Question

The number of integral points (x, y) (that is 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

Answer 1

Answer: (A)

133

Answer 2

We have, 3x + 5y = 2007

Ž x + $\frac { 5 y } { 3 }$ = 669

Clearly, 3 must divide 5y and so y = 3k for some k Ī N. Thus, x + 5k = 669

Ž 5k £ 688

Ž k £ $\frac { 688 } { 5 }$ Ž k £ 133.

Thus, the odered pairs (x, y) can be given by

(669 – 5k, 3k), 1 £ k £ 133.