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

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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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Joined: 01 Mar 2015
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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

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$$(-1, 1)$$

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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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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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 Retired Moderator V
Joined: 22 Jun 2014
Posts: 1093
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20 GPA: 2.49
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Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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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]

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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

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

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 V
Joined: 02 Sep 2009
Posts: 58391
The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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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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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 V
Joined: 02 Sep 2009
Posts: 58391
Re: The (x, y) pair (-1, 1) satisfies which of the following equations?  [#permalink]

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

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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

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS Re: The (x, y) pair (-1, 1) satisfies which of the following equations?   [#permalink] 23 Jan 2019, 23:28
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