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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The graph of the equation xy = k, where k < 0, lies in which two of th

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Math Expert V
Joined: 02 Sep 2009
Posts: 65785
The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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4
39 00:00

Difficulty:   5% (low)

Question Stats: 79% (00:59) correct 21% (01:07) wrong based on 1782 sessions

### HideShow timer Statistics The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment: 2015-10-16_0900.png [ 3.35 KiB | Viewed 32095 times ]

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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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12
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Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

My Solution:

If k < 0 then the product of x and y = -k

It is only possible when either x or y is negative.

If x is negative and y positive (-x,y) = Quadrant II

If x is positive and y negative (x,-y) = Quadrant IV

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##### General Discussion
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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1
Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

y=k/x (0,0); when x is +ve y will be negative and vice versa --> Quadrant 2 and 4 Answer (D)
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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2
Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

x, y will be different in SIGN, meaning that x <0, y>0 or x>0, y<0

=> Ans: D
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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2
2
xy = k
and k <0
=> x< 0 or y <0
So ,the coordinates will have opposite signs .

Quadrant 2 : (-x , y )

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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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1
XY=K and K<0 ; so we can say that
1. X is negative y is positive
2. X is positive y is negative
3. neither of them will not be zero

Hence to satisfy above conditions; equation xy<o has to be in 2nd and 4th quadrant where one of them will be positive and another will be negative.
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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1
Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

D - If you the graph of y=1/x then just take the reflection of that curve about the axis to get y=-1/x
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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3
Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
The attachment 2015-10-16_0900.png is no longer available

To answer any such question, the easiest way is to choose the value of unknowns as per the given constraint (e.g. k = -10 or -20 etc.) and then substitute value of one of the variables and calculate the value of other variable as per the given expression (xy=k in this case) and finally plot them to answer the question

Please refer the figure below with assumed value of k = -10

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File comment: www.GMATinsight.com Solution_!.jpg [ 97.19 KiB | Viewed 27591 times ]

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The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Can this equation be brought into the y=mx+b form or is it a quadratic. If it can then what is the slope for this equation considering it has two different lines in different quadrants?

Thanks!
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

We know xy<0.
So x&y will have opposite signs. Now in Q3 & Q1, x&y have equal signs. So only possible placement for line will be out of Q1 and Q4.
That means line xy=k will lie on Q3&Q4.

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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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1
Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

Solution:

We are given the equation xy = k, where k is negative. It follows that x and y must have opposite signs. That is, either x is positive and y is negative, which is only possible in Quadrant IV, or, x is negative and y is positive, which is only possible in Quadrant II.

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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

xy=k ==>xy=k+0
y=k/x +0
equation for line is y=mx+b
So we know y intercept is 0 which means when x=0, y=0
Meaning the line is passing through the origin (0,0) ==> perfect.
Now we need to figure out the slope==> k is the slope==> it is negative (given in question stem)==> line starts in Q II passes through the origin (0,0) and enters Q IV

Answer should have Q II and Q IV in it.
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
2015-10-16_0900.png

here,
K=negative
xy=k
xy=(-)
(-) (+)=(-) ----->which indicates quadrant II
(+) (-)=(-) ----->which indicates quadrant IV

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The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Top Contributor
Attached is a visual that should help. I suggest picking a simple negative number for k, such as -1, to make the concept more clear.

Note that the question doesn't say what k equals, so you are allowed to set the value of k to any negative number, and it should still work.
Attachments Screen Shot 2017-05-30 at 4.07.06 PM.png [ 76.29 KiB | Viewed 22332 times ]

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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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If k < 0 then the product of x and y = -k

It is only possible if either x or y is negative.

x is -ve & y +ve (-x,y) = Quadrant II

Option should be A, C, D

Lets look at point second condition
x is +veand y -ve (x,-y) = Quadrant IV

Ans D
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Please do not overcomplicate the question at hand. We are told that x * y = k and k<0. So x*y<0 meaning that there are two possible combinations:

x * y < 0 when

(1) negative * positive, OR
(2) positive * negative

Now it is plain simple: (1) lies in the II quadrant while (2) is in the IV quadrant.
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Re: The graph of the equation xy = k, where k < 0, lies in which two of th  [#permalink]

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Bunuel wrote: The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

(A) I and II
(B) I and III
(C) II and III
(D) II and IV
(E) III and IV

Kudos for a correct solution.

Attachment:
The attachment 2015-10-16_0900.png is no longer available

Graphical solution. Since xy < 0, either x or y is negative.
Attachment: xy = k.png [ 41.89 KiB | Viewed 3035 times ]

_________________ Re: The graph of the equation xy = k, where k < 0, lies in which two of th   [#permalink] 06 Mar 2020, 02:43

# The graph of the equation xy = k, where k < 0, lies in which two of th  