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The number of integral points (x,y) (i.e, x and y both are integers) which lie in the first quadrant but not on the coordinate axes and also on the st

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The number of integral points (x,y) (i.e, x and y both are 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
A. 133
B. 135
C. 138
D. 140
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Correct Answer - A
We have
`3x+5y=2007 or x+(5y)/(3)=669`
Clearly, 3 must divide 5y and so `y=3k`, for some `kinN`. Thus,
`x+5k=669`
or `5kle668`
`kle(668)/(5)or kle133`
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