the given question stem can be reduced to :

(-x/3+2/y)(-x/3-2/y)=12-------(1)

Case 1: x/3 + 2/y = 6
Take out negative common from the second part of the question stem . Thus you can reframe (1) as (-x/3+2/y)*-(x/3+2/y)=12

Susbstituting, x/3 + 2/y = 6 we get 2 equations ,

(-x/3+2/y)=-2 and x/3 + 2/y = 6...Thus Sufficient( as you can find 'x')

Case 2: x/3 - 2/y = 2
Take the negative sign common from first part of the question stem to rephrase (1) as -(x/3-2/y)(-x/3-2/y)=12.

Substituting, x/3 - 2/y = 2 , you will again get 2 equations from which you can find 'x'

Hence Answer is D

Hope this helped

[zealous87]

I think i missed out, but doesnt (-2/y)^2 =4/y^2?

If so, why cannot y=-2/y?

I get your explanation perfectly, i just need a reason for y not equal to (-2/y).

Thanks!

[gokul_nair1984]

I get what you are trying to say, y=-2/y can also be true:

We can have 4 cases:
1. x=x/3, y=2/y(ie;both x and y are positive)
2. x=x/3 , y=-2/y(x-positive, y-negative)
3. x=-x/3, y=2/y(x-negative , y- positive)
4. x=-x/3, y=-2/y(ie; both x and y are negative)

This is our question stem:
(-x/3+2/y)(-x/3-2/y)=12-------(1)
Term1 [b]Term 2

For Case 1: Take '- sign' common from Term 2 and substitute x=x/3, y=2/y
For Case 2: Take '-ve sign' common from Term 1 and substitute x=x/3 , y=-2/y
For Case 3:Substitute directly in the first term
For Case 4 :Substitute directly in the second term


This just means whatever case it might be out of the 4 given cases you can always find a solution by appropriate substitution and dividing the same further with the two statements

[zealous87]

Thanks. This works out fine.

[kaushaldave]

One way of looking at this is:
1) can equation 1 (statement 1) solve x = yes
2) can the equation 2 (statement 2) solve x = yes
Since this is DS, it definitely tells us that each statement alone is sufficient.
Fore e.g: x/3+2/y=6, which means 2/y=6-x/3. Now if we substitue this value of y in our main equation x^2/9-4/y^2=12 you can solve for x. Since its DS we dont need the answer. Same way you will get a value for y in the 2nd equation too. Plug in that value and you can solve x.
So, just by a little visual run, you can solve this as well. Not sure if this is the right way or a risky way unless you are exremely confident.
Thanks for the post

[mschwrtz]

ty

[nikhil.baveja]

Sorry for opening up the thread, but I still don't understand something, and its pretty fundamental, that I cannot do under-root of anything in this entire statement for eg i cannot do a undr-root of 12 as it may be 6or -6 and on left hand side I cannot do an under-root of x^2 /9 as I don't know wether its X or -X similarly whether its +-9, so how should one approach this?

[tim]

can you explain more about what you mean by "under-root" and what your specific question is? i'm not able to understand what you're asking..

[nikhil.baveja]

Sorry Tim,

by under-root I meant Square root
I understand that exponent with even powers have hidden base, therefore I am confused with this question.
if you can clarify, and also if you can point me to some post/article as to where I can square root something in Gmat conditions

[tim]

okay i still must not understand your question, because i don't see how the square root of 12 can be 6. but here's the general principle to keep in mind: if the GMAT gives you a square root sign in the problem, there is only one answer, and it must not be a negative number. So if in other words if they ask you for the square root of nine, it's three. On the other hand, if the GMAT gives you something like a quadratic, and you decide on your own to insert a square root into the problem, then you must account for positive and negative solutions if appropriate. So for instance if the GMAT gives you a problem that says x^2 = 9 and you decide to take the square root of both sides, then your solution must be x = 3 or -3..

[velchal_rao]

I did this :

x(square ) - y(square ) = (x+y) (x - y)

looking at the condition given in the problem and the statements
(i thought they were clues )

condition is in the form x(square) - y(square )
STATEMENT 1: is in the form (x + y)

without the help of STATEMENT 2 , using STATEMENT 1 alone we can find (x - y)

now solve like two two equations , two variables and get values


Similar logic for STATEMENT 2

So , the answer is "D"

[RonPurewal]

I did this :

x(square ) - y(square ) = (x+y) (x - y)

looking at the condition given in the problem and the statements
(i thought they were clues )

condition is in the form x(square) - y(square )
STATEMENT 1: is in the form (x + y)

without the help of STATEMENT 2 , using STATEMENT 1 alone we can find (x - y)

now solve like two two equations , two variables and get values


Similar logic for STATEMENT 2

So , the answer is "D"

Yep.