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How many points (x, y) lie on the line segment between (22, 12 2/3) and (7, 17 2/3) such that x and y are both integers?
A. 4
B. 5
C. 7
D. 8
E. 9
A. 4
B. 5
C. 7
D. 8
E. 9
28 Oct 2010, 19:03
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The line joins the points (7, 17 2/3) and (22, 12 2/3).
The slope of the line will be (17 2/3 - 12 2/3)/(7 - 22) = -1/3
What does a slope of -1/3 imply? It implies that for every decrease of 1 unit in the value of y, x will increase by 3 units or in other words, for every decrease of 1/3 in value of y, x will increase by 1 unit.
Start from the left end point. When value of y becomes 17 i.e. a reduction of 2/3 , value of x will be increase by 2 and will become 9. When value of y reduces by another 1 unit, value of x will increase by 3 units and will become 12 and so on... You will have 5 integral values of y (17, 16, 15, 14 and 13). For each of these values, x will be integral.
Ques.jpg [ 8.16 KiB | Viewed 33529 times ]
The last point in the diagram above is 13, not 12.
The slope of the line will be (17 2/3 - 12 2/3)/(7 - 22) = -1/3
What does a slope of -1/3 imply? It implies that for every decrease of 1 unit in the value of y, x will increase by 3 units or in other words, for every decrease of 1/3 in value of y, x will increase by 1 unit.
Start from the left end point. When value of y becomes 17 i.e. a reduction of 2/3 , value of x will be increase by 2 and will become 9. When value of y reduces by another 1 unit, value of x will increase by 3 units and will become 12 and so on... You will have 5 integral values of y (17, 16, 15, 14 and 13). For each of these values, x will be integral.
Attachment:
Ques.jpg [ 8.16 KiB | Viewed 33529 times ]
The last point in the diagram above is 13, not 12.
28 Oct 2010, 18:48
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slope = (17 2/3 - 12 2/3) / (7 - 22) = -1/3
y = mx + b => 12 2/3 = -22/3 + b => b = 20
y = -x/3 + 20
Only integer values work, and the only multiples of 3 between 7 and 22 for x values are 9, 12, 15, 18 and 21, thus 5 points.
y = mx + b => 12 2/3 = -22/3 + b => b = 20
y = -x/3 + 20
Only integer values work, and the only multiples of 3 between 7 and 22 for x values are 9, 12, 15, 18 and 21, thus 5 points.
