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Point (P, Q) is in the coordinate plane. Is P > Q?

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Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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26 Feb 2015, 05:41
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Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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26 Feb 2015, 08:29
1
1
1) P is positive is x=0 line all points in 1, 4 quadrants insufficient as we don't have any idea about Q
2) Y=X+1
y=x is the line where all the y's =x's so y=x+1 is offset by 1 and hence all the x will be always be smaller than y. PQ will lie above so they will follow same trend. Sufficient.

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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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26 Feb 2015, 08:45
(1) Insufficient. There are several possibilities.
(2) Sufficient. If P=1 and Q=2, the answer to the question is no. If P=-2 and Q=-1, the answer is no. So Q is always going to be more than P.

I think it's B
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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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02 Mar 2015, 06:47
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Bunuel wrote:
Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

We see the x > y type question in the prompt, which makes us suspect that the line y = x will play an important part at some point.

Statement #1 just tells us P is positive, nothing else. The point (P, Q) = (4, 2) has the property that P > Q, but the point (P, Q) = (4, 5) has the property that P < Q. Clearly, just knowing P is positive does nothing to help us figure out whether P > Q. Statement #1, by itself, is wildly insufficient.

Statement #2 is intriguing. It discusses not the line y = x but the line y = x + 1. What is the relationship of those two lines? First of all, they are parallel: they have the same slope. The line y = x has a y-intercept of zero (it goes through the origin), while the line y = x + 1 has a y-intercept of 1. This means: any point on the line y = x + 1 must be above the line y = x. If (P, Q) is on y = x + 1, then it is above y = x, which automatically means Q > P. We can give a definite “no” answer to the question. By itself, Statement #2 is sufficient.

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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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27 Apr 2015, 05:10
Bunuel wrote:
Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

Kudos for a correct solution.

s1 -> P>Q OR P<Q so not sufficient.
s2 -> y=x+1 which means y is always 1 more than x it suggests in y is always more than x. Hence we get a definite ans. which is No p is not greater than Q. Hence it is sufficient.

Ans. is B

I have a confusion regarding statement 2. What does it mean? Point (p,q) lies on the line or above the line y=x+1? Well I think in both the cases ans. would be same. Bunuel pl. look into this.
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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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27 Apr 2015, 05:38
nailgmat2015 wrote:
Bunuel wrote:
Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

Kudos for a correct solution.

s1 -> P>Q OR P<Q so not sufficient.
s2 -> y=x+1 which means y is always 1 more than x it suggests in y is always more than x. Hence we get a definite ans. which is No p is not greater than Q. Hence it is sufficient.

Ans. is B

I have a confusion regarding statement 2. What does it mean? Point (p,q) lies on the line or above the line y=x+1? Well I think in both the cases ans. would be same. Bunuel pl. look into this.

Hello nailgmat2015, you are right, in this case answer will be the same in both cases.
"above on line" mean "lies on the line"
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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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27 Apr 2015, 10:45
Harley1980 wrote:
nailgmat2015 wrote:
Bunuel wrote:
Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

Kudos for a correct solution.

s1 -> P>Q OR P<Q so not sufficient.
s2 -> y=x+1 which means y is always 1 more than x it suggests in y is always more than x. Hence we get a definite ans. which is No p is not greater than Q. Hence it is sufficient.

Ans. is B

I have a confusion regarding statement 2. What does it mean? Point (p,q) lies on the line or above the line y=x+1? Well I think in both the cases ans. would be same. Bunuel pl. look into this.

Hello nailgmat2015, you are right, in this case answer will be the same in both cases.
"above on line" mean "lies on the line"

Thanks Harley1980
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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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08 Aug 2015, 11:41
PathFinder007 wrote:
Point (P, Q) is in the coordinate plane. Is P > Q?

Statement #1: (P, Q) is closer to the x-axis than to the y-axis.

Statement #2: Point (P, Q) is above the line y = x + 1.

stmt 1: any number on x axis is closer to X axis than y axis ,for example ( 2,0) yes P> Q but if it is (-2,0) in this case P< Q
so stmt1 is insufficient

stmt 2: y=x+1 , y intercept =1 and slope m =1

y=x+1 line will lie above lien y=x, so any point you select on y=x+1 , P<Q so ans is NO

so stmt2 sufficient
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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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20 Dec 2017, 18:11
Bunuel niks18 chetan2u

Quote:
Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

I am clear why St 1 is insufficient,
For St 2 I tried to solve using intercepts equation (x,0) and (0,y) and found that two points
on the line are (-1,0) and (0,1). I could not conclude with certainty about P = Q and hence
concluded that St 2 is insufficient.

Also note that slope of both y = x and y = x+1 are same
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Re: Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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20 Dec 2017, 19:11
Bunuel niks18 chetan2u

Quote:
Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

I am clear why St 1 is insufficient,
For St 2 I tried to solve using intercepts equation (x,0) and (0,y) and found that two points
on the line are (-1,0) and (0,1). I could not conclude with certainty about P = Q and hence
concluded that St 2 is insufficient.

Also note that slope of both y = x and y = x+1 are same

If (P, Q) were ON the line y = x + 1, then we'd have that Q = P + 1 but since it's ABOVE, then Q > P + 1. If Q is more than P + 1, then Q is definitely more than P, so we have a NO answer to the question.
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Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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20 Dec 2017, 19:28
Bunuel

Quote:

My Q was to ascertain sufficiency of St 2.
I am using y = mx + c for knowing nature of line from slope and intercepts.
For the two given lines:
(1) y = x -> Slope = 1, and the y- intercept is 0, or in other words line must pass through (0,0) and (1.1)
(2) y = x + 1 ->Slope =1, and the y- intercept is 1, or in other words line must pass through (-1,0) and (0,1)

In other words Line represented by Eq (2) is parallel to line represented by (1) but 'shifted' upwards because of positive
y intercept, making a confirm "NO" answer to this statement. Is this approach correct ?
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Point (P, Q) is in the coordinate plane. Is P > Q?  [#permalink]

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20 Dec 2017, 19:36
Bunuel

Quote:

My Q was to ascertain sufficiency of St 2.
I am using y = mx + c for knowing nature of line from slope and intercepts.
For the two given lines:
(1) y = x -> Slope = 1, and the y- intercept is 0, or in other words line must pass through (0,0) and (1.1)
(2) y = x + 1 ->Slope =1, and the y- intercept is 1, or in other words line must pass through (-1,0) and (0,1)

In other words Line represented by Eq (2) is parallel to line represented by (1) but 'shifted' upwards because of positive
y intercept, making a confirm "NO" answer to this statement. Is this approach correct ?

Yes, if you understand why the parallel line shifted up by 1 compared to the line y = x must have Q > P. It's basically the same as the approach given here: https://gmatclub.com/forum/point-p-q-is ... l#p1492536
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Point (P, Q) is in the coordinate plane. Is P > Q?   [#permalink] 20 Dec 2017, 19:36
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