The number of integral points (x,y) (i.e...

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

A

133

B

135

C

138

D

140

Text Solution

Verified by Experts

The correct Answer is:

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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