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Math Expert V
Joined: 02 Sep 2009
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Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (01:26) correct 37% (01:47) wrong based on 188 sessions

### HideShow timer Statistics Line L passes through points R(0, -5 ) and S(4,0) (see figure above). Point P with coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

Attachment: CG.png [ 12.48 KiB | Viewed 3962 times ]

Attachment: 2015-06-24_1012.png [ 6.72 KiB | Viewed 2377 times ]

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Originally posted by Bunuel on 09 Jun 2013, 04:42.
Last edited by Bunuel on 15 Oct 2017, 09:49, edited 2 times in total.
Renamed the topic, edited the question, added the figure and the tags.
Math Expert V
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Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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1
1 Line L passes through points (0, -5) and S (4, 0) (see figure above). Point P with coordinates (x, y) is a point on line L. Is xy > 0 ?

(1) x > 4. Look at the diagram: since point P is on line L, and x > 4, then point P must be in the I quadrant, where both x and y coordinates of a point are positive. Thus xy > 0. Sufficient.

(2) y > -5. Again, from the diagram it follows that point P is either in the IV quadrant (here x is positive and y is negative --> xy < 0) or in the I quadrant (here both x and y are positive --> xy > 0). Not sufficient.

Hope it's clear.
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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1
vinijo wrote:
Thanks a ton for your time Bunuel..

But it is still not clear to me, since x>4 , x could be in either first quadrant or fourth ,in first quadrant x and y are both positive
so xy>0 but in fourth quadrant x is positive and y negative so xy<0..

Since A is only telling about x and nothing about y how can we presume that y>0 as well so why A??

Look at the diagram below:
Attachment: CG.png [ 12.25 KiB | Viewed 3815 times ]
Now, since X-coordinate of point P is more than 4 AND point P is on line L, then it must be on the red part of the line, where Y-coordinate is positive too.

Hope it's clear.
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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1
1
Quote:
Line L passes through points R(0, -5 ) and S(4,0) (see figure above). Point P with coordinates (x, y) is a point on Line L Is xy > 0?

For xy>0, x and y should have the same sign (positive X positive >0 and negative X negative >0) and not equal to 0.

In this case, that means that the point P should be in I or III quadrant.

1) x > 4

If x >4, then it should be right of the point S (4,0), and as the slope is positive, y will be > 0 and point P is in the first quadrant. Sufficient.

(2) y > - 5

If y > -5, point P is to the right of point R (0,-5), hence it can be in quadrants I and IV, if it's in I then xy >0, if it's in IV then xy <0 (because y<0 and x>0).

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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vinijo wrote:
Line L passes through points (0,-5) and S (4,0). Point P with coordinates (x,y) is a point on line L .
Is xy>0??

(1) x>4
(2) y>-5

The equation of the line is$$\frac{x - x_1}{x_1 - x_2} = \frac{y - y_1}{y_1 - y_2}$$

$$\frac{x - 0}{0 - 4} = \frac{y + 5}{-5 - 0}$$

5x - 4y = 20

1) If x>4, 5x > 20. So, y must be greater than 0. Sufficient.

2) If y>-5, y can be 0 in which case x would be 4 or y can be 5 in which case x would be 8. So xy can be 0 or 40. Insufficient.

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Thanks a ton for your time Bunuel..

But it is still not clear to me, since x>4 , x could be in either first quadrant or fourth ,in first quadrant x and y are both positive
so xy>0 but in fourth quadrant x is positive and y negative so xy<0..

Since A is only telling about x and nothing about y how can we presume that y>0 as well so why A??
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Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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24. Coordinate Geometry

Attachment: 2015-06-24_1012.png [ 6.72 KiB | Viewed 4509 times ]

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Bunuel wrote: Line L passes through points R(0, -5 ) and S(4,0) (see figure above). Point P with coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

Kudos for a correct solution.

Attachment:
2015-06-24_1012.png

Question : is a point on Line L Is xy > 0?

for xy to be greater than zero, the sign of x and y both be same (either both positive or both Negative)

Question REDEFINED : Does point P lie in the 1st Quadrant or 3rd Quadrant?

