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zealous87
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Post subject: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y  Posted: Sun Aug 15, 2010 1:05 pm |
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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.
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gokul_nair1984
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Post subject: Re: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y Posted: Mon Aug 16, 2010 5:39 am |
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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
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zealous87
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Post subject: Re: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y Posted: Mon Aug 16, 2010 11:01 pm |
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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!
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gokul_nair1984
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Post subject: Re: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y Posted: Tue Aug 17, 2010 2:18 am |
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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
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zealous87
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Post subject: Re: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y Posted: Tue Aug 24, 2010 1:04 am |
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Thanks. This works out fine.
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kaushaldave
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Post subject: Re: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y Posted: Tue Aug 24, 2010 9:51 pm |
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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
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mschwrtz
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Post subject: Re: If x2/9 – 4/y2 = 12, what is the value of x? (1) x/3 + 2/y Posted: Fri Sep 03, 2010 3:13 am |
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