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

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.

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

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

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

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.

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 ?

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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