If 0

Question

If  0<x<2  and  0<y<2  on the  xy -plane, what is the probability that  x+y<1 ?
 
A.  \frac{1}{2}

B.  \frac{1}{4}

C.  \frac{1}{6}

D.  \frac{1}{8}

E.  \frac{1}{10}

gmatophobia · Answer

Given: 0<x<2  and  0<y<2 .

We can represent x = 2, and y = 2 using straight lines as shown.

The region represented by  0<x<2  and  0<y<2  is the square represented by OABC.

The line  x+y = 1  has its x-intercept and y-intercept at (1,0) and (0,1) respectively. The line has a negative, slope and is shown in the figure.

The region below the line represents  x+y<1 . The common overlap of the region represented by  x+y<1  and the region represented by  0<x<2  and  0<y<2  is the triangle represented by OMN.

Required Probability =  \frac{	ext{Favorable Region}}{	ext{Total Region}}

Favorable Region = Area of  	riangle OMN  =  \frac{1}{2} * 1 * 1 = \frac{1}{2}

Total Region = Area of square OABC =  2 * 2   = 4

Required Probability =  \frac{\frac{1}{2}}{4} = \frac{1}{8}

Option D

MBhavya · Answer

Is there any other way of solving this question? Why are you taking the whole square region and the triangle region. I am not able to understand

Regor60 · Answer

This is the simplest way to solve this problem.

By stipulating that 0<X<2 and 0<Y<2, the question is saying that any point (X,Y) that satisfies the constraints is possible to be selected.

So, any point in a 2x2 region could possibly be selected.

The question is then asking what is the probability that a sub region of the 2x2 is selected.

That sub region is defined by the constraint X+Y<1 or Y<1-X.

So the probability is:

(Area of subregion)/(Area of total region)

Posted from my mobile device

If 0 < x < 2 and 0 < y < 2 on the xy-plane, what is the probability

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions