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Bunuel
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How many points (x y), where x and y are integers, lie inside of the t 05 May 2020, 04:57
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95% (hard)

Question Stats:

26% (01:52) correct 74% (01:57) wrong based on 80 sessions

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How many points (x y), where x and y are integers, lie inside of the triangular region with vertices (0, 0), (0, 31), and (31, 0) ?

A. 435
B. 450
C. 464
D. 465
E. 466


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GMATinsight
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How many points (x y), where x and y are integers, lie inside of the t 05 May 2020, 07:46
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Bunuel
How many points (x y), where x and y are integers, lie inside of the triangular region with vertices (0, 0), (0, 31), and (31, 0) ?

A. 435
B. 450
C. 464
D. 465
E. 466


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The step-by-step solution to this HARD problem is explained well in Video

Answer: Option A


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How many points (x y), where x and y are integers, lie inside of the t 05 May 2020, 06:53
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Mapping the co-ordinates will give a right-angled triangle in the I quadrant.

Since we need to calculate the points inside the triangle, the base will be of length 31-1-1 = 29.
Next line will have 28 points, 27 and so on.

Total points = 29*30/2 = 435.

A is the answer.
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How many points (x y), where x and y are integers, lie inside of the t 26 May 2020, 21:13
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Chethan92
Mapping the co-ordinates will give a right-angled triangle in the I quadrant.

Since we need to calculate the points inside the triangle, the base will be of length 31-1-1 = 29.
Next line will have 28 points, 27 and so on.

Total points = 29*30/2 = 435.

A is the answer.
Show more


Hi
Could you please explain the steps as your method seems to be really quick and easy to solve?
Could you please explain the step where you calculated the total points?
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How many points (x y), where x and y are integers, lie inside of the t 26 May 2020, 22:23
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riagarg07
Chethan92
Mapping the co-ordinates will give a right-angled triangle in the I quadrant.

Since we need to calculate the points inside the triangle, the base will be of length 31-1-1 = 29.
Next line will have 28 points, 27 and so on.

Total points = 29*30/2 = 435.

A is the answer.


Hi
Could you please explain the steps as your method seems to be really quick and easy to solve?
Could you please explain the step where you calculated the total points?
Show more

riagarg07

The method explained in short has been well explained in detail in the video. You may watch it for clear understanding.
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How many points (x y), where x and y are integers, lie inside of the t 28 Jan 2023, 19:22
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Hi Bunuel GMATinsight,

I chose to do the latter part of the question using Combinatorics.

To find the points that lie within the triangular region formed, we use x+y <31

Now, this gives us 15 possible values of x and 15 possible values of y (It is given that x & y are integers) i.e 30 values in total from which any 2 values can be picked (pls note: possible values include integers from 1-15 inclusive)

Using the formula, we get 30C2
Solving: 30!/28!x2!=435

Please let me know whether this way of solving is correct.

Thank you :)
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Bunuel
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