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

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

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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

Project PS Butler : Question #24

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Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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17 Nov 2018, 11:03
1
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

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Joined: 09 Mar 2016
Posts: 1230
Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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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]

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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

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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Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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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

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]

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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

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 !
_________________
______________________________
Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

Please let me know if I'm wrong somewhere and help me to learn
Math Expert
Joined: 02 Sep 2009
Posts: 58391
The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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23 Jan 2019, 22:22
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]

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23 Jan 2019, 22:32
I am wondering why $$-1^2 = +1$$ where as $$-Y^2 = -(Y*Y)$$?
_________________
______________________________
Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

Please let me know if I'm wrong somewhere and help me to learn
Math Expert
Joined: 02 Sep 2009
Posts: 58391
Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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23 Jan 2019, 23:15
1
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]

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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

Re: The (x, y) pair (-1, 1) satisfies which of the following equations?   [#permalink] 23 Jan 2019, 23:28
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