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If x2/9 4/y2 = 12, what is the value of x? (1) x/3 + 2/y = 6

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If x2/9 4/y2 = 12, what is the value of x? (1) x/3 + 2/y = 6 [#permalink] New post 25 Jul 2008, 23:46
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If x2/9 – 4/y2 = 12, what is the value of x?

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

(2) x/3 – 2/y = 2
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Re: DS: value of x (n3.17) [#permalink] New post 26 Jul 2008, 08:03
IMO D.

2 equations 2 variable (1 equation from question and one from statement).

From 1 the equation 4/y^2 = 36+x^2/9-4x
From 2 the equation 4/y^2 = 4+X^2/9+4x/3

Last edited by abhijit_sen on 26 Jul 2008, 10:14, edited 1 time in total.
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Re: DS: value of x (n3.17) [#permalink] New post 26 Jul 2008, 08:20
same reasoning as above for D . Two eqns, two unknowns, so each statement on its own should be sufficient ... dont have to bother to solve :)
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Re: DS: value of x (n3.17) [#permalink] New post 26 Jul 2008, 09:18
Good explanation.

OA is D
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Re: DS: value of x (n3.17) [#permalink] New post 26 Jul 2008, 10:01
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pmenon wrote:
same reasoning as above for D . Two eqns, two unknowns, so each statement on its own should be sufficient ... dont have to bother to solve :)

please note that I also did not solve to the end. But we do need to solve it till the point I solved. Because it might happen that we end up in a quadratic equation in X, which might give you 2 value in which case A alone or B alone may not be sufficient and we may have to go for combined value.
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Re: DS: value of x (n3.17) [#permalink] New post 26 Jul 2008, 10:17
Good explanation Abhijit.

Kudos for you.
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Re: DS: value of x (n3.17) [#permalink] New post 26 Jul 2008, 22:29
abhijit_sen wrote:
pmenon wrote:
same reasoning as above for D . Two eqns, two unknowns, so each statement on its own should be sufficient ... dont have to bother to solve :)

please note that I also did not solve to the end. But we do need to solve it till the point I solved. Because it might happen that we end up in a quadratic equation in X, which might give you 2 value in which case A alone or B alone may not be sufficient and we may have to go for combined value.


well said. abhijit.

In exam, if I have time, I will make sure I solve to the end.
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Re: DS: value of x (n3.17) [#permalink] New post 29 Jul 2008, 01:19
abhijit_sen wrote:
IMO D.

2 equations 2 variable (1 equation from question and one from statement).

From 1 the equation 4/y^2 = 36+x^2/9-4x
From 2 the equation 4/y^2 = 4+X^2/9+4x/3

in exam if I have no time to solve to the end, what are signals to recognize the suff anwer. As you mentioned above, 2 equations 2 variable, but one is a line, one is a quadratic equation, so they can cut each other at 2 points so we have 2 value, or 1 point or no point. So it it hard to pick the answer if we don't solve to the end.
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Re: DS: value of x (n3.17) [#permalink] New post 29 Jul 2008, 01:50
The way I would solve this is as below.

x^2/9 - 4/y^2 = 12 or (x/3+2/y)(x/3-2/y) = 12

Stmt 1: if x/3 + 2/y is 6 then x/3-2/y will become 2.

We can add the two equations and get 2x/3 = 8 or x = 12.

Similarly, Stmt2.

Hence, answer is D.
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Re: DS: value of x (n3.17) [#permalink] New post 29 Jul 2008, 06:00
scthakur wrote:
The way I would solve this is as below.

x^2/9 - 4/y^2 = 12 or (x/3+2/y)(x/3-2/y) = 12

Stmt 1: if x/3 + 2/y is 6 then x/3-2/y will become 2.

We can add the two equations and get 2x/3 = 8 or x = 12.

Similarly, Stmt2.

Hence, answer is D.


can you elaborate this "We can add the two equations and get 2x/3 = 8 or x = 12."?
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Re: DS: value of x (n3.17) [#permalink] New post 30 Jul 2008, 12:41
judokan wrote:
If x2/9 – 4/y2 = 12, what is the value of x?

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

(2) x/3 – 2/y = 2



x2/9 – 4/y2 = 12 -->
(x/3+2/y)(x/3 - 2/y)=12 --(equation A)

(1) x/3 + 2/y = 6 -----(equation B)
substitute (1) above value into equation (A)
(x/3+2/y)(x/3 - 2/y)=12 --> 6 (x/3 - 2/y)=12
--> x/3 - 2/y =2 --- (equation C)
we have two equations.. two unknowns... must be sufficient
(2) x/3 – 2/y = 2 -- (C)
(x/3+2/y)2=12 --> 2 (x/3 - 2/y)=6
we have two equations.. two unknowns... must be sufficient


Did you observe that State1 * State 2 = Question..---> then we can say that Answer D...(when State1 & State2 are not quartic/cubic.. higher power.. have only two unknown variables.)
No calculations..required..
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Re: DS: value of x (n3.17) [#permalink] New post 03 Aug 2008, 07:46
judokan wrote:
If x2/9 – 4/y2 = 12, what is the value of x?

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

(2) x/3 – 2/y = 2


IMO D

since given that :
(x/3 + 2/y)(x/3 – 2/y)=12

(1) says x/3 + 2/y = 6
=> (x/3 – 2/y)=12/6=2 => combining these two x=12 SUFF

(2) says x/3 – 2/y = 2
=> x/3 + 2/y = 6 => combining these two x=12 SUFF

IMO D
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Re: DS: value of x (n3.17)   [#permalink] 03 Aug 2008, 07:46
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