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The (x, y) pair (-1, 1) satisfies which of the following equations?

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HKD1710
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The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   17 Nov 2018, 10:38
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The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


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E
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   17 Nov 2018, 11:03
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HKD1710 wrote:
The \((x, y)\)pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Putting x = -1 and y = 1 in all equations
I. \(2x^3 - y^2 = -3\)
=> -2 - 1 = -3
=> -3 = -3
Satisfy

II. \(2x^2 - y^3 = 1\)
=> 2 - 1 = 1
=> 1 = 1
Satisfy

III. \(x^2 - 2y^3 = -1\)
=> 1 - 2 = -1
=> -1 = -1
Satisfy

All equations are satisfied

Answer choice (E)

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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   17 Nov 2018, 11:21
\((-1, 1)\)

I. \(2 (1-)^3 - 1^2 = -3\) ---> -2-1 = -3 YES
II. \(2x^2 - y^3 = 1\) ----> 2(1)- 1 =1 YES
III. \(x^2 - 2y^3 = -1\) ----> 1 -2 (1) = -1 YES


E
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The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 07:23
HKD1710 wrote:
The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Project PS Butler : Question #24


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Hi HKD1710

why in equation

I. \(2x^3 - y^2 = -3\)

\(- y^2\) = -1 and not +1?

I know there is some reason behind that but don't know what it is. Could you please assist.
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HKD1710
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 11:56
Gmatprep550 wrote:
HKD1710 wrote:
The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Project PS Butler : Question #24


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Hi HKD1710

why in equation

I. \(2x^3 - y^2 = -3\)

\(- y^2\) = -1 and not +1?

I know there is some reason behind that but don't know what it is. Could you please assist.


\(y=1\)

\(y^2 = 1^2\)

\(y^2 = 1\)

\(- y^2 = - 1\)
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 22:17
HKD1710 wrote:
Gmatprep550 wrote:
HKD1710 wrote:
The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Project PS Butler : Question #24


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Hi HKD1710

why in equation

I. \(2x^3 - y^2 = -3\)

\(- y^2\) = -1 and not +1?

I know there is some reason behind that but don't know what it is. Could you please assist.


\(y=1\)

\(y^2 = 1^2\)

\(y^2 = 1\)

\(- y^2 = - 1\)



But \(- y^2\) also = - y * - y =- 1 * - 1 which = + 1 hence would like to know when to follow above method described by you. I am sure we will follow that if \(y^2\) would have provided in bracket for ex \(-(y^2)\)

Hope you are getting where I am getting confused.

Thanks !
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The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 22:22
Expert Reply
Gmatprep550 wrote:
HKD1710 wrote:
Gmatprep550 wrote:
The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III



Hi HKD1710

why in equation

I. \(2x^3 - y^2 = -3\)

\(- y^2\) = -1 and not +1?

I know there is some reason behind that but don't know what it is. Could you please assist.


\(y=1\)

\(y^2 = 1^2\)

\(y^2 = 1\)

\(- y^2 = - 1\)



But \(- y^2\) also = - y * - y =- 1 * - 1 which = + 1 hence would like to know when to follow above method described by you. I am sure we will follow that if \(y^2\) would have provided in bracket for ex \(-(y^2)\)

Hope you are getting where I am getting confused.

Thanks !


No. \(-y^2=-(y*y)\). On the other hand \((-y)*(-y) = y^2\).
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 22:32
I am wondering why \(-1^2 = +1\) where as \(-Y^2 = -(Y*Y)\)?
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 23:15
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Gmatprep550 wrote:
I am wondering why \(-1^2 = +1\) where as \(-Y^2 = -(Y*Y)\)?


\(-1^2=-(1^2) =-1\), while \((-1)^2=1\).
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   23 Jan 2019, 23:28
simply plugin for x,y (-1,1) ; all options are valid
IMO E

HKD1710 wrote:
The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Project PS Butler : Question #24


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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink] New post   17 Nov 2021, 08:24
HKD1710 wrote:
The \((x, y)\) pair \((-1, 1)\) satisfies which of the following equations?

I. \(2x^3 - y^2 = -3\)
II. \(2x^2 - y^3 = 1\)
III. \(x^2 - 2y^3 = -1\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Project PS Butler : Question #24


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Plug in the values \((-1, 1)\) in all the options (I), (II) & (III) , all satisfies, Answer must be (E)
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations? [#permalink]
17 Nov 2021, 08:24
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