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26 Nov 2022, 13:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (02:02) correct
71%
(01:50)
wrong
based on 91
sessions
History
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Result
Not Attempted Yet
How many different points (x, y), where x and y are both positive integers, in xy-plane satisfy the inequality x+y ≤ 200?
A. 199
B. 200
C. 399
D. 19000
E. 20000
A. 199
B. 200
C. 399
D. 19000
E. 20000
26 Nov 2022, 13:48
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Let's plot the line x + y = 200 on the x-y plane.
The area covered between the Quadrant 1 and the line is the area in which the points can lie.
The y - intercept = 200
The x - intercept = 200
OPQR is a square. There are 200 * 200 points in the square which are integers as the x and y coordinates can be selected in 200 ways.
However, our area of interest is in the area covered by \(\triangle POR\)
Number of points = 200 * 200 / 2 = 20000
However, note this also includes points which are on the axis. We have to eliminate those points as x and y are both positive.
Looking at the options the closest option is D. Note, that there is a huge gap in terms of value between Option C and Option D, hence we can rule out all other options.
Option D
The area covered between the Quadrant 1 and the line is the area in which the points can lie.
The y - intercept = 200
The x - intercept = 200
OPQR is a square. There are 200 * 200 points in the square which are integers as the x and y coordinates can be selected in 200 ways.
However, our area of interest is in the area covered by \(\triangle POR\)
Number of points = 200 * 200 / 2 = 20000
However, note this also includes points which are on the axis. We have to eliminate those points as x and y are both positive.
Looking at the options the closest option is D. Note, that there is a huge gap in terms of value between Option C and Option D, hence we can rule out all other options.
Option D
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25 Jan 2025, 10:40
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Bunuel
Bunuel - Are these choices accurate?
My approach for this was to identify pattern and calculate number of points which is
x = 1, 0<y<200
x = 2, 0<y<199
.
.
.
x = 198, 0<y<3
x = 199, 0<y<2
Summing all these values results into sequence => 1 + 2 + 3 + ... + 199 => (199/2)*(1+199) => 19900
Couldn't find any option matching this exact value.
