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In the rectangular coordinate plane, a rectangular region has vertices

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In the rectangular coordinate plane, a rectangular region has vertices  [#permalink]

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New post 08 Jul 2018, 12:22
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A
B
C
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Difficulty:

  55% (hard)

Question Stats:

57% (03:01) correct 43% (03:08) wrong based on 35 sessions

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In the rectangular coordinate plane, a rectangular region has vertices (2.5, 4.5), (2.5, −1.5), (−7.5, 1.5), and (−7.5, 4.5). If a point from within the rectangle is to be randomly selected such that both the x- and y-coordinates are integers, what is the probability that both coordinates of the selected point are negative?

A) 1/11
B) 7/60
C) 2/15
D) 16/77
E) 4/15
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Re: In the rectangular coordinate plane, a rectangular region has vertices  [#permalink]

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New post 08 Jul 2018, 14:19
manishbatra92 wrote:
Is it C?

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app


OA is B. I got C as well because I divided the area with negative coordinates by the entire area. The distinction according to the OA is that it wants just integer coordinates. Was hoping someone could provide a faster way to solve it
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Re: In the rectangular coordinate plane, a rectangular region has vertices  [#permalink]

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New post 08 Jul 2018, 14:43
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TippingPoint93 wrote:
manishbatra92 wrote:
Is it C?

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app


OA is B. I got C as well because I divided the area with negative coordinates by the entire area. The distinction according to the OA is that it wants just integer coordinates. Was hoping someone could provide a faster way to solve it


First of all, the question seems wrong.
We can't have a rectangular region with co-ordinates (2.5, 4.5), (2.5, −1.5), (−7.5, 1.5), and (−7.5, 4.5).
The bold-faced co-ordinate must be (−7.5, -1.5).

So, I am solving the sum with vertices as (2.5, 4.5), (2.5, −1.5), (−7.5, -1.5), and (−7.5, 4.5).
In the rectangular region,We have horizontal or x-co-ordinates from -7.5 to 2.5 with accepted integer values from -7 to 2. So, total integer points : 10
Similarly, We have vertical or y-co-ordinates from -1.5 to 4.5 with accepted integer values from -1 to 4. So, total integer points : 6

So, total no of integer co-ordinates in the xy-plane:- 10*6=60

Total no of (x,y) pairs with x and y are negative integers :-
x: -7 to -1, so x can have 7 values/positions.
y: -1, so only one position of y
So, total no of (x,y) vertices=7*1=7

Required probability=\(\frac{7}{60}\)

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

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Re: In the rectangular coordinate plane, a rectangular region has vertices  [#permalink]

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New post 08 Jul 2018, 17:47
PKN wrote:
TippingPoint93 wrote:
manishbatra92 wrote:
Is it C?

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app


OA is B. I got C as well because I divided the area with negative coordinates by the entire area. The distinction according to the OA is that it wants just integer coordinates. Was hoping someone could provide a faster way to solve it


First of all, the question seems wrong.
We can't have a rectangular region with co-ordinates (2.5, 4.5), (2.5, −1.5), (−7.5, 1.5), and (−7.5, 4.5).
The bold-faced co-ordinate must be (−7.5, -1.5).

So, I am solving the sum with vertices as (2.5, 4.5), (2.5, −1.5), (−7.5, -1.5), and (−7.5, 4.5).
In the rectangular region,We have horizontal or x-co-ordinates from -7.5 to 2.5 with accepted integer values from -7 to 2. So, total integer points : 10
Similarly, We have vertical or y-co-ordinates from -1.5 to 4.5 with accepted integer values from -1 to 4. So, total integer points : 6

So, total no of integer co-ordinates in the xy-plane:- 10*6=60

Total no of (x,y) pairs with x and y are negative integers :-
x: -7 to -1, so x can have 7 values/positions.
y: -1, so only one position of y
So, total no of (x,y) vertices=7*1=7

Required probability=\(\frac{7}{60}\)

Ans. (B)


Thank you, PKN. I thought it was odd as well when I drew the image.
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Re: In the rectangular coordinate plane, a rectangular region has vertices &nbs [#permalink] 08 Jul 2018, 17:47
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