Statement 1: x > 4

For x to be greater than 4, the point P must lie on the line towards the right of point S. [As per the figure]
Towards the right of Point S, every part of the Line is in 1st Quadrant

Hence SUFFICIENT

Statement 2: y > - 5

For y to be Greater than -5, the point P must lie on the line towards the Right of point R. [As per the figure]
Towards the right of Point R, Some part of the Line is in 4th Quadrant and Some part is in 1st Quadrant

Hence NOT SUFFICIENT

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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From the diagram we can say that Line L passed from quadrant 1,3 and 4. If we know where (x,y) lies we would be able to say x*y>0 or not.
A) x>4 , no info about y so Insufficient
B) Y>-5 , no information about x so Insufficient

A+B, X>4 but Y can be negative or positive so as Y>-5( y= -5 or 0 or +4) so still Insufficient.

Thanks,
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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lipsi18 wrote:
From the diagram we can say that Line L passed from quadrant 1,3 and 4. If we know where (x,y) lies we would be able to say x*y>0 or not.
A) x>4 , no info about y so Insufficient
B) Y>-5 , no information about x so Insufficient

A+B, X>4 but Y can be negative or positive so as Y>-5( y= -5 or 0 or +4) so still Insufficient.

Thanks,

Hi lipsi18,

I hope you might want to consider the inference of Statement-1

There is no information about Y needed as you can see in the figure that when x co-ordinate is greater than 4 then the part of line falls in only 1st Quadrant where both x and y will essentially be positive hence x*y will be positive thereby giving the unique answer of the question.

Hence, SUFFICIENT
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Bunuel wrote: Line L passes through points R(0, -5 ) and S(4,0) (see figure above). Point P with coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

Kudos for a correct solution.

Attachment:
2015-06-24_1012.png

MANHATTAN GMAT OFFICIAL SOLUTION:

First, note that this is a Yes/No Data Sufficiency question.

Line L passes through three quadrants:

Quadrant I, where x and y are both positive, so xy > 0 and the answer is “yes.”
Quadrant III, where x and y are both negative, so xy > 0 and the answer is “yes.”
Quadrant IV, where x is positive and y is negative, so xy < 0 and the answer is “no.”

If you can determine what quadrant point P is in, you will have sufficient information to answer the question. Also, if you know that point P is in either quadrant I or quadrant III, that would also be sufficient.

(1) SUFFICIENT: If x > 4, then Point P is in Quadrant I, so xy > 0 and the answer is “yes.”

(2) INSUFFICIENT: If y > -5 , then Point P could be in either Quadrant I (xy > 0) or Quadrant IV (xy < 0).

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Line L passes through points R (0, -5 ) and S (4,0)(see figure above). Point P with
coordinates (x, y) is a point on Line L Is xy > 0?
(1) x > 4
(2) y > - 5
Attachments Capture.PNG [ 5.44 KiB | Viewed 3513 times ]

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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PathFinder007 wrote:
Line L passes through points R (0, -5 ) and S (4,0)(see figure above). Point P with
coordinates (x, y) is a point on Line L Is xy > 0?
(1) x > 4
(2) y > - 5

Hi Bunuel,

Could you please provide your comments on this. Why x can not be in quarter 4. And this is an positive slope so x and y will have different sign so it should be <0. according to MGMAT xy>0. Please clarify

Thanks
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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PathFinder007 wrote:
PathFinder007 wrote:
Line L passes through points R (0, -5 ) and S (4,0)(see figure above). Point P with
coordinates (x, y) is a point on Line L Is xy > 0?
(1) x > 4
(2) y > - 5

Hi Bunuel,

Could you please provide your comments on this. Why x can not be in quarter 4. And this is an positive slope so x and y will have different sign so it should be <0. according to MGMAT xy>0. Please clarify

Thanks

I will try to answer this.

For x>4 and the point P to lie on the line L, the only case possible for x,y to lie in the 1st quadrant. If you look closely at the graph provided, the line post x>4, lies entirely in quadrant 1. Thus x>0 and y>0 in the 1st quadrant giving you xy>0 for statement 1.

Thus statement 1 is sufficient.

You can check it this way, equation of a line passing through (4,0) and (0,-5) is:

$$\frac{y-0}{x-4} = \frac{-5-0}{0-4}$$ --->$$4y=5x-20$$

Now if a point P with coordinates (x,y) has to be in quadrant 4, y <0

So from the equation of the line, 4y=5x-20---> 5x-20/4< 0 ---> 5x-20< 0 ---> x<4. Thus, a point on line L with y<0 can only be true for x<4. As statement 1 mentions that x>4, point P can not lie in quadrant 4.

