In the xy-coordinate plane, a rectangle has the vertices (3.3, 3.3), (

Question

In the xy-coordinate plane, a rectangle has the vertices (3.3, 3.3), (3.3, -7.3), (-2.3, -7.3), (-2.3, 3.3). If a point from within the rectangle is randomly selected such that x and y are integers, what is the probability that both coordinates are positive?

(A) \(\frac{3}{22}\)

(B) \(\frac{225}{1484}\)

(C) \(\frac{1089}{5936}\)

(D) \(\frac{75}{371}\)

(E) \(\frac{8}{33}\)

Show Answer

Official Answer

A

(A)  \frac{3}{22}

(B)  \frac{225}{1484}

(C)  \frac{1089}{5936}

(D)  \frac{75}{371}

(E)  \frac{8}{33}

starredastro · Answer

The area of the whole rectangle is:
a. 3.3+2.3 = 5.6 breadth
b. 3.3+7.3 = 10.6 length
area = breadth * length = 10.6*5.6 = 59.36

The area of the portion where both X & Y are positive is 
a. 3.3-0 = 3.3 breadth
b. 3.3-0 = 3.3 length
Area = breadth* length = 3.3*3.3 = 10.89

The Probability of selecting both x and y as positive should be the area of:
The square (3.3*3.3) /  The area of the total rectangle which is  (5.6*10.6) 
Hence the answer should be C =  1089/ 5936

filipembribeiro · Answer

So, the official answer is:

Right answer: (A) 3/22

Explanation:
First of all, do not make this more complicated than it is. Do not try to calculate the dimensions of the rectangle; recognize, instead, that you are dealing with all integers on the x-axis from -2 to 3, inclusive, and on the y-axis from -7 to 3, inclusive. This gives you a total of  6 × 11 = 66  possible points. And if both of them are positive, you are looking at 1 to 3 inclusive on the x-axis and 1 to 3 inclusive on the y-axis, for a total of  3 × 3 = 9  possible points. Your correct answer, then, is  9/66 = 3/22 .

Kinshook · Answer

In the xy-coordinate plane, a rectangle has the vertices (3.3, 3.3), (3.3, -7.3), (-2.3, -7.3), (-2.3, 3.3).

If a point from within the rectangle is randomly selected such that x and y are integers, what is the probability that both coordinates are positive?

Integer x-coordinates in the rectangle = {-2,-1,0,1,2,3} = 6
Positive integer x-coordinates in the rectangle = {1,2,3} = 3
Integer y-coordinates in the rectangle = {-7,-6,-5,-4,-3,-2,-1,0,1,2,3} = 11
Positive integer y-coordinates in the rectangle = {1,2,3} = 3

Integer coordinates in the rectangle = 6*11 = 66

Integer coordinates in the rectangle with positive coordinates = 3*3 = 9

If a point from within the rectangle is randomly selected such that x and y are integers, the probability that both coordinates are positive =  \frac{9}{66} = \frac{3}{22}

IMO A

In the xy-coordinate plane, a rectangle has the vertices (3.3, 3.3), (

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

In the xy-coordinate plane, a rectangle has the vertices (3.3, 3.3), (

Prep Toolkit

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