First slide

Cartesian plane

Question

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 $3 x + 5 y = 2007$ is equal to

Moderate

A

133
B

135
C

138
D

140

Solution

$\begin{array}{l} 3 x + 5 y = 2007 \Rightarrow x + \frac{5 y}{3} = 669 \\ Clearly, 3 must divide 5 y and so y = 3 k, \\ ∴ x + 5 k = 669 \\ \Rightarrow 5 k \leq 668 \\ \Rightarrow k \leq 133 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App