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Q.

The number of integral points (x, y) (i.e., x and y are both integers) which lie in the first quadrant but not on the coordinate axes and also on the straight line  3x+5y=2007 is equal to

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a

133

b

135

c

138

d

140

answer is A.

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Detailed Solution

3x+5y=2007⇒x+5y3=669 Clearly, 3 must divide 5y and so y=3k , ∴ x+5k=669⇒5k≤668⇒ k≤133
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