Q.

The number of integral points x,y ( i.e., x and y both are integers) which lies in the first quadrant but not on the coordinates axes and also on the straight line 3x+5y=2007 is equal to

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a

133

b

135

c

138

d

140

answer is A.

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Detailed Solution

We have 3x+5y=2007 or x+5y3=669Clearly, 3 must divide 5y and so y=3k, and y=3k, for some k∈N. Thus, x+5k=669or 5k≤668or k≤6685 or k≤133
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The number of integral points x,y ( i.e., x and y both are integers) which lies in the first quadrant but not on the coordinates axes and also on the straight line 3x+5y=2007 is equal to