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CGP EDU Academic Team
Published on: August 13, 2026
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
Text Solution
Verified by ExpertsThe correct answer is:
A
We have, 3x + 5y = 2007
⇒ x + 
= 669
Clearly, 3 must divide 5y and so y = 3k for some k ∈ N. Thus, x + 5k = 669
⇒ 5k ≤ 688
⇒ k ≤ 
⇒ k ≤ 133.
Thus, the odered pairs (x, y) can be given by
(669 – 5k, 3k), 1 ≤ k ≤ 133.
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