Hope this helps.
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Pritishd wrote:
Line L passes through points R (0, -5 ) and S (4,0). Point P with
coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

As per my reasoning, if xy>0 then either both x and y should be +ive (1st Quad) or both should be -ive (3rd Quad)
(1) does not provide information on the y coordinate. Because if y is negative, then P will be in 4th Quad where xy<0, and if y is positive then P will be in the 1st quad where xy>0

Same for (2), there is no info. on the x coordinate.

Combining both (x,y)=(4,-5) P is in 4th quad so xy<0. C should be sufficient.

Kindly help me in identifying the mistake I am making.

Hi Pritishd,
look at th epoints given
R (0, -5 ) and S (4,0)...
what does it tell you when x moves from 0 to 4, y moves from -5 to 0..
so the line is intersecting x axis at y=-5 and y axis at x=4..
so when x>4, y will move from -ive value to positive value ..
And so is Suff..

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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Pritishd wrote:
Line L passes through points R (0, -5 ) and S (4,0). Point P with
coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

As per my reasoning, if xy>0 then either both x and y should be +ive (1st Quad) or both should be -ive (3rd Quad)
(1) does not provide information on the y coordinate. Because if y is negative, then P will be in 4th Quad where xy<0, and if y is positive then P will be in the 1st quad where xy>0

Same for (2), there is no info. on the x coordinate.

Combining both (x,y)=(4,-5) P is in 4th quad so xy<0. C should be sufficient.

Kindly help me in identifying the mistake I am making.

You could have prevented the confusion by first finding the equation (this should be your 1st step when you deal with coordinate geometry questions (lines in particular)).

As the intercepts of the line are 4 and -5 (along x and y respectively), equation of the line becomes:

x/4 + y/-5 = 1 ---> 5x-4y=20 is the equation.

Per statement 1: x>4 ---> either you can draw the line and see that this statement will definitely be sufficient as all the (x,y) points after x>4 will also make y>0 or get this information from the equation as follows:

5x-4y=20 ---> x = (20+4y)/5 > 4 ---> y >0. Thus xy>0. sufficient.

Per statement 2: y > -5 , again either use the equation or use the line information (once you draw it!).

From the equation, y=(5x-20)/4 > -5 , giving you x > 0 but now since there are values for y that lie in the ranges -5<y<0 (giving you xy<0) and 0<y (giving you xy >0). Thus you get 2 different answers for "is xy>0" and hence this statement is NOT sufficient. Refer to the attached image for better understanding of sufficiency of this statement.

Attachment: 3-07-16 6-57-02 AM.jpg [ 49.42 KiB | Viewed 2551 times ]

A is thus the correct answer.

Hope this helps.
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Line L passes through points R (0, -5 ) and S (4,0). Point P with
coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

Modify the original condition and the question. If coordinates (x,y) passes through (0,-5),(4,0), the question is if there is a point on quadrant 1 or quadrant 3 in order to satisfy xy>0. However, in 1), which means (x,y) is on quadrant 1, which is sufficient. Therefore, the answer is A.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Bunuel wrote: Line L passes through points R(0, -5 ) and S(4,0) (see figure above). Point P with coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

Kudos for a correct solution.

Attachment:
2015-06-24_1012.png

Key to this question- just remember the criteria given in both statements relative to the line

Statement 1

If x is greater than 4 then any value that corresponds to the line must have a y value greater than 0

Suff

Statement 2

If y is greater than -5 then it could either still be a coordinate with a negative y value which would make xy negative or it could be above o which would make xy pso

Insuff

Thus
"A'
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Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  [#permalink]

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Bunuel wrote: Line L passes through points R(0, -5 ) and S(4,0) (see figure above). Point P with coordinates (x, y) is a point on Line L Is xy > 0?

(1) x > 4
(2) y > - 5

Attachment:
CG.png

Attachment:
2015-06-24_1012.png

#1
seeing the graph we can say for x>4 and since the point is on line L so y has to be +ve ;hence xy>0 sufficient
#2
y>-5
x can be either + or -ve so insufficient
IMO A Re: Line L passes through points R(0, -5 ) and S(4,0) (see figure above).   [#permalink] 23 Nov 2019, 08:30
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# Line L passes through points R(0, -5 ) and S(4,0) (see figure above).  