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, Q) is closer to the x-axis than to the y-axis.

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

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nick1816 · Answer

whether (P,Q) lies below the line y=x

Statement 1-

Given |y|<|x| (highlighted in blue in diagram 1)

if Q<0, then (P,Q) lies above y=x
if Q>0, then (P,Q) lies below y=x

Insufficient

Statement 2-

The region above y=x+1 always lie above y=x

Sufficient

B

Ag03 · Answer

Even with statement B, the point can still lie in quadrant 3. How will the condition satisfy in that case?

Can,Will · Answer

gmatophobia  
can you explain statement 2 ? I am not able to understand.

gmatophobia · Answer

Hey  AnujL

Statement 2 mentions that "Point (P, Q) is above the line y = x + 1.". To understand this, let's plot the line y = x + 1 on the x-y plane.

Line x = y, has a positive slope and passes through the origin (shown in red).

Line y = x + 1, lies one unit above the line x. Therefore the line y = x + 1, will be parallel to the line y = x, and will lie at an distance of 1 unit from the line.

If the above explanation is confusing, we can also plot this line by finding the x-intercept and the y-intercept.

x-intercept of the line -

0 = x + 1

x = -1

So the line cuts the x-axis at (-1,0)

y-intercept of the line -

y = 0 + 1

y = 1

So the line cuts the y-axis at (0,1)

We can draw a line passing through these two points. The line is shown in green.

Statement 2 tells us that point (P, Q) is above the line y = x + 1. Hence point P lies in the region shaded in green.

Note: In this region, the value of y is always greater than the value of x+1 (i.e. y > x + 1)

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

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GMAT Data Sufficiency (DS) Questions

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

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