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If x - y = 9, which of the following would be sufficient to

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Farina
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If x - y = 9, which of the following would be sufficient to [#permalink] New post   19 Jul 2020, 23:09
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If \(x - y = 9\), which of the following would be sufficient to determine the values of both x and y individually?

Indicate all possible equations.

A. x + y = 13
B. x² - y² = 117
C. (x - y)² = 81
D. (x + y)² = 16
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A,B
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sukrut96
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   19 Jul 2020, 23:20
Why not D ? We can take root such that x + y = 4 and then add the equations to get individual values of x and y. It is not specified that x and y are integer values.
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 01:56
sukrut96 wrote:
Why not D ? We can take root such that x + y = 4 and then add the equations to get individual values of x and y. It is not specified that x and y are integer values.


It will be +4 and -4 I think..two roots I guess
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 02:22
Farina wrote:
sukrut96 wrote:
Why not D ? We can take root such that x + y = 4 and then add the equations to get individual values of x and y. It is not specified that x and y are integer values.


It will be +4 and -4 I think..two roots I guess


Yes, but still we can find out the values.
x - y = 9 and x + y = +-4
On adding the two equations, we get, x can be 6.5 or 2.5 (based on which value one chooses). And accordingly by substituting the value in first equation, we can find out y.
If the question mentioned that x and y are integers, then only A and B would satisfy the condition.
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 02:42
sukrut96 wrote:
Farina wrote:
sukrut96 wrote:
Why not D ? We can take root such that x + y = 4 and then add the equations to get individual values of x and y. It is not specified that x and y are integer values.


It will be +4 and -4 I think..two roots I guess


Yes, but still we can find out the values.
x - y = 9 and x + y = +-4
On adding the two equations, we get, x can be 6.5 or 2.5 (based on which value one chooses). And accordingly by substituting the value in first equation, we can find out y.
If the question mentioned that x and y are integers, then only A and B would satisfy the condition.


Well acc. to the source the answers are A and B. I was also confused that is why posted the question here. Lets wait for the experts.
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 02:48
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Okay sure :), can you please specify the source.
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 05:33
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I disagree.

First, this is not a goo question and the wording is NOT from the GRE



however, pick up B for instance: it is \(x^2-y^2=117\)

\(x-y \times x+y=117\)


But x-y is 9 and x+y must be 13

However, x-y for being nine we could have a lot of values for x and y and the same for 13

which of the following would be sufficient to determine the values of both x and y individually?

I have some thought on this question
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 05:50
Carcass wrote:
I disagree.

First, this is not a goo question and the wording is NOT from the GRE



however, pick up B for instance: it is \(x^2-y^2=117\)

\(x-y \times x+y=117\)


But x-y is 9 and x+y must be 13

However, x-y for being nine we could have a lot of values for x and y and the same for 13

which of the following would be sufficient to determine the values of both x and y individually?

I have some thought on this question


Carcass this question is from GRE tests of the greprepclub
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Farina
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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 05:51
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sukrut96 wrote:
Okay sure :), can you please specify the source.

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Re: If x - y = 9, which of the following would be sufficient to [#permalink] New post   20 Jul 2020, 07:54
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Mah.....

I am not the expert of the quant tests. For sure they know better than me :roll:
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