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

Question

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 .

ynaikavde · Answer

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.

I think answer is B

viktorija · Answer

(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

Bunuel · Answer

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.

Answer = B.

M3sSiaH · Answer

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.

Harley1980 · Answer

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

M3sSiaH · Answer

Thanks  Harley1980

sunita123 · Answer

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

adkikani · Answer

Bunuel   niks18   chetan2u

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

Bunuel · Answer

What is your question?

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.

adkikani · Answer

Bunuel

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 ?

Bunuel · Answer

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?

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