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Please refer to the figure, if A is a point in

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Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 18:07
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:43) correct 27% (02:12) wrong based on 49 sessions

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GMATBusters’ Quant Quiz Question -2


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Please refer to the figure, if A is a point in the shaded region, then the point could be
A. (2,3)
B. (-3,4)
C. (4,7)
D. (8,3)
E. (13,6)

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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 18:12
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 18:17
For a point inside shaded region, the point must satisfy the equation
x-2y<0
x-2y=0 intersects y =5 hence x cannot be more than 10
A. (2,3)=-4
B. (-3,4) cannot be as figure in 1st quadrant
C. (4,7) cannot be as if y>5
D. (8,3)=2
E. (13,6) cannot be as x >10

A is the answer

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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 18:32
A is a point in the yellow shadow region that is surrounded among line x=0, y=5 and 0=x-2y => y=x/2 line.
from this we can find range of each x and y.
intersection of y=5 line y=x/2 line is 5=x/2 => x=2.5, x=0 (line) so x range is between 0 and 2.5
intersection of x=0 line y=x/2 line is y=0/2 => y=0, y=5 (line) so y range is between 0 and 5
answer choice could be between (x, y) => (0-2.5, 0-5)
therefore, A is right
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 18:47
This question is testing for the knowledge in inequalities.
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 20:03
Although, i don't know the approach but still i'll give a try.

Based on the figure, the shaded region is less than 2.5 on x axis. So it can never be option C, D and E.
x axis can also not be less than 0. So, B is also out. So, A is can be the correct answer.

Ans. A.
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 20:24
Please refer to the figure, if A is a point in the shaded region, then the point could be
A. (2,3)
B. (-3,4)
C. (4,7)
D. (8,3)
E. (13,6)


Since x= 2y => x largest value can be 10
y = 5 => y values can be only less than 5 for the point to be in the shaded region.

Since A and the shaded region lies in the 1st quadrant :-
x has to be greater than 0 and less than 10 and y has to be greater than 0 and less than 5 for the point to be in the shaded region

Only 1 option fits that -> 2,3

Answer - A
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 22:23
Solution:

Question 2: Please refer to the figure, if A is a point in the shaded region, then the point could be

A. (2,3)
B. (-3,4)
C. (4,7)
D. (8,3)
E. (13,6)

In order to solve this question, we need to first observe that the figure is plotted on grid that is similar to graph paper and the distance between the integer coordinates on each of the X axis and Y axis is 1 unit. For example, point y = 5 on Y axis is 5 units away from the origin (0,0). Moreover, it is asked in this question that we need to find a point A in the shaded region of the graph and the right coordinates of point A are required to be identified from the given options.

We can eliminate the wrong options and select the right option by looking at the area of shaded region in the graph that is a right angled triangle. In the shaded triangle, one side is Y = 5 units or (5,0) and in case of other side, y-coordinate is 5 and x-coordinate can be found by looking at the grid distance on x-axis from the origin. X-coordinate is 2.5 units away from the origin (0,0). Thus, the coordinates of three vertices of the triangle are (0,0), (0,5) and (2.5,5).
. Now, by looking at the given options in the question, we can easily eliminate option B,C,D and E because any option with y-coordinate value > 5 or x-coordinate value < 0 is clearly incorrect as the shaded region lies in the first quadrant in which values of both X and Y coordinates are positive.

Option A i.e.; (2,3) is the correct answer.
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 15 Feb 2020, 23:32
Please refer to the figure, if A is a point in the shaded region, then the point could be
A. (2,3) -- this is the possible answer--for x = 2 for point to lie in shaded region it should lie between (2,1) and (2,5) - (correct)


B. (-3,4)--this is not possible since x coordinates of points in shaded regions should be positive

C. (4,7)-- for x = 4 for point to lie in shaded region it should lie between (4,2) and (4,5) but y co-ordinate of the given option is greater than 5 so out

D. (8,3)-- for x = 8 for points to lie in shaded region it should lie between (8,4) and (8,5) but y coordinate of the given option is less than 4 so out

E. (13,6) -- this again is not possible shaded region is till x = 10
if we solve x-2y = 0 and y = 5 we get x = 10
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 16 Feb 2020, 05:31
Considering the figure is not drawn to scale:

if y intercept given is 5, then x-intercept will be 10.

So all of the options within the range of 0<x<=10 & 0<y<5, can be considered.

Now, I dont know if my logic 100% correct, but if we see the graph: y is almost half of x, so we can go ahead with the option : (8,3) as our answer.
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Re: Please refer to the figure, if A is a point in  [#permalink]

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New post 17 Feb 2020, 23:07
Even D satisfy ur condition: " x has to be greater than 0 and less than 10 and y has to be greater than 0 and less than 5 for the point to be in the shaded region"
The reasoning is not perfect
shameekv1989 wrote:
Please refer to the figure, if A is a point in the shaded region, then the point could be
A. (2,3)
B. (-3,4)
C. (4,7)
D. (8,3)
E. (13,6)


Since x= 2y => x largest value can be 10
y = 5 => y values can be only less than 5 for the point to be in the shaded region.

Since A and the shaded region lies in the 1st quadrant :-
x has to be greater than 0 and less than 10 and y has to be greater than 0 and less than 5 for the point to be in the shaded region

Only 1 option fits that -> 2,3

Answer - A

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Re: Please refer to the figure, if A is a point in   [#permalink] 17 Feb 2020, 23:07

Please refer to the figure, if A is a point in